Answer:
D) 7.5%
Step-by-step explanation:
We can solve this through guessing and checking, or we can do this mathematically. We will try both approaches.
Mathematically:
We know that to get the extra $30 if we have $100, is a 30% interest. Now, since we have 4x 100, and these numbers are inversely proportional, we will need to divide 30 by 4. Doing this gives us 30/4 = 7.5, so the answer is 7.5%.
Guess and Check:
This way is a bit slower, but we will go through each answer and find how much money we would get from them. So, we would take our percent, change it to a number of that percent, considering we are taking it from 100, and multiply it by 4 since we have $400. We will get each of these respectively:
A) 3% = 3 * 4 = $12
B) 4.5% = 4.5 * 4 = $18
C) 6% = 6 * 4 = $24
D) 7.5% = 7.5 * 4 = $30
As you can see, D) gives us that extra $30, so the answer is D) 7.5%.
Hope this helped!
Can you help me with this
The graph of the given equation y=2x+1 is attached below.
How to find the function which was used to make graph?There are many tools we can use to find the information of the relation which was used to form the graph.
A graph contains data of which input maps to which output.
Analysis of this leads to the relations which were used to make it.
For example, when the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
The equation y=2x+1 gives the following information:
The slope is 2
The line intercepts is 1 on the y axis
First, we would put a point or a dot on (0,1) on the y axis. Then start making 2 points above and below my original point. IT would do this by using the slope 2/1.
By using my slope we know that (1,3) and (-1,-1).
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Suppose $P(x)$ is a polynomial of smallest possible degree such that: $\bullet$ $P(x)$ has rational coefficients $\bullet$ $P(-3)
The value of polynomial p(x) when x=0 is 35.
What is a polynomial?
An expression made up of indeterminates and coefficients and utilising solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables is referred to as a polynomial.
The complete question is as follows:
Suppose p(x) is a polynomial of smallest possible degree such that: bullet p(x) has rational coefficients bullet p(-3) = p(\sqrt 7) = p(1-\sqrt 6) = 0 bullet p(-1) = 8 determine the value of p(0).
Given,
p(x) is a polynomial of smallest degree where
p(-3) = p(√7) = p( 1-√6) = 0
p(-1) = 8
So the factors of p are (x+3),(x-√7) and (x - 1+√6)
Given p has rational coeffecients. So we should remove √7 and √6. This can be done by multiplying with conjugates.
(x-√7)*(x+√7) = x²-7
(x-1+√6) * (x-1-√6) = (x-1)² - √6² = x²-2x+1-6 = x²-2x-5
Now the polynomial can be written as
p(x) = c (x+3)(x²-7) (x²-2x-5 )
Here c is a constant and can be determined using p(-1) = 8
p(-1) = c ( -1+3)(-1² - 7 )(-1²-2*(-1) -5)
8 = c(2)(-6)(-2)
c = 1/3
Now the polynomial p(x) = 1/3(x+3)(x²-7) (x²-2x-5 )
Therefore p(0) = 1/3 (3) (-7)(-5) = 35
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Don’t know need help
I think that the answer would be 14
An aircraft hangar is semi-cylindrical with
diameter 40 m and length 50 m. A helicopter
places a cable across the top of the hangar, and
one end is pinned to the corner at A. The cable
is then pulled tight and pinned at the opposite
corner B. Determine the length of the cable.
On solving the provided question, we can say that - the volume of the cylinder will be V = 3.14 * 20*20*50 = 62800
what is radius?The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle. Diameter
volume of the cylinder -
V = [tex]\pi r^2h[/tex]
r = 40/2 = 20
h = 50
V = 3.14 * 20*20*50 = 62800
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What is the difference of the two polynomials 9x2 8x 2x2 3x?
The difference between the two polynomials (9x²+8x) - (2x²+3x) is:
7x² + 5x.
Polynomial:
A polynomial is a type of algebraic expression where the exponents of all variables must be integers. The exponent of each polynomial variable must be a non-negative integer. A polynomial consists of a constant and a variable, but you cannot divide a polynomial by a variable.
Example: Express the polynomial 5 + 2x + x2 in standard form.
