Find the center of dilation.
• Triangle B is a dilation of A with approximately what scale factor?
• Triangle A is a dilation of B with approximately what scale factor?
• Triangle B is a dilation of C with approximately what scale factor?

Answer: C

Step-by-step explanation:

The vertical shift upward by 8 units compared to the graph of f(x).

The horizontal shift 3 units to the left compared to the graph of f(x).

A parent function is a fundamental function that acts as the model for a group of connected functions. The shape and location of a parent function on the coordinate plane can be changed by applying a transformation to the parent function.

Given that: The parent function, f (x) = \(\sqrt{x}\) and new function

g (x) = \(8 + \sqrt{(4x+12)}\)

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The probability that the sum of the pips selected that is at least 11 would be = 1/12.

To determine the probability of the selected events, the formula for problem should be used which is given below;

Probability = possible outcome/sample space

Possible outcome = at least 11 = (5,6),(6,5),(6,6)

= 3

Sample space = 36

Probability = 3/36 = 1/12

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The absolute value of |-32| is 32; absolute value of |27| is 27; absolute value of |-12| is 12; absolute value of -|14| is -14.

The Absolute value |x| of a real number x is the non-negative value of x without regard to its sign.

|x| = x ; |-x| = x

Therefore absolute value of

|-32| = 32

|27| = 27

|-12| = 12

- |14| = - 14

Absolute value describes the distance from zero that a number is on the number line , without considering direction. The absolute value of a number is never negative. Sometimes a sign is attributed to a numeric value to signify the direction, in addition to the value.

The absolute value of a number is defined as its magnitude irrespective of the sign of the number.

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To solve this problem one must be aware of the concepts of standard deviation and variance of raw data.

There is a direct formulae to calculate the variance of the data,

Variance = \(σ^{2} =\frac{Sigma(xi-m)^{2}}{n}\)

Now here we need to verify ∑x and ∑\(x^{2}\).

∑x = 21+19+15+32+27

     = 114

and ∑\(x^{2}\) = \(21^{2} +19^{2} +15^{2} +32^{2} +27^{2}\)

             = 441+361+225+1024+729

             = 2780

So, the given relation is true.

Now the variance of the given data by putting the values in the formulae is  equal to 45.2.

And Standard deviation=\(\sqrt{Variance}\)

                                     = \(\sqrt{45.2}\)

                                      = 6.72

And for population α²=36.16 and deviation=6.01.

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Complete Question

The mean height of women in a country (ages 20-29) is 64.4 inches. A random sample of 75 women in this age ground is selected. what is the probability that the mean height for the sample is greater than 65 inches? assume \(\sigma = 2.97\)

Answer:

The value is  \(P(X > 65) = 0.039715\)

Step-by-step explanation:

From question we are told that

  The mean is \(\mu = 64.4 \ inches\)

  The  sample size is  \(n = 75\)

The probability that the mean height for the sample is greater than 65 inches is mathematically represented as

     \(P(X > 65) = P[\frac{X - \mu }{ \sigma_{\= x} } > \frac{65 - 64.4 }{ \sigma_{\= x} } ]\)

Where  \(\sigma _{\= x }\) is the standard error of mean which is evaluated as

     \(\sigma_{\= x } = \frac{\sigma}{\sqrt{n} }\)

=>   \(\sigma_{\= x } = \frac{2.97}{\sqrt{75} }\)

=>    \(\sigma_{\= x } = 0.343\)

Generally \(\frac{X - \mu }{ \sigma_{\= x } } = Z(The \ standardized \ value \ of \ X )\)

       \(P(X > 65) = P[Z> \frac{65 - 64.4 }{0.342 } ]\)

So  

    \(P(X > 65) = P[Z >1.754 ]\)

From the z-table  the value of  

     \(P(X > 65) = P[Z >1.754 ] = 0.039715\)

     \(P(X > 65) = 0.039715\)

Answer:

47.5

Step-by-step explanation:

Answer:

- 36

Step-by-step explanation:

1. y= - \(\frac{1}{9}\) x --> substitute y with 4 (given value)

2. 4 = - \(\frac{1}{9}\) x --> by multiplying 9 both side get rid of the 1/9

         (4= - \(\frac{1}{9}\) x)9 --> 36= - x

3. multiply " - " to both side to make "- x" to "x" --> (36= - x) - --> - 36 = x

          - 36 = x => x = -36

the correct option is D:

" The inverse relation must pass the vertical line test."

Remember that a relation is only a function if each value in the domain is only mapped into a single value in the range.

All functions need to pass what is called the "vertical line test" this means that if you draw a vertical line on the graph of the function, the vertical line can intersect the graph at most one time. If the vertical line intercepts the graph two or more times, then it is not a function.

From this we conclude that the correct option is D:

" The inverse relation must pass the vertical line test."

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Answer:

What three consecutive integers have a sum of 87? Which means that the first number is 28, the second number is 28 + 1 and the third number is 28 + 2. Therefore, three consecutive integers that add up to 87 are 28, 29, and 30. We know our answer is correct because 28 + 29 + 30 equals 87 as displayed above.

Step-by-step explanation:

Consecutive integers are as simple as 1, 2, 3!  

Integers are consecutive if one follows another.  How do we "jump" from one integer to the next?  We add 1, right?  7, 8 and 9 are three consecutive integers.  Add one to 7 to get 8 and add one more to get 9.

Now lets think about this in algebraic terms.  Lets name these consecutive integers , x, y and z.  

The problem tells us that their sum is -87.  (Recall, "sum" is just a fancy word for the answer when we add.)

x+y+z = -87  

Here is the trick!  We need to rewrite this equation so that we have only one variable.  Easy!

y is one more that x, so y= x+1

And z is one more than y, so z= y+1.  But y is also equal to (x+1)!  So z=y+1=(x+1)+1=x+2

Now we have a problem that we can solve!  x+(x+1)+(x+2)=-87.  

