When reflected across a line of symmetry, a shape having that line of symmetry will fall on itself. These are the actual claims:
(1) The rectangle's diagonals will line up exactly with one another.
(2) A rectangle's diagonals are symmetry lines.
We deduce from the question that the rectangle is mirrored across the symmetry line.
When done, the rectangle's half will fall directly on the other half.
This indicates that the rectangle's diagonal will line up perfectly with the opposite diagonal.
According to the aforementioned claim, a rectangle's diagonal is also its line of symmetry.
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Can you help me find this answer?
Step-by-step explanation:
These two angles are same side corresponding interior angles so they are equal to each other
[tex]5x + 20 = 120[/tex]
[tex]5x = 100[/tex]
[tex]x = 20[/tex]
What is the following product? rootindex 3 startroot 5 endroot times startroot 2 endroot.
The product of the given irrational number ∛5 × √2 is equal to
option b. [tex]\sqrt[6]{200}[/tex]
As given in the question,
Given irrational numbers are:
∛5 × √2
Take the least common multiple of 3 and 2
Least common multiple of 3 and 2 is 6.
∛5 = [tex]5^{2 \times\frac{1}{2}\times \frac{1}{3} }[/tex]
= [tex]\sqrt[6]{5^2}[/tex]
= [tex]\sqrt[6]{25}[/tex]
√2 = [tex]2^{3 \times\frac{1}{3}\times \frac{1}{2} }[/tex]
=[tex]\sqrt[6]{2^3}[/tex]
= [tex]\sqrt[6]{8}[/tex]
Product of ∛5 × √2 is given by:
∛5 × √2 = [tex]\sqrt[6]{25} \times \sqrt[6]{8}[/tex]
= [tex]\sqrt[6]{25 \times 8}[/tex]
= [tex]\sqrt[6]{200}[/tex]
Therefore, the product of the given irrational number is equal to [tex]\sqrt[6]{200}[/tex] .
The complete question is:
What is the following product?
∛5 × √2
a. [tex]\sqrt[6]{10}[/tex]
b. [tex]\sqrt[6]{200}[/tex]
c. [tex]\sqrt[6]{500}[/tex]
d. [tex]\sqrt[6]{10000}[/tex]
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the following are the amount of time, in minutes, that it took a random sample of 20 technicians to perform a certain task: 18.1 20.3 18.3 15.6 22.5 16.8 17.6 16.9 18.2 17.0 19.3 16.5 19.5 18.6 20.0 18.8 19.1 17.5 18.5 18.0 assuming that the sample came from a symmetric continuous distribution, use the sign test at the 0.05 level of significance to test the null hypothesis that the mean of the population is 19.4 against a 2-sided alternative. perform the test using: (a) the binomial distribution; (b) the normal approximation to the binomial distribution.
The normal approximation to the binomial distribution is C ( n , r ) * p^r * q^n - r .
a )
the binomial distribution .
Null hypothesis H0: μ = 19.4
Alternative hypotheses H1: μ ≠ 19.4
19.4 with minus sign, we get
n = 20, x = 4 and n/2 = 10
Here x < n/2
Therefore, from table the computed P-Value is.
b )
the normal approximation to the binomial distribution ,
P = 2P(X ≤ 4 when θ = 1/2 )
= 2 (0.0059)
= 0.0118
Hence the P value, 0.0118, is less than 0.05, the null hypothesis must be rejected, and we conclude that the mean of the population is not 19.4 minutes.
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Given that ∠X≅∠D, and DE≅XW, what is the third congruence needed to prove that ΔXWY≅ΔDEC by ASA?
A
∠Y≅∠C
B
∠Y≅∠E
C
∠W≅∠C
D
∠W≅∠E
Answer:
(A) ∠Y ≅ ∠C.
Step-by-step explanation:
To prove that two triangles are congruent by ASA (Angle-Side-Angle), you need to show that two angles in one triangle are congruent to two corresponding angles in the other triangle, and that the side between the two angles is congruent to the corresponding side in the other triangle.
Given that ∠X ≅ ∠D and ∠DE ≅ ∠XW, the third congruence needed to prove that ΔXWY ≅ ΔDEC by ASA is:
(A) ∠Y ≅ ∠C
This is because ∠Y and ∠C are the corresponding angles in the two triangles that have not been shown to be congruent.
So the answer is (A) ∠Y ≅ ∠C.