To express the above polynomial in standard form, first check the degree of the polynomial.
The degree of the given polynomial is two. Write an expression involving the degree of the polynomial.
There is a term with variable exponent less than 2, i.e.1, then write it down.
Finally, we write a term with the variable exponent 0 as the constant term.
According to the Question:
Given polynomials is:
(9x²+8x) - (2x²+3x)
First, multiply the negative sign in the second polynomial
i.e., (9x²+8x) - (2x²+3x)
= 9x²+8x - 2x²-3x
Now, evaluate those terms who have same variables
= 9x² - 2x² +8x-3x
= 7x² + 5x
Hence, the difference between polynomials are: 7x² + 5x.
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How do you find f inverse?
Inverse of function is written by using notation f⁻¹
What is inverse of function?The function that can be reversed into another function is termed as inverse function. It is also called anti function. There are different types of inverse function such as inverse trigonometric function, inverse rational function, inverse log function and so on.
We can determine an inverse function by interchanging the elements that present in the given expressions.
How do we find f inverse?Inverse of the function f is denoted by notation f⁻¹
let, we have given a function, f(x) = 8x + 9
now, we need to find the inverse of the above function.
in the first step we write the function using y and set equal to x
x = 8y +9
in the next step, we arrange to make the y subject,
x - 9 = 8y
8y = x - 9
y = (x - 9)/ 8
use the notation f⁻¹ = (x - 9)/ 8
this is the inverse of function f.
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Mario has 3/4 cups of chocolate chips needs 1/3 cup to make a batch of cookies how many batches can Mario make if he uses all of his chocolate chips
In the given equation, Mario can make 2.25 batches of cookies using all of his chocolate chips.
How to find the given equation?First, you can find out how many total cups of chocolate chips Mario has by multiplying the number of cups per unit (3/4) by the number of units (1).
[tex]3/4 cups * 1 = 3/4 cups\\[/tex]
Then you can divide the total amount of chocolate chips Mario has by the amount of chocolate chips needed per batch:
[tex]3/4 cups / 1/3 cup/batch = 3/4 cups * 3/1 cup/batch = 9/4 cups/batch[/tex]
Finally, you can convert this to a whole number by dividing both the numerator and denominator by their greatest common factor, which is 1:
[tex]9/4 cups/batch = (9/1) / (4/1) = 9/4 = 2.25 batches[/tex]
Mario can make 2.25 batches of cookies using all of his chocolate chips.
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The number cube with sides labeled 1 through 6 is rolled.
Which events are likely to occur? Select all that apply. Multiple select question. A) rolling a 1 or a 2 B) rolling an odd number C) rolling an even number D) rolling a a number less than 6 E) rolling a number greater than 2
Answer:
Events D and E are likely to occur.----------------------------------------
The number cube has sides 1 through 6. The probability of each number is same, 1/6.
Given events below, see how likely they are to occur:
A) rolling a 1 or a 2,
this is a 2/6 = 1/3 < 1/2, not likely;B) rolling an odd number,
this is a 3/6 = 1/2, not likely;C) rolling an even number,
this is a 3/6 = 1/2, not likely;D) rolling a a number less than 6,
this is 5/6 > 1/2, likely to occur;E) rolling a number greater than 2,
this is a 4/6 = 2/3 > 1/2, likely to occur.What is the discriminant of 3x^2 2x 1 0?
The discriminant of quadratic equation 3x^2 + 2x + 1 =0 is -8
We know that the standard form of quadratic equation is ax^2 + bx + c = 0, with a ≠ 0
The discriminant of quadratic equation ax^2 + bx + c = 0 is:
D = b^2 - 4ac
Comparing given quadratic equation 3x^2 + 2x + 1 =0 with ax^2 +bx + c = 0 we get,
a = 3, b = 2 and c = 1
So, the discriminant of given equation would be,
D = b^2 - 4ac
D = 2^2 - 4(3)(1)
D = 4 - 12
D = -8
Therefore, the discriminant is D = -8
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Define an exponential function, f(x), which passes through the points (0,125) and (3,8). Enter your answer in the form a*b^x
Answer:
Step-by-step explanation:
put (0, 125) in a*b^x, we get a = 125, then put (3,8) in 125*b^x, we get 125*b^3=8
b^3=8/125
b=2/5
then the answer is 125*(2/5)^x
How many solutions exist for the given equation 3 x 10 6 3 x 12?
