Answer:
38%
Step-by-step explanation:
Answer:
38% is correct
ED2021
List all the 4-tuples in the relation {(a,b,c,d) | a,b,c,d∈!+ , a+b+c+d = 6}
We have a total of seven 4-tuples that satisfy the given relation.The given relation is {(a,b,c,d) | a,b,c,d∈!+ , a+b+c+d = 6}. It can be understood as the set of 4-tuples (a, b, c, d) such that a, b, c, and d are positive integers and their sum is equal to 6.
Let's now list all the possible 4-tuples that satisfy the given relation. The possible combinations are as follows: (1, 1, 1, 3), (1, 1, 2, 2), (1, 2, 1, 2), (2, 1, 1, 2), (1, 2, 2, 1), (2, 1, 2, 1), and (2, 2, 1, 1).
Here's a brief explanation on how these 4-tuples were obtained. Let a, b, c, and d be positive integers such that a+b+c+d = 6. The least possible value that each variable can take is 1.
So, we start with a=1 and find all possible values of (b, c, d) that satisfy the given equation. Then, we move to a=2 and repeat the process. Finally, we list all the possible 4-tuples that we obtained.
Thus, we have a total of seven 4-tuples that satisfy the given relation.
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blake bike east at 5m/s. five seconds later he speeds up to 9 m/s.
what is his change in velocity? what is his acceleration?
Answer:
The answer is down below
Step-by-step explanation:
v-u=◇velocity
[tex] = 9 - 5[/tex]
◇velocity =4ms‐¹
acceleration =◇velocity/time
[tex]a = \frac{4}{5} [/tex]
[tex]a = 0.8m {s}^{ - 2} [/tex]
Change in velocity:
[tex] \sf \:final \: velocity - initial \: velocity = change \: in \: velocity[/tex]
[tex] \therefore \tt \delta \: v = 9 - 5 \\ \tt = 4m {s}^{ - 1} [/tex]
To find acceleration:
[tex] \rm \: a = \frac{ \triangle \: v}{\triangle \: t} [/tex]
[tex] \rm \: a = \frac{ 4}{5 - 0} = \frac{4}{5} = 0.8m {s}^{ - 1} [/tex]
Four equal-sized equilateral triangles form a larger equilateral triangle, as shown
below.
EF-2a
ED=3b
a) Express FB in terms of b
b) Express FD in terms of a and b
c) Express CB in terms of a and b
Give each answer in its simplest form
a) To express FB in terms of b, we need to consider the relationship between FB and EF. Since EF is equal to 2a, we can substitute this value into the expression for FB:
FB = EF - FB
= (2a) - (2a)
= 0
Therefore, FB is equal to 0 in terms of b.
b) To express FD in terms of a and b, we can use the given relationship between ED and FD. ED is equal to 3b, so we can substitute this value into the expression for FD:
FD = ED - FB
= (3b) - (0)
= 3b
Therefore, FD is equal to 3b in terms of a and b.
c) To express CB in terms of a and b, we need to consider the relationship between CB and EF. Since EF is equal to 2a, we can substitute this value into the expression for CB:
CB = EF - EB
= (2a) - (FB + FD)
= (2a) - (0 + 3b)
= 2a - 3b
Therefore, CB is equal to 2a - 3b in terms of a and b.
A portion of the Quadratic Formula proof is shown. Fill in the missing statement.
Statements Reasons
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c all over 4 times a squared plus b squared over 4 a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation
the quantity x plus b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Rewrite the perfect square trinomial on the left side of the equation as a binomial squared
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared Take the square root of both sides of the equation
? Simplify the right side of the equation
The missing statement in the proof of the Quadratic Formula involves simplifying the right side of the equation by taking the square root of the numerator, resulting in x plus b over 2a equals plus or minus √((b^2 - 4ac)) all over 4a squared.