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B i the midpoint of AC. D i the midpoint of CE. DE=5 and AE=18. What i the length of BD?
The length of BD is 9 units when considering the idea of a line segment's midpoint.
What is midpoint of line segment ?A midpoint is a point that lies on a line connecting two other locations and is in the middle of the line. The midpoint is the point on the middle of the line that is equally distant from the two points if a line is drawn connecting the two points. The midpoint is the point B that lies halfway between any two points, let's say A and C. As a result, measuring the length of the line segment and dividing it by two will yield the midway.
According to the given information :
AE = 18, DE = 5
However, D is the middle of CE
CE = 2 × 5 = 10
The line CE will become 10
But AE is the total length of the line segment and it is equal to 18
AE = AC + CE
AC = AE - CE
AC = 8
If AC = 8 , BC = 1/2AC
BC = [tex]\frac{8}{2}[/tex]
BC = 4
The BD becomes BC + CD
BD = 9 units
The length of BD is 9 units when considering the idea of a line segment's midpoint.
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Characterize the slope of the line in the graph
it must be A because it's is going down word
Answer:
Slope is negative
Step-by-step explanation:
from one point to the next, it goes down 1 (-1) and over 4 (4)
or, from one point it goes left 4 (-4) and up 1 (1) just depending on how tou look at it.
1.) in the number 4658.21987 what digit is in the hundredths place
2.) in the number 4716.054321 what digit is in the ten-thousands place
Answer:
1)1
2)3
Step-by-step explanation:
Have a look at some tables online
Write an equation for the line.
Answer:
y = 2x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (1, 0) ← 2 points on the line
m = [tex]\frac{0-(-2)}{1-0}[/tex] = [tex]\frac{0+2}{1}[/tex] = [tex]\frac{2}{1}[/tex] = 2
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = 2x - 2 ← equation of line
Answer:
y = 2x - 2
Step-by-step explanation:
The equation y = mx + b is a standard form of a linear equation in one variable. It represents a straight line on a graph
In this equation, y is the dependent variable, which is the variable that is being measured or predicted. The independent variable is x, which is the input or cause in the relationship.
The coefficient m is the slope of the line, which tells you the rate of change between the two variables. It represents how much the value of y changes for each unit change in the value of x. A positive slope means that the line goes up as you move from left to right, while a negative slope means that the line goes down.
- Our slope is positive
- slope (m) = rise / run = 2/1 = 2
The constant b is the y-intercept, which is the point where the line crosses the y-axis. It represents the value of y when x is equal to 0.
- Our y-intercept is -2
m is 2 and b is -2, the equation y = 2x - 2 represents a line with a slope of 2 and a y-intercept of -2. This means that for every 1 unit increase in the value of x, the value of y increases by 2 units, and the line crosses the y-axis at the point (0, -2).
9. You decide to invest $500 into a 4-year CD that pays 2.85% interest
compounded monthly.
Use the compound interest formula:A = P(1 + r/n) ^nt to give:
a. The future value in 4 years.
b. The interest gained in 4 years.
Answer:
$560.30 & $60.30
Step-by-step explanation:
A = $560.30
A = P + I where
P (principal) = $500.00
I (interest) = $60.30
Write the equation of the line in fully simplified slope-intercept form.
You see from the graph that when x = 0, y = 2 so the y-intercept is ( 0 , 2).
you are given points (-6 , 3) and (6 , 1). Find slope:
slope = change in y / change in x
slope = (3 - 1) / (-6 - 6)
slope = 2/-12
slope = -1/6
slope-intercept form: y = mx + b where m = slope and b = y intercept.
y = -1/6x + 2
help i really need this answer please
Tim lives 2/3 as far from school as Felipe. Felipe walks to school and then walks to
Tim's house after school. What expression represents the total distance
Felipe walked?
Answer: x + 2/3(x)
Step-by-step explanation:
x = distance F walks to school
2/3(x) = distance T walks to school
Felipe walks first to school, then walks to Tim's house, so total distance Felipe walks: x + 2/3(x)
what is 24 in scientific notation
Answer:
2.4 × 101
Step-by-step explanation:
that is 24 in scientific notation
Answer:
24 * 10^1
Step-by-step explanation:
Hope this helps. :)
Woof Woof Dog School offers dog training classes. This session, there are 7 puppies
enrolled in classes for every 4 adult dogs enrolled.