Combining term.:  3x+3=-87  

Subtract 3 from both sides of the equation:  3x=84

Divide each side of the equation by 3:  x=28

We have solved for x, but we are not done!  We need to find y and z.  I know you can do this.  Remember y is one more than x and z is one more than y.

Check your work!  Make sure these three consecutive numbers do in fact add up to -87.

9514 1404 393

Answer:

  18, 21

Step-by-step explanation:

Let x represent the smaller number. Then x+3 is the larger number, and the other relation between them is ...

  3(x+3) = (7/10)(5x)

  6x +18 = 7x . . . . . multiply by 2 and simplify

  18 = x . . . . . . . . . . subtract 6x

The two numbers are 18 and 21.

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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Answer:

A

Step-by-step explanation:

sub y = x - 1 into equation 1

2x + x - 1 = 5

3x = 6

x = 2

sub x = 2 into equation 2

y = 2 - 1

y = 1

Answer:

A. is the correct answer.

Hope I helped.

Answer:

Expanding the given expression:

2(x+3) + 4(x+1) = 2x + 6 + 4x + 4

= 6x + 10

Therefore, the equivalent expression is 6x+10.

Step-by-step explanation:

Answer

option c is correct

use bodmas rule

solve brackets

2x+6+4x+4

=6x+

The transformation illustrated in the figure is translation.

Translation is a Transformation process in which the size or shape of a figure is not changed rather it only changes the coordinates of the vertices that make up that shape by moving them from one point to another.

Analysis:

Both shapes are congruent, since all the vertices remain in their respective positions even though they were moved and no change in the shape or size, then the transformation process is Translation.

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Answer:

10.5 : 12 : 13.5

Step-by-step explanation:

12 ÷ 8 = 1.5 (multiply this by all of the known numbers

8 x 1.5 = 12

7 x 1.5 = 10.5

9 x 1.5 = 13.5

Answer:

7 : 8 : 9 = 21/2 : 12 : 27/7

Step-by-step explanation:

GIVEN ;                     7 : 8 : 9 = ? : 12 : ?

                           7/24 : 8/24 : 9:24 = ? : 12/x : ?

                                            8/24 = 12/x  

                                            x = 12 ×  24/8

                                                   x = 36                                  

therefore the other two ratio's are

                                7/24 = ?/36

                                  ? = 36 × 7/24

                                   ? = 21/2

                                      and

                               9/24 = ?/36

                               ? = 36 × 9/24

                                ? = 27/2

im not quite confident with this answer, but i hope it helps!

The sketch of the front elevation and the side elevation of the prism are added as an attachment

From the question, we have the following parameters that can be used in our computation:

The prism

Using the figure as a guide, we understand that:

The front elevation is a rectangle of 2m by 0.5m

While the side elevation is a rectangle merged with a trapezoid

Next, we draw the elevations (see attachment)

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Answer:

x=9

Step-by-step explanation:

9x-7=5x+29

9x=5x+36

4x=36

x=9

Hopes this helps please mark brainliest

Answer:20%

Step-by-step explanation:

5(100)/25=20

Answer: I believe the answer is 45°

Step-by-step explanation: Hope it helps :)

Answer:

Step-by-step explanation:

sin M=8/22

\(\angle ~M=sin ^{-1}(\frac{8}{22}) \approx~21.32^\circ\)

Answer:

90 seconds

Step-by-step explanation:

The rocket will hit the ground when h(t) = 0. This can be solved by solving the equation 0 = 1440t - 16t², which can be rearranged to 0 = 16t² - 1440t. Factoring this equation yields 0 = (16t - 90)(t + 90). This equation has two solutions, t = 90 or t = -90. Since a rocket cannot be in the air for a negative amount of time, the rocket will hit the ground after 90 seconds.

Answer: The Silo is 44 meters tall

Step-by-step explanation:

To find the height of the silo, first you have to divide the drawing height (33cm) by 1.5 to get the unit rate. Then multiply the 22 by 2 to get 44 meters (The height of the silo)

The correct way to calculate the percent change between the original value of $750 and the new value of $1,000 is option C.

C. (1,000 - 750)/750 = 250/750 = 1/3 ≈ 0.3333 = 33.33%

Therefore, the correct answer is option C, which represents a percent change of approximately 33.33%.

1) y = -3x and y = -3x + 2: inconsistent system of equations.

2) y = x - 5 and -2x + 2y = - 10: consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.

The given equation are:

The graph for each system of equations is plotted.

1) y = -3x and y = -3x + 2

From the graph 1 it is shown that the lines for the each equation form the parallel lines.

Thus, system of equations are inconsistent.

2) y = x - 5 and -2x + 2y = - 10

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

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Answer:

You take 1,000 because it's in the thousandths place of 1,255. The value of that one is 1,000 so you multiply that times 100, which is the value of 1 in 82,175.

Answer:

y = 2x -2

Step-by-step explanation:

y = mx + b

We need the slope (m) and the y-intercept (b) to write the eqation.

The slope is the change in y over the change in x.  We can see from the table that the y is changing by 2 as the x changes by 1

So the slope is 2/1 which is the same as 2

The slope (m) is 2.

The y-intercept is the place where the line crosses the y axis.  It is at the point (0,b).  When x is zero, what is y?  If we follow the patter and move to the number before x is 1, we get x = 0.  That means that we have to move back 2 units of the y's.  That would be -2.  So the y-intercept is the point (0,-2).

The y-intercept (b) is -2

y = 2x - 2

Answer:

Step-by-step explanation:

took the pretest