The missing statement in the proof of the Quadratic Formula, we need to simplify the right side of the equation:
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared
To simplify the right side, we can take the square root of the numerator and denominator separately:
√(b squared minus 4 times a times c) = √((b^2 - 4ac))
Now, substituting the simplified expression into the equation, we have:
x plus b over 2 times a equals plus or minus √((b^2 - 4ac)) all over 4 times a squared
This completes the missing statement in the proof of the Quadratic Formula.
In conclusion, the missing statement in the proof of the Quadratic Formula involves simplifying the right side of the equation by taking the square root of the numerator, resulting in x plus b over 2a equals plus or minus √((b^2 - 4ac)) all over 4a squared.
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I really need help with this question. It is attached
The equation of line A is y = 4.
The equation of line B is y = 0.
What is the equation of line A and line B?The equation of lines A and B is calculated by applying the general equation of line as follows;
Mathematically, the formula for the general equation of lines is given as;
y = mx + b
where;
m is the slope of the lineb is the y intercept of lineFor line A, the equation is determined as;
y = 0x + 4
the slope of the this line is zero
y = 4
For line B, the equation is determined as
y = 0x + 0
the slope and y intercept of the this line is zero
y = 0
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what is rhe square root of 50 ?
Answer:
Step-by-step explanation: 5√2
Questions 16. Santhosh and Co. Chennai, opened a branch at Trichy on 1.1.2018. The following Information relate to the branch for the year 2018.
40,000
36,000
9,000
7200
3,600
30,000
16,200
300
3,000
Prepare branch account to find out the profit or loss of branch. Santosh & Co, Chennai opened its branch in Trichy on 1.1.2018. The action for 2018 is as follows
Credit sales at branch
Office expenses by Head office
Cash remittance to branch for petty cash Stock 31.12.2018
Goods sent to Branch
Salaries paid by head office
Debtors 31.12.2018
Petty cash on 31.12.2018
Cash sales at branch
of
The preparation of the branch's income statement for Santosh & Co. Chennai is as follows:
Branch of Santosh & Co. Chennai
Income StatementFor the year ended December 31, 2018
Sales revenue $40,300
Cost of goods sold 4,200
Gross profit $36,100
Expenses:
Office expenses $36,000
Salaries 3,600
Total expenses $39,600
Loss $3,500
What is an income statement?An income statement is a financial statement prepared at the end of an accounting period to determine the profit or loss generated by a business or branch.
The profit or loss is the difference between the total revenue and the total expenses for the accounting period.
Credit sales at branch 40,000
Office expenses by Head office 36,000
Cash remittance to branch for petty cash 9,000
Goods sent to Branch 7,200
Salaries paid by head office 3,600
Debtors 31.12.2018 30,000
Petty cash on 31.12.2018 16,200
Cash sales at branch 300
Stock of 31.12.2018 3,000
Sales revenue $40,300 ($40,000 + $300)
Cost of goods sold $4,200 ($7,200 - $3,000)
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Name two pairs of congruent angles
The two pairs of congruent angles are determined as angle XWY and angle YZX.
What are congruent angles?Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.
So congruent angles are two or more angles that are identical or equal to each other.
From the given diagram , the pair of angles are congruent to each other.
Angle XWY is congruent to angle YZX, this is because vertical opposite angles in a cyclic quadrilateral are equal in measure.
Thus, the two pairs of congruent angles are determined as angle XWY and angle YZX.
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write inequality shown y=-11/7x-4
Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:
y ≤ -11/7x - 4
This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.
Step-by-step explanation: .
If you divide each value in the data set below by 5, what are the mean, median, mode, and range of the resulting data set?
9214709
The mean is
(Type an integer or decimal rounded to the nearest hundredth as needed.)
Please helppppp
Answer:
To find the mean, median, mode, and range of the resulting data set after dividing each value by 5, we need to perform the calculations. Here are the steps:
Original data set: 9214709
Step 1: Divide each value by 5:
Resulting data set: 1842941.8
Step 2: Calculate the mean:
To find the mean, we sum up all the values in the resulting data set and divide by the total number of values:
Mean = (1842941.8) / 1 = 1842941.8
Therefore, the mean of the resulting data set is 1842941.8.