Pick the diagram that models the ratio in the story.
puppies
adults
puppies
adults
If there are 42 more puppies than adult dogs enrolled in classes this session, how many dogs
are enrolled altogether?
dogs
The diagram that models the ratio in the story is the first diagram.
Puppies = Seven green boxes.
Adults = Four violet boxes.
There are 66 dogs enrolled together.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of puppies = 7
Number of adult dogs = 4
This can be written as,
7 puppies = 4 adult dogs
Multiply 6 on both sides.
42 puppies = 24 adult dogs
Now,
The total number of enrolled dogs.
42 + 24 = 66 dogs
Thus,
The ratio that models the story is the first diagram.
The total number of enrolled dogs is 66.
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Formulas are NOT used to solve a real-world problem of converting inches to feet.
O True
O False
Which of the following equations is NOT a form of a linear equation?
y = mx + b
y- y₁ = m (x − x₁)
Ax+By = C
y= ax² + bx + c-
y = kx
Answer:
the third onei
Step-by-step explanation:
it describes a quadratic equation/
PLEASE HELP ME OUT!!!!!!!!
GIVING BRAINLIEST
Fill in the blank with the correct response. If 24 is increased to 30, the percent of increase is %.
Answer:
there is a 25% increase from 24 to 30
Step-by-step explanation:
30-24/24 x 100
6/24x 100
0.25x100
25%
Answer:
[tex]\begin{align} \% \text{ Increase} &= \dfrac {\text{Final - Initial}}{\text{Initial}} \times 100 \\ \\ &= \dfrac {30 - 24}{24} \times 100 \\ \\ &= \dfrac {6}{24} \times 100 \\ \\ &= 0.25 \times 100 \\ \\ &= 25 \% \end{align} [/tex]
There is a 25 % increase from 24 to 30.
Sixty one minus twenty nine
Answer:
Step-by-step explanation:
32
A cell phone carrier charges a monthly fee of $20 and also charges customers $0.05 per text message. The function C(t)+0.05t+20 represents the cost of C, per month based on t text messages in a month.
Which best describes the domain of the function?
All real numbers
All real numbers that are multiples of 0.05
All whole numbers
All whole numbers for 0 to 20
Answer:500
Step-by-step explanation:
What is the area of this composite figure?
10 ft
10 ft
6 ft
2 ft
Answer:
88 ft^2
Step-by-step explanation:
we can make this a full 10 by 10 rectangle and find the area
10x10
100
And now we subtract the 6 by 2 triangle area that we added
6x2
12
100-12
88 ft^2
Hopes this helps please mark brainliest
Answer:
Answer = 88 ft²
Step-by-step explanation:
Step 1: Divide the composite shape into two separate parrellagrams
1. Dimensions of shape 1: Length is 10 ft, and width is 4 ft
2. Dimensions of shape 2: Length is 8 ft, and width is 6 ft
Step 2: Multiply the length by the height of each shape
Area = lw
3. Area of shape 1: 10 ft ∙ 4 ft = 40 ft²
4. Area of shape 2: 8 ft ∙ 6 ft = 48 ft²
Step 3: Add both areas together to get the total area of the composite shape
5. 40 ft² + 48 ft² = 88 ft²
Hence, the total area of this composite figure is 88 ft²
Mr. Hill also teaches gym. He has 20 soccer balls and 3 teams of
students. He gives the same number of balls to each team.
Can Mr. Hill divide 20 balls into 3 equal groups?
»)
>>>
>>)
Yes
No
I am not sure.
Answer:No, because you cant divide 20 balls into 3 equal groups.
Step-by-step explanation:
PLSS HELP ASAP!! 30 PTS
Triangle ABC has vertices A(0, -1), B(6, 5), and C(-4, 3).
Which statement about triangle ABC is true?
Answer:
The coordinates of the vertices of triangle ΔABC, A(0, -1), B(6, 5), and C(-4, 3), indicates that the triangle ΔABCD is a right triangle with all sides of different length.
Step-by-step explanation:
A local dry cleaner interviewed 10 candidates for the positions of cashier, washer, salesperson, and delivery driver. How many ways can they fill the 4 positions?
A. 14
B. 210
C. 5,040
D. 151,200
Answer:
How many ways can they fill the 4 positions?
The Answer is B. 210
Answer: b. 210
Step-by-step explanation:
Joseph and Raquel are building a scale model of the Alamo Mission for their Texas history project using a scale in which 2 inches represents 30 feet. The enclosed area of the Alamo Mission was 480 feet long and 160 wide.
