The table shows the outputs, y, for different inputs, x:

Input (x) 2 5 9 12
Output (y) 20 15 12 8



Part A: Do the data in this table represent a function? Justify your answer. (3 points)

Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points)

Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points)

V=a^3 and volume=Length × Width × Height are the two ways to calculate the volume of cube.

Three-dimensional space is a geometric setting in which three values  are required to determine the position of an element.

A cube is a three-dimensional figure with 6 faces, 8 vertices and 12 edges.

In a cube all the sides are equal like a square.

So the volume of cube can be measured by

V=a^3

where a is the measure of a side.

And the volume of cube can also be found by

volume=Length × Width × Height

Hence V=a^3 and volume=Length × Width × Height are the two ways to calculate the volume of cube.

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Answer:  The required scale factor that is used for the dilation is 3.

Step-by-step explanation:  Given that the rectangle ABCD is transformed to A'B'C'D' by a dilation.

We are to find the scale factor that is used for the dilation.

We know that

the scale factor of dilation is defined as

[tex]S=\dfrac{\textup{the length of a side of the dilated figure}}{\textup{the length of the corresponding side of the original figure}}.[/tex]

From the graph, we see that

in rectangle ABCD, the length the side AB is 2 units

and

the length of the corresponding side A'B' in the dilated rectangle A'B'C'D' is 6 units.

Therefore, the scale factor of dilation is given by

[tex]S=\dfrac{A'B'}{AB}=\dfrac{6}{2}=3.[/tex]

Thus, the required scale factor that is used for the dilation is 3.

Answer: Conditional statement

Step-by-step explanation:

In discrete mathematics, a conditional statement denoted by "if R then S " is an if-then statement where R represents a hypothesis and S represents a conclusion.

For example : If a number is divisible by 6 ,then it must be divisible by 2 ."

Here, Hypothesis R: " number is divisible by 6"

Conclusion S: "it must be divisible by 2"

Hence, an conditional statement  has the form " if A, then B" .

Answer:

line HJ

Step-by-step explanation:

we know that

The equation of the line that has a slope of [tex]3[/tex] and a y-intercept at [tex](0, 0)[/tex] is equal to

[tex]y=3x[/tex] -----> is a proportional relationship

Remember that

If two lines are parallel , then their slopes are the same

Find the slope of the line HJ

[tex]H(-1,-4), J(1,2)[/tex]

The formula to calculate the slope between two points is equal to

[tex]m=\frac{2+4}{1+1}[/tex]

[tex]m=\frac{6}{2}[/tex]

[tex]m=3[/tex]

therefore

The line HJ is parallel to the line [tex]y=3x[/tex]

Answer:

1,890 is the sum of the first 30 terms of the equation .

Step-by-step explanation:

[tex]a_n=4n+1[/tex]

if , n = 1

[tex]a_1=4\times 1+1=5[/tex]

If, n = 2

[tex]a_2=4\times 2+1=9[/tex]

If, n = 3

[tex]a_3=4\times 3+1=13[/tex]

The arithmetic sequence comes out to be:

5, 9, 13........

a = 5

d = [tex]a_2=a_1=9-5=4[/tex]

The sum of first 30 terms is given by:

[tex]S_n=\frac{n}{2}\times (2a+(n-1)d)[/tex]

[tex]S_{30}=\frac{30}{2}\times (2\times 5+(30-1)\times 4)[/tex]

[tex]S_{30}=1,890[/tex]

1,890 is the sum of the first 30 terms of the equation .

To solve the equation 9|9-8x|=2x+3, follow these steps: remove the absolute value by considering both positive and negative cases, combine like terms, solve for x, and simplify the solutions.

To solve the equation 9|9-8x|=2x+3, we need to isolate the variable x. Let's start by removing the absolute value by considering both positive and negative cases.

Case 1: Positive

9-8x = 2x+3

Combine like terms: -8x - 2x = 3 - 9

-10x = -6

Divide both sides by -10: x = -6/-10

Simplify: x = 0.6

Case 2: Negative

-(9-8x) = 2x+3

Distribute the negative sign: -9+8x = 2x+3

Combine like terms: 8x - 2x = 3 + 9

6x = 12

Divide both sides by 6: x = 12/6

Simplify: x = 2

Therefore, the solutions to the equation are x = 0.6 and x = 2.

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Answer: $25

Step-by-step explanation: you are not trying to make a profit. You are just trying to cover your cost and they cost $25 to make.

To graph the equation y = 4/5x - 7, plot the y-intercept at -7 and use the slope to find a second point before drawing a line through the two points.

To graph the equation y = 4/5x - 7, follow these steps:

Answer: The answer is C.

A Linear parent function is a function of the form f(x) = x

or y = x. This is the simplest of the linear functions, where the slope is 1 and the function pases for the point (0,0) (which is the same of saying that the intercept is 0).

a) isnt a linear function.

b) is a quadratic function.

d) is also a linear function, but it has a slope = 2, so it isn't the linear parent function.

Answer: 2(x+3)(x+3)

i just took the test

divide total weight by weight of each box

10250 / 20.5 = 500 boxes total

Answer:

one of these is wrong cause i got a three out of four but thats better than nothing i guess.

Step-by-step explanation:

x≤0, y=1, x≥1, this one is the one i think is wrong but y=-1