Please note that for the median, mode, and range calculations, we need more than one value in the data set. As the original data set only contains one value, we cannot proceed with those calculations.
Step-by-step explanation:
Answer:
The mean, also known as the average, is a measure of central tendency that is calculated by adding up all the values in a data set and then dividing by the number of values in the set. For example, if you have a data set with the values 1, 2, and 3, the mean would be calculated as (1 + 2 + 3) / 3 = 2.
The median is another measure of central tendency that represents the middle value in a data set when the values are arranged in ascending order. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is calculated as the average of the two middle values.
For example, if you have a data set with the values 1, 2, and 3, the median would be 2 because it is the middle value when the values are arranged in ascending order. If you have a data set with the values 1, 2, 3, and 4, the median would be calculated as (2 + 3) / 2 = 2.5 because there are an even number of values and the two middle values are 2 and 3.
find the slope of 1,5 and 0,4
Determine the equation of the circle with center 100pts
Answer:
(x - 8)² + (y - 5)² = 400
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r the radius
the radius is the distance from the centre to a point on the circle
use the distance formula to calculate r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (8, 5 ) and (x₂, y₂ ) = (- 4, 21 )
r = [tex]\sqrt{(-4-8)^2+(21-5)^2}[/tex]
= [tex]\sqrt{(-12)^2+16^2}[/tex]
= [tex]\sqrt{144+256}[/tex]
= [tex]\sqrt{400}[/tex]
= 20
then with (h, k ) = (8, 5 ) and r = 20, the equation of the circle is
(x - 8)² + (y - 5)² = 20² , that is
(x - 8)² + (y - 5)² = 400
Answer:
[tex](x-8)^2+(y-5)^2=400[/tex]
Step-by-step explanation:
The standard equation of a circle is:
[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]
where:
(h, k) is the center.r is the radius.The given center of the circle is (8, 5).
To find the value of r², substitute the circle and the given point (-4, 21) into the equation and solve for r².
[tex]\begin{aligned}(-4-8)^2+(21-5)^2&=r^2\\(-12)^2+(16)^2&=r^2\\144+256&=r^2\\400&=r^2\end{aligned}[/tex]
Finally, substitute the center and r² into the formula to create an equation of the circle with the given parameters:
[tex]\boxed{(x-8)^2+(y-5)^2=400}[/tex]
Can someone help me please
Denis's and Dasha's methods use different operations to simplify the expressions in different orders.
Denis's method uses addition, subtraction, and multiplication operations, but Dasha's method does not.
What are multiplication operations?Multiplication operations are described as using mathematical operation that indicates how many times a number is added to itself.
Denis's Assignment
2* 6+2w-54
12+2w = 54
12-12+2w= 54-12
2w=42
w= 21
Dasha's Assignment
54-2* 6
54-12= 42
The two widths add to 42 cm
42/ 2-21
We can see that Dasha's method also uses addition and subtraction operations, but she simplifies the expression by performing the operations in a different order.
She subtracts the product of 2 and 6 from 54.
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(12sin(pi/2x)*lnx)/((x³+5)(x-1))
lim as x approaches 1
The limit of the given function as x approaches 1 is 0.
To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:
1. Begin by substituting x = 1 into the numerator:
[tex]\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\][/tex]
2. Now, substitute x = 1 into the denominator:
(1³ + 5)(1 - 1) = 6(0) = 0
3. Finally, divide the numerator by the denominator:
0/0
The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:
4. Take the derivative of the numerator:
[tex]\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\][/tex]
5. Take the derivative of the denominator:
[tex]\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\][/tex]
6. Substitute x = 1 into the derivatives:
Numerator: [tex]\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\][/tex]
Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6
7. Now, reevaluate the limit using the derivatives:
lim as x approaches 1 of [tex]\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\][/tex]
= 0 / 6
= 0
Therefore, the limit of the given function as x approaches 1 is 0.