There are no solutions for the equation 3x106 3x12.
The equation 3x106 3x12 can be rearranged to 3x106 - 3x12 = 0. This is a linear equation and can be solved using the equation ax+b=0, where a is the coefficient of the variable and b is the constant.
In this case, a = 3 and b = -3x106. To solve this equation, we can use the quadratic formula, which states that x = -b ± √b2 - 4ac / 2a.
Substituting the values for a, b, and c yields x = -(-3x106) ± √(3x106)2 - 4(3)(-3x106)/2(3). Simplifying this yields x = 3x106 ± √9x1012 - 36x1012/6.
This simplifies to x = 3x106 ± √-27x1012/6. Since the square root of a negative number is not a real number, this equation has no real solutions. Therefore, there are no solutions for the equation 3x106 3x12.
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Simplify the expression.
[tex](1+\frac{x}{y} )(\frac{4y^{2} }{x^{2} -y^{2} } )[/tex]
Answer:
4y / x-y
Step-by-step explanation:
First change 1 to y/y. This allows us to rewrite the first term as a single fraction.
We can also factor the denominator of the second term.
x^2 - y^2 factors into (x - y)(x + y)
The y cancels and also the term x+y cancels. See image.
PLEASE HELP. I'LL DO ANYTHING THAT'LL BENEFIT YOU.
If you double the amount of fluid ounces, the amount of cups also double
There is a proportional relationship between the number of fluid ounces and the number of cups. So, the number of cups would change by the same factor as the number of fluid ounces.
The cost of renting equipment is sometimes proportional; because, it depends on whether the equipment has a rental fee and charge per hour or just a charge per hour. Option A.The cost of mailing a letter is proportional to the weight. The cost of mailing a 6-ounce letter is $2.82. Option BThe donation is proportional to the dinner bill
The donation for a dinner bill of $50 is $9
How to determine proportional relationship?If there are 8 fluid ounces in one cup
8 : 1 = 16 : x
8/1 = 16/x
8 × x = 16 × 1
8x = 16
x = 16/8
x = 2
The difference between weight = 1
The difference between cost = $0.68 - $0.47
= $0.21
$0.89 - $0.68
= $0.21
$1.10 - $0.89
= $0.21
Cost of mailing 6-ounce letter
1 : 0.47 = 6 : x
1/0.47 = 6/x
1 × x = 6 × 0.47
x = $2.82
The donation for a dinner bill $50 is
Dinner bill : donation
25 : 4.50 = 50 : x
25/4.50 = 50/x
25 × x = 50 × 4.50
25x = 225
x = 225/25
x =$ 9
Therefore, there is a proportional relationship between two quantities if there is an equal change in the values of both quantities.
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Factor each polynomial completely.
a. 5a²c - 3a²d + 5b²c-3b²d
b. x^2n+ 6x^n +9
Put the letters into the correct order to make worlds. Then match them to the definitions
oiffce psorin hlostipa ctotgae fcatyor gtues-hsoue
1. A room or building where people work at desks……..
2. A small hotel that is not very expensive………
3. A building where people are sent if they have committed a crime……..
4. A building where people go if they ill……..
5. A building where people make things, often using machines………
6. A small attractive house in the country……….
*************
1. A: Excuse me, can you tell me (1) the way to how far for the station?
B: Yes, sure. (2) Take/Turn left at the traffic lights and you'll see the station (3) in front / by
front of you.
2. A: Excuse me, (4) is it far / can you direct to the museum?
B: No. Just go (5) straight off / straight on for about half a kilometre and the museum is
(6) on / at your right.
Answer:
Step-by-step explanation:
Given the answer for part D, write an expression that will tell you the direction the robot is going if, in the course of its journey, it turns left 21 times and turns right 22 times. Does the order the robot makes the turns in matter for the purpose of knowing the direction it is finally facing?