What should the length of the enclosed area of the scale model be in inches?
Use synthetic division to solve (×3 + 1) = (X - 1). What is the quotient?
The required quotient is x² + x + 1 + (2/ x -1) which is determined by the synthetic division.
What is the Quotient?A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient.
Use the divisor and find x :
x - 1 = 0 add 1
x= 1
Now we'll divide with the number one:
Take the coefficients from the terms in front of them.
Make careful to include 0's for x² and x since all terms must be included.
set it up with a 1 in a box:
1| 1 0 0 1 bring the first number down
____________
1 multiply the boxed number by the first number and add it to the second number
1| 1 0 0 1
____+1_____ repeat with the rest of the terms
1 1
1| 1 0 0 1
___+1_+1_+1
1 1 1 2
When you're finished, use the new numbers to build an equation that begins with a term that has one fewer degree than the previous equation.
Because there is a remnant, divide it by the original divisor.
final answer:
x² + x + 1 + (2/ x -1)
Thus, the required quotient is x² + x + 1 + (2/ x -1) which is determined by the synthetic division.
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You make $10 an hour babysitting and $20 an hour lifeguarding. You need to make at least $120 next week to buy a concert ticket. You can work at most 10 hours a week. Use y for number of hours babysitting and x for hours lifeguarding
Answer:
5 hours lifeguarding and two hours babysitting.
Step-by-step explanation:
5(20) = 100
10(2) = 20
100 + 20 = 120
8.121 Round 8.121 to the nearest tenth.
Online there is an item that usually costs $20 is advertised as being 25% off.
What is the discount?
What is the sale price of the item?
Answer: The discount is 25% * $20 = $5.
The sale price of the item is $20 - $5 = $15.
A car drives down a road in such a way that its velocity (in m/s) at time t (seconds) is v(t)=2t1/2+1. Find the car's average velocity (in m/s) between t=4 and t=8
Average velocity of the car as calculated from the given data is 6m/s.
The average velocity is calculated by dividing the total distance travelled by the whole time that has passed. Given the velocity as a function of time, you may integrate the velocity function from t = 4 to t = 8 to determine the total distance travelled.
The opposite of taking a derivative is to integrate; in other words, the function I get when I take a derivative is 2t1/2 + 1. Assuming you are aware of how to do that If not, you can input the aforementioned integral into your TI-84 to obtain the result.
The integral turns out to be
(4/3)t^3/2 + 4t so x(t)
= (4/3)t3/2 + 4t and x(8) - x(4)
= (4/3)(8)3/2 + 4(8) - [(4/3)(4)3/2 + 4(4)]
= 24 meters
The distance travelled in total was 24 meter and it took 4 seconds (8-4) to do it, so the average velocity is 24 /4 = 6 m/s.
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(f)-3 =9 and g(-3) =2 find (f+g)(-3)
The value of f(-3) + g(-3) Or (f + g)(-3) is 11.
What is a composite function?When the output of one function is given to the input of another function they are called composite functions. In (fog)x which is [f{g(x)}] here the out of the function g(x) is the input of the function f(x).
Given, f(-3) is 9 and g(-3) is 2.
We know f(x) + g(x) = (f + g)(x).
∴ (f + g)(-3) = 9 + 2.
(f + g)(-3) = 11.
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Which graph is defined by f(x) = x² + 5|x| + 6?
O A.
OB.
O C.
O D.
graph A
graph B
graph C
graph D
The attached graph is defined by f(x) = x² + 5|x| + 6.
What is the graph function?
The graph of a function f is the set of all points in the plane of the form (x, f(x)). We could also define the graph of f to be the graph of the equation y = f(x). So, the graph of a function is a special case of the graph of an equation.
We have,
y = x² + 5|x| + 6
we know,
|x|² = x² use this ,
y = |x|² + 5|x| + 6
Steps for drawing y = |x|² + 5|x| + 6
step1 :- first draw y = x² + 5x + 6, this graph is quadratic equation .
step2:- Leave the part of y=x² + 5x + 6 right side to the y-axis and also take its image with respect to the y-axis as a plane mirror.
step3 :- now remove the part of y = x² + 5x + 6 to left side from y - axis .
now your graph is ready
you can see in the figure attached.
Hence, the attached graph is defined by f(x) = x² + 5|x| + 6.
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