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Point A is at (0,-2). vector AB is <-4,3>.
vector AC is <2,5>
a.) Find the magnitude of both vectors
b.) Find the angle between both vectors
C) Find a vector perpendicular to vector AB
d. Vector M = 2 vector AB + vector AC . Find the direction and magnitude of vector M
e.) Find the area of Δ ABC
r = r2
1 − r=(−2 i^ −2 j^ +0 k^ )−(4 i^ −4 j^ +0 k^ )
⇒ r =−6 i^ +2 j^ +0 k^
∴∣ r ∣= (−6)2 +(2) 2 +0 2
= 36+4
= 40
=210
A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature. The above option D is appropriate.
Computer graphics known as vector graphics allow for the direct creation of visual pictures using geometric structures such as points, lines, curves, and polygons that are defined on a Cartesian plane.
Any pathogen that conveys and spreads an infectious agent into other living things is referred to be a vector. These vectors could be bacteria or parasites.
The above option D is correct.
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Marianna finds an annuity that pays 8% annual interest, compounded quarterly. She invests in this annuity and contributes $10,000 each quarter for 6 years. How much money will be in her annuity after 6 years? Enter your answer rounded to the nearest hundred dollars.
The amount of money in Marianna's annuity after 6 years will be approximately $300,516.
To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:
A = P * ((1 + r/n)^(n*t) - 1) / (r/n)
Where:
A = the final amount in the annuity
P = the regular contribution (each quarter) = $10,000
r = annual interest rate = 8% = 0.08
n = number of compounding periods per year = 4 (since it's compounded quarterly)
t = number of years = 6
Plugging in the values:
A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)
Calculating this expression:
A ≈ 10000 * ((1.02)^24 - 1) / 0.02
A ≈ 10000 * (1.601032449136241 - 1) / 0.02
A ≈ 10000 * 0.601032449136241 / 0.02
A ≈ 10000 * 30.05162245681205
A ≈ 300,516.22
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Answer:
304200
Step-by-step explanation:
To find the value of P6, use the savings annuity formula
PN=d((1+r/k)N k−1)r/k.
From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives
P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).
Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.
Rounding as requested, our answer is 304200.
find by a digit to make the number divisible by 3 1234?
A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.
To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.
Let's calculate the sum of the digits in 1234:
1 + 2 + 3 + 4 = 10
The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.
To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.
The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.
1234 + 2 = 1236
we obtain the number 1236, which is divisible by 3.
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Compare the graph of Car A to the table of Car B to determine:
a. The rate of each car,
b.
Which has the greatest speed,
C. How many times faster is the fastest car. (example: 2, 3 or 4 times faster)
Car A is 2 times Faster than Car B during the first hour.
The graph of Car A is a straight line, indicating that it is traveling at a constant speed.
The graph shows that Car A is traveling 100 miles in 2 hour .The table of Car B shows that it travels 50 miles in 1 hour, 100 miles in 2 hours, and 150 miles in 3 hours. Thus, the rate of Car B is increasing, as it travels at a faster speed during each hour compared to the previous hour.To find the rate of each car, we need to divide the distance by the time. For Car A, rate = distance ÷ time = 100 miles ÷ 2 hours = 50 miles per hour.
For Car B, we can find the average rate for each hour by dividing the distance traveled during that hour by the time. Thus, the rates are: First hour: 50 miles per hour Second hour: 50 miles ÷ 1 hour = 50 miles per hour Third hour: 50 miles ÷ 1 hour = 50 miles per hour By comparing the rates, we see that both cars are traveling at the same speed during the second and third hours. However, during the first hour, Car A is traveling faster than Car B.