The answer to part D is in the picture...
The robot is moving in the direction indicated by the formula ((i)²¹*(-i)²²)d, or in the beginning direction.
What is complex plain?
When a line is rotated in the complex plane either clockwise or anticlockwise, it is multiplied by -i or I depending on which direction the line is rotated. The direction vector is rotated 90 degrees in the clockwise direction to make a right turn. It is the same as increasing the complex number by -i.
A left turn is represented as a 90° anticlockwise rotation of the direction vector. It is comparable to increasing the complex number by i.
There are 21 left turns of the robot. The direction vector will now be di21. Once it has been rotated 22 times to the right, the direction vector will now be (di²¹)*(-i)²²=d((i)²¹*(-i)²²).
Consequently, the robot's current direction is:
d((i)²¹*(-i)²²)= di²¹⁺²²=di⁴³= d(-i)= -di
No matter what, the direction will always be the same, hence the sequence is irrelevant.
Hence, the equation that will indicate where the robot is moving is ((i)²¹*(-i)²²)d, or in the starting direction. Furthermore, the final direction it faces does not depend on the order.
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Is the area of an equilateral triangle is 9 root 3 cm square then the semi perimeter of the triangle is?
The equilateral triangle has a 9 root 3 cm square area, and its semi-perimeter is 9 cm.
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
given
area of equilateral triangle = [tex]9\sqrt{3}cm^{2}[/tex]
formula of area of equilateral triangle = [tex]\frac{\sqrt{3}a^{2} }{4} sq.units[/tex]
a = side of triangle
[tex]\frac{\sqrt{3}a^{2} }{4} sq.units[/tex] = [tex]9\sqrt{3}cm^{2}[/tex]
[tex]a^{2} = \frac{4* 9\sqrt{3} }{\sqrt{3} }[/tex]
[tex]a^{2} = 36\\ a = 6 cm[/tex]
since equilateral triangle all sides are equal
perimeter of triangle = 6 + 6 + 6
= 18cm
the semi perimeter of the triangle = 18 /2 = 9 cm
The equilateral triangle has a 9 root 3 cm square area, and its semi-perimeter is 9 cm.
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REALY HELP ME PLEASE!!!!!!
The equation of line in slope intercept form is,
⇒ y = x - 2
When the graph is shift down 9 units.
Then, Equation of line become,
⇒ y = x - 11
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (2, 0) and (0, -2).
Now,
Since, The equation of line passes through the points (2, 0) and (0, -2).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 2 - 0) / (0 - 2)
m = - 2 / -2
m = 1
Thus, The equation of line with slope 1 is,
⇒ y - 0 = 1 (x - 2)
⇒ y = x - 2
And, When the graph is shift down 9 units.
Then, Equation of line become,
⇒ y = x - 2 - 9
⇒ y = x - 11
Therefore, The equation of line in slope intercept form is,
⇒ y = x - 2
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What is the value of 2 by 7 and 3 by 7?
the value of 2 by 7 and 3 by 7 is: 5/7. This can be solved using the concept of fraction of addition.
What is the fraction?A fraction is a piece of the entire. The number is stated in arithmetic as a quotient, which signifies the numerator divided by the denominator. Both are integers in a straightforward fraction. The numerator or denominator of a complex fraction is a fraction. A suitable fraction has a numerator that is smaller than its denominator.
Three main fractional kinds exist. They come in three varieties: appropriate fractions, incorrect fractions, and mixed fractions. The numerator and denominator words are known as fractions. We define its kinds in light of these two words.
the value of 2 by 7 and 3 by 7 is:
= (2/7) + (3/7)
= 5/7
When adding the fractions 2/7 and 3/7 we get 5/7, as the denominator is same.
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In the sequence generated by the formula an=(-1)n+1(5)n , which of the following terms has the greatest value? Assume an > 0.