Thus, Car A has the greatest speed.To determine how many times faster Car A is compared to Car B during the first hour, we can divide their rates. The rate of Car A is 50 miles per hour, while the rate of Car B is 50 miles per hour. Therefore, Car A is traveling at the same speed as Car B during the second and third hours. During the first hour, Car A is traveling twice as fast as Car B. Thus, Car A is 2 times faster than Car B during the first hour.
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The test scores for a local DMV had an average of 20 and a standard deviation of 5. Hank scored a 23.
What is the z-score for Hank?
We need to find the z-score for Hank using the above formula.z = (x - μ) / σ= (23 - 20) / 5= 0.6So, the z-score for Hank is 0.6.
The z-score measures the number of standard deviations a particular value is away from the mean. A positive z-score indicates that Hank's score is above the mean, while a negative z-score would indicate a score below the mean. In this case, a z-score of 0.6 suggests that Hank's score is 0.6 standard deviations above the average.
The z-score is a measure of the number of standard deviations that a value is above or below the mean of a distribution. It is calculated using the formula z = (x - μ) / σ, where x is the value being evaluated, μ is the mean of the distribution, and σ is the standard deviation.
The given problem states that the test scores of a local DMV had an average of 20 and a standard deviation of 5.
So, the mean μ = 20 and the standard deviation σ = 5.Hank scored a 23. This means that his score is 0.6 standard deviations above the mean of the distribution.
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An isosceles triangle below hss equal sides where PQ = PR and base angles of 65⁰. QX = XR= 2.64cm. Find a) PQ b) PX
The PQ is 2.265 cm and PX is 3.73 cm.An isosceles triangle of equal sides where PQ = PR and base angles of 65⁰. QX = XR= 2.64cm
Let's solve the problem step by step.
a) PQ: Since the triangle is isosceles and PQ = PR, we can conclude that angle PQR = angle PRQ. We also know that the sum of the angles in a triangle is 180 degrees.
Given that the base angles are 65 degrees each, we can calculate angle PQR as follows:
180 - 65 - 65 = 50 degrees
Now, let's consider triangle PQR. It is an isosceles triangle, with PQ = PR and angle PQR = angle PRQ = 50 degrees.
We are given that QX = XR = 2.64 cm. Using this information, we can apply the Law of Cosines to find PQ.
The Law of Cosines states:
c^2 = a^2 + b^2 - 2ab * cos(C)
In triangle PQR, a = PQ, b = PQ, and C = 50 degrees. Let's plug in the values:
(PQ)^2 = (2.64)^2 + (2.64)^2 - 2 * 2.64 * 2.64 * cos(50)
(PQ)^2 = 6.9696 + 6.9696 - 2 * 2.64 * 2.64 * 0.64278760968
(PQ)^2 = 6.9696 + 6.9696 - 8.81269008562
(PQ)^2 = 5.12650991438
Taking the square root of both sides, we get:
PQ = √5.12650991438
PQ ≈ 2.265 cm
b) PX: To find PX, we can use the Pythagorean theorem in triangle PXR.
In triangle PXR, we have the right angle at X. PX is the hypotenuse, and QX (or XR) is one of the legs.
Using the Pythagorean theorem, we have:
(PX)^2 = (QX)^2 + (XR)^2
(PX)^2 = (2.64)^2 + (2.64)^2
(PX)^2 = 6.9696 + 6.9696
(PX)^2 = 13.9392
Taking the square root of both sides, we get:
PX = √13.9392
PX ≈ 3.73 cm
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grade 11 2022 June common test mathematics memorandum?
Note that the roots of the equation Unequal and rational (Option D)
How is this so ?The roots of the equation (x - 3)² = 4 can be found by taking the square root of both sidesof the equation.
x - 3 = ±√4
⇒ x - 3 = ±2
Solve for x
For the positive square root.
x - 3 = 2
x = 2 + 3
x = 5
For the negative square root.
x - 3 = -2
x = -2 + 3
x = 1
Since the equation has two roots, x = 5 and x = 1. These roots are unequal and rational. (Option D)
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Full Question:
Although part of your question is missing, you might be referring to this full question:
The roots of the equation (x - 3)² = 4 are
A.Unequal and irrational.
B.Equal and rational.
C. Equal and irrational.
D. Unequal and rational.
pls help and draw it so it's more easier
In this rectangle, there are two lines of symmetry.
A line of symmetry is a line that divides a shape into two equal halves, such that each half is a mirror image of the other. The lines of symmetry in a rectangle are vertical and horizontal.
Vertical Line of Symmetry:
A vertical line of symmetry runs from the top to the bottom of the rectangle, dividing it into two equal halves. Each half is a mirror image of the other. To identify the vertical line of symmetry in a rectangle, you can visualize folding the rectangle along a line from top to bottom. The left and right sides of the folded rectangle will match perfectly.
Horizontal Line of Symmetry:
A horizontal line of symmetry runs from one side of the rectangle to the other, dividing it into two equal halves. Each half is a mirror image of the other. To identify the horizontal line of symmetry in a rectangle, imagine folding the rectangle along a line from left to right. The top and bottom sides of the folded rectangle will align perfectly.
I find the lines of symmetry in a rectangle, you can also observe its properties. In a rectangle, opposite sides are parallel and equal in length, and all interior angles are right angles (90 degrees). By considering these characteristics, you can determine that the vertical and horizontal lines passing through the center of the rectangle will be the lines of symmetry.
Understanding the lines of symmetry in a rectangle is essential in various applications, such as geometry, design, and architecture. These lines allow for balanced and symmetrical arrangements, providing aesthetic appeal and structural stability.
Final answer:
In following rectangle, there are two lines of symmetry.
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What is the 36th derivative of f(x)=cos2x?
The 36th derivative of f(x) = cos(2x) is [tex]2^{17}[/tex]* cos(2x).
To find the 36th derivative of the function f(x) = cos(2x), we can apply the chain rule repeatedly. The chain rule states that if we have a composite function y = f(g(x)), then its derivative is given by dy/dx = f'(g(x)) * g'(x).
Let's start by finding the first few derivatives of f(x) = cos(2x):
f'(x) = -2sin(2x)
f''(x) = -4cos(2x)
f'''(x) = 8sin(2x)
f''''(x) = 16cos(2x)
We observe a pattern where the derivatives of cos(2x) alternate between sin(2x) and cos(2x), with the signs changing accordingly.
Based on this pattern, we can see that the 36th derivative will be:
f^(36)(x) =[tex](-1)^{17} * 2^{17} *[/tex] cos(2x)
Simplifying this expression, we have:
f^(36)(x) = [tex]2^{17} * cos(2x)[/tex]
Therefore, the 36th derivative of f(x) = cos(2x) is[tex]2^{17[/tex] * cos(2x).
It's important to note that in this case, the number 36 is even, and since the derivatives of cos(2x) follow a repeating pattern every 4 derivatives, the sign (-1) raised to the power of 17 accounts for the change in sign in the 36th derivative.
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1. The slant height of a cone is 5cm and the radius of its base is 3cm. Find correct to the nearest
whole number the volume of the cone (A) 48cm3 (B) 47cm3 (C) 38cm3 (D)13cm3
The volume of the cone is 13 cm³. option D
How to determine the volumeTo determine the volume of the cone, we have that;
The formula for calculating the volume of a cone is expressed as;
Volume = (1/3)πr ²√(L ² - r ²).
Such that;
r is the radiusL is the slant heightSubstitute the values, we have;
Volume = 1/3 × 3.14 ² × √(25 - 9)
Find the squares, we get;
Volume, V = 1/3 × 9. 86 × √16
Find the square root
Volume, V = 1/3 × 9.86 × 4
Volume, V = 13 cm³
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Help me pleaseeeee :(
Answer:
(b) f(x) = -1/x⁹ and g(x) = -8x +4
(d) f(x) = x⁹ and g(x) = -1/(-8x +4) . . . . . alternate solution
Step-by-step explanation:
You want to decompose h(x) = -1/(-8x +4)⁹ into f(x) and g(x) such that h(x) = f(g(x)).