The term that have the greatest value is
aₙ₊₁₅How to find the term that will have the greatest valueThe knowledge of negative and positive number is necessary here.
numbers less than zero are negative while numbers greeter than zero are positive
Negative terms in an odd exponent remains negative hence less than zero in even exponent the negative changes to positive and becomes greater than zero
For the expression aₙ = (-1)ⁿ⁺¹(5)ⁿ the teem that determines whether the expression is greater that zero is (-1)ⁿ⁺¹. therefore
n + 1 must be even
n must be odd for n + 1 to be even hence the greatest number here is aₙ₊₁₅ a(n+15)
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y-int coordinates of y=x^2-5x+6, please explain
The y intercepts of the quadratic equation y = x² - 5x + 6 is given by (0 , 6)
and the x intercepts are ( 3 , 0 ) and ( 2, 0 )
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
y = x² - 5x + 6 be equation (1)
On simplifying the equation , we get
y = x² - 2x - 3x + 6
Taking the common factors of the equation , we get
y = x ( x - 2 ) - 3 ( x - 2 )
On factorizing the equation , we get
y = ( x - 3 ) ( x - 2 )
To find the y intercepts , substitute the value of x = 0 , we get
y = ( 0 - 3 ) ( 0 - 2 )
y = ( -3 ) ( -2 )
So , y = 6
Hence , the y intercepts of the equation is ( 0 , 6 )
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Please help
Find the value of x
Find the measure of the two marked angles
PLEASE ALSO FIND X
The value of x is 8 and the measure of the two marked angles is 60°.
Which angles are corresponding and adjacent?When an angle's vertex and side are shared by another angle, the two angles are said to be neighboring angles. The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.
we know that ,
10x-20=7x+4 (it is corresponding opposite angle)
3x=24
x=8
the value of x is 8.
the measure of the two marked angles is 10*8-20= 80°-20°= 60°.
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30 PTS: Please help me
You can earn money by shoveling your neighbors' driveways in the winter and get paid $10 per hour. What is a function that would define this situation? Define the domain and range of this function and describe reasonable values for each.
The function that will define the situation is y = 10x
The domain: {0, ∞)
The range: {0, ∞)
How to write the functionThe function that will define the situation is a linear function of the form
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The equation as described in the problem is represented using linear function as as follows
c = there is no condition defined here hence = 0
m = cost of per hour = $2.50
x = time in hours
y = amount paid in hours
y = 10x
The domain in this case is time from 0 to infinity {0, ∞)
The range is also {0, ∞)
there are no limitations to hep set the range and domain
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Write the explicit formula for the sequence below:
The explicit formula for the sequence will be an = 10 + 5n. The correct option is C.
What is arithmetic progression?The sequence in which every next number is the addition of the constant quantity in the series is termed as the arithmetic progression.
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Given series is 15,20,25,30,...,
The common difference is d = 20 - 15 = 5
First term is, 15
The formula can be written as,
an = a₁ + d(n-1)
an = 15 + 5 ( n - 1 )
an = 15 + 5n - 5
an = 10 + 5n
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The amount of money in a savings account is given by � = 580(1.03)" where t is the
time in years. After how many years will the account have reached $1000? Clearly
demonstrate your strategy for figuring it out.
An initial investment of $580, earning 3% annually-compounded interest, will take 18.429 years (investment period) to reach $1,000.
How the period is determined?The period for the investment to accumulate to $1,000 at 3% compounded interest is computed using an online finance calculator.
The parameters required include identifying the interest rate, compounding period, present investment, and future value., from the given formula:
A = 580(1.03)^t
$1,000 = 580(1.03)^18.429
Investment Period:I/Y (Interest per year) = 3%
PV (Present Value) = $580
PMT (Periodic Payment) = $0
FV (Future Value) = $-1000
Results:
N = 18.429
= 18 years and 5 months
Total Interest = $420
Thus, for the account to reach $1,000, it will take 18 years and 5 months.
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Question Completion:A = 580(1.03)^t
Solve this problem?
step by step
The value of x is 9.32 after solving using the Pythagoras theorem.
What is Pythagoras Theorem?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side.
The diagram has 4 corners namely - A, B, C and D.
Draw a perpendicular through B.
The intersecting point at line AD is named as E.
It can be seen in figure that EDCB is a rectangle and falls under the category of parallelogram.
So, angle ADC = angle DEB = angle AEB = 90° .