CompositionThe composition h(x) = f(g(x)) means that the function g(x) will replace x in the definition of f(x).
It is often convenient to look at the order of operations when asked to decompose a function like this. Here, the parenthetical expression (-8x+4) is raised to the 9th power and its opposite reciprocal is found. This suggests that f(x) can be a function that finds the opposite reciprocal of a 9th power, matching choice B. Thus, a reasonable choice is ...
(b) f(x) = -1/x⁹ and g(x) = -8x +4
Also ...We note that the reciprocal of a 9th power is also the 9th power of a reciprocal. A negative sign is preserved by the odd power. This means that another reasonable choice for the decomposition is ...
(d) f(x) = x⁹ and g(x) = -1/(-8x +4)
__
Additional comment
We list choice B first because that one is probably the one you're supposed to claim as the answer. However, this question has two correct decompositions among those listed. You may want to discuss this with your teacher.
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HELP PLEASE I DONT GET THIS
so the idea being, we have a system of equations of two variables and 4 equations, each one rendering a line, for this case these aren't equations per se, they're INEquations, so pretty much the function will be the same for an equation but we'll use > or < instead of =, but fairly the function is basically the same, the behaviour differs a bit.
we have a line passing through (-6,0) and (0,8), side one
we have a line passing through the x-axis and -6, namely (-6,0) and the y-axis and -4, namely (0,-4), side two
we have a line passing through (0,-4) and (6,4), side three
now, side four is simply the line connecting one and three.
the intersection of all four lines looks like the one in the picture below, so what are those lines with their shading producing that quadrilateral?
well, we have two points for all four, and that's all we need to get the equation of a line, once we get the equation, with its shading like that in the picture, we'll make it an inequality.
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{8 -0}{0 +6} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = \cfrac{4}{3} ( x +6) \\\\\\ y=\cfrac{4}{3}x+8\hspace{5em}\stackrel{\textit{side one} }{\boxed{y < \cfrac{4}{3}x+8}}[/tex]
[tex]\rule{34em}{0.25pt}\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{-4 -0}{0 +6} \implies \cfrac{ -4 }{ 6 } \implies - \cfrac{2}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = - \cfrac{2}{3} ( x +6) \\\\\\ y=-\cfrac{2}{3}x-4\hspace{5em}\stackrel{\textit{side two} }{\boxed{y > -\cfrac{2}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{0}}} \implies \cfrac{4 +4}{6 -0} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{0}) \implies y +4 = \cfrac{4}{3} ( x -0) \\\\\\ y=\cfrac{4}{3}x-4\hspace{5em}\stackrel{ \textit{side three} }{\boxed{y > \cfrac{4}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{6}}} \implies \cfrac{ 4 }{ -6 } \implies - \cfrac{2}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{6}) \\\\\\ y=-\cfrac{2}{3}x+8\hspace{5em}\stackrel{ \textit{side four} }{\boxed{y < -\cfrac{2}{3}x+8}}[/tex]
now, we can make that quadrilateral a trapezoid by simply moving one point for "side four", say we change the point (0 , 8) and in essence slide it down over the line to (-3 , 4). Notice, all we did was slide it down the line of side one, that means the equation for side one never changed and thus its inequality is the same function.
now, with the new points for side for of (-3,4) and (6,4), let's rewrite its inequality
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{4 -4}{6 +3} \implies \cfrac{ 0 }{ 9 } \implies 0[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ 0}(x-\stackrel{x_1}{(-3)}) \implies y -4 = 0 ( x +3) \\\\\\ y=4\hspace{5em}\stackrel{ \textit{side four changed} }{\boxed{y < 4}}[/tex]
Find the smallest whole number by which 16087 should be multiplied or divided to get a perfect square
There is no whole number by which you can multiply or divide 16087 to make it a perfect square.
To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.
In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.
To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.
A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.
Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.
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A train travels 70 feet in 1/10th of a second. At this same speed, how many feet will it travel in 3 and 1/2 ( three and one half) seconds?
Answer:
the train will travel 245 feet in 3 and 1/2 seconds
Step-by-step explanation:
To determine the distance the train will travel in 3 and 1/2 seconds, we can use a proportion based on the given information.
Let's set up the proportion:
70 feet / (1/10 second) = x feet / (3 1/2 seconds)
To solve this proportion, we can first convert the mixed number 3 1/2 to an improper fraction.
3 1/2 = 7/2
Now we can rewrite the proportion:
70 / (1/10) = x / (7/2)
To simplify the proportion, we can multiply the numerator and denominator of the right side by 10/1:
70 / (1/10) = (x * 10) / (7/2)
Simplifying further, we get:
70 * (10/1) = x * (10/7/2)
700 = x * (20/7)
To find x, we can divide both sides of the equation by (20/7):
x = 700 / (20/7)
x = 700 * (7/20)
x = 245 feet
Therefore, at the same speed, the train will travel 245 feet in 3 and 1/2 seconds.
What is the area of the parallelogram 60ftx67ft-52ft
To find the area of a parallelogram, you need to multiply the base by the height. In this case, the given dimensions are 60ft (base) and 67ft (height), and you need to subtract 52ft from the height.
New height = 67ft - 52ft = 15ft
Area of the parallelogram = Base * Height = 60ft * 15ft = 900 square feet.
Therefore, the area of the parallelogram is 900 square feet.
~~~Harsha~~~
Prove the following?
X is an inductive set, then {X [tex]\in[/tex] x is transitive} is also an inductive set. Consequently, every n [tex]\in[/tex] N is transitive.
To prove the statement, we need to demonstrate that if X is an inductive set, then the set {[tex]X \in x[/tex]is transitive} is also an inductive set.
Let's break down the proof into two parts:
If X is an inductive set, then {[tex]X \in x[/tex] is transitive} is a subset of X:
To show that {[tex]X \in x[/tex]is transitive} is a subset of X, we need to prove that every element in {[tex]X \in x[/tex] is transitive} is also an element of X.
If X is an inductive set, it means that X contains the empty set (∅) and for every element x in X, the successor of x (denoted as S(x)) is also in X. Now, consider an arbitrary element y in {[tex]X \in x[/tex] is transitive}. By definition, y is a transitive set.
Since X is inductive, it contains the empty set and for every element in X, its successor is also in X. Thus, y must also be in X, and {[tex]X \in x[/tex] is transitive} is a subset of X.
{[tex]X \in x[/tex] is transitive} is an inductive set:
To show that {[tex]X \in x[/tex] is transitive} is an inductive set, we need to demonstrate that it satisfies the properties of an inductive set.
First, we prove that the empty set (∅) is an element of {EX: x is transitive}. Since the empty set is transitive (it vacuously satisfies the definition of transitivity), it belongs to {[tex]X \in x[/tex] is transitive}.
Second, we prove that for every element y in {[tex]X \in x[/tex] is transitive}, its successor S(y) is also in {[tex]X \in x[/tex] is transitive}. Let y be an arbitrary element in {[tex]X \in x[/tex] is transitive}.
By definition, y is a transitive set. We need to show that S(y) is also a transitive set. Since X is inductive, it means that for every element x in X, its successor S(x) is also in X. Applying this property to y, we conclude that S(y) is in X. Since S(y) is in X, it is also in [tex]X \in x[/tex] is transitive}. Hence, {[tex]X \in x[/tex] is transitive} satisfies the property of an inductive set.
By proving both parts, we have shown that if X is an inductive set, then {[tex]X \in x[/tex] is transitive} is also an inductive set. Consequently, every [tex]n \in N[/tex] is transitive.
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