Now, side BC = ED = 5.
So, side AE = 18 - 5 = 13.
Here, it can be seen that triangle ABE is a right-angled triangle.
So, to get the measurement of side BE, apply the Pythagoras theorem -
c^2 = a^2 + b^2
Where, a is perpendicular, b is base and c is hypotenuse.
So, according to the diagram -
(16)^2 = (13)^2 - (BE)^2
(BE)^2 = (16)^2 - (13)^2
(BE)^2 = 256 - 169
(BE)^2 = [tex]\sqrt{87}[/tex]
(BE)^2 = 9.32
Now, as EDCB is a rectangle so, side BE = side CD.
Therefore, the value for side CD = x = 9.32.
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How do you find Y1 and y2 on a graph?
The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).
Now, According to the question:
Finding Slope From Two Points Formula
The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁). Here,
m = slope of the line
x₁ = the x-coordinate of the first point
y₁ = the y-coordinate of the first point
x₂ = the x-coordinate of the second point
y₂ = the x-coordinate of the second point
Then rise from A to B = y₂ - y₁
Run from A to B = x₂ - x₁
Then the slope, m = rise/run = (y₂ - y₁) / (x₂ - x₁)
Hence, we derived the slope formula.
Here are the steps to find the slope of a line given two points on it.
In the first point, denote the x coordinate with x₁ and denote the y-coordinate with y₁.In the second point, denote the x coordinate with x₂ and denote the y-coordinate with y₂.Find the differences y₂ - y₁ and x₂ - x₁.Divide the difference of y-coordinates by the difference of x-coordinates to find the slope (m). i.e., m = (y₂ - y₁) / (x₂ - x₁).Learn more about Slope at:
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at a local cafeteria there are 10 vegetable selections available how many three vegetable plates maybe made
The number of vegetable plates can be made = 120
We know that a combination is nothing but a way of selecting items from a collection. In combination the order of selection does not matter.
We know that a formula for a combination is,
^nC_r = n! / r!(n - r)!
where, ^nC_r = number of combinations
n = total number of items in the collection
r = number of choosing items from the collection
and n! = n × (n - 1) × (n - 2) × . . . × 1
Here, we have n = 10 and r = 3
Using combination formula, the total number of plates made:
^10_C_3
= 10! / (3! × (10 - 3)!)
= 10! / (3! × 7!)
= (10 × 9 × 8 × 7!) /( 3! ×7!)
= (10 × 9 × 8) / (3 × 2 × 1)
= (90 × 8) / 6
= 720/6
= 120
Therefore, 120 vegetable plates maybe made
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What is one of the main differences between a 401(k) and a Roth 401(k)?
O A. A Roth 401(k) is offered by banks, while a 401(k) is offered by an
employer.
B. The amount you can contribute depends on your age.
C. Contributions are taxed differently.
D. You have to be different ages in order to withdraw money.
Onr of the main differences between a 401(k) and a Roth 401(k): Contributions are taxed differently.
The correct answer is an option (C)
The difference between a 401(k) and a Roth 401(k) is that 401(k) is the income taxes on distribution whereas the Roth 401(k) is the income taxes on contribution.
Roth 401(k) is funded with after-tax money.
You can withdraw after-tax money once you reach retirement age.
A traditional 401(k) allows you to make contributions before taxes.
But in traditional 401(k) you have to pay income tax on the distributions in retirement.
Therefore, the main difference is: the income taxes on your contributions.
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A scale model of a building is 16 inches long. The actual building is 62 feet long. In the model, the door is 2.4 inches tall. How tall is the actual door?
The scale model door of 2.4 inches is 9.3 ft tall in the actual building.
What is scaling?By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape.
What is cross-multiplication?By multiplying the numerator of one fraction by the denominator of another and the first term's denominator by the numerator of another, we can do cross multiplication.
Given that:
16 inches = 62 ft
2.4 inches = x ft
To calculate the actual value cross multiply the values:
[tex]x= \frac{(62)(2.4)}{16} \\\\x= 9.3 ft[/tex]
Hence, the actual door is 9.3 ft tall.
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