2. y + 2x = 12 for D = {2,3,4}
What’s the domain and range

The inverse function of f(x) = -0.75x is [tex]\(f^{-1}(x) = -\frac{4}{3}x\)[/tex].

To find the inverse function [tex]\( f^{-1}(x) \)[/tex]for the given function f(x) = -0.75x , you can follow these steps:

1. Start with the original function:

   f(x) = -0.75x

2. Replace f(x)  with y:

   y = -0.75x

3. Swap x and y to solve for x:

x = -0.75y

4. Solve for y:

  Divide both sides by -0.75:

[tex]\( y = \frac{x}{-0.75} )\\ \( y = -\frac{4}{3}x \)[/tex]

5. Replace y with [tex]\( f^{-1}(x) \)[/tex]:

[tex]\( f^{-1}(x) = -\frac{4}{3}x \)[/tex]

So, the inverse function for f(x) = -0.75x  is [tex]\( f^{-1}(x) = -\frac{4}{3}x \)[/tex].

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Final answer:

The response provides the inverse function of f(x) = -0.75x step-by-step.

Explanation:

Given: f(x) = -0.75x

To find the inverse function f-1(x):

Replace f(x) with y: y = -0.75x

Swap x and y: x = -0.75y

Solve for y: y = x/-0.75 = -4/3x

Therefore, f-1(x) = -4/3x

Answer:

8.0

Step-by-step explanation:

8.0 cause you move it over one place value which would be your tenth place

Answer:

16x^4 is your answer

Step-by-step explanation:

Answer: look below

Step-by-step explanation:

Write: -7-(-3)=-4

Solve: -7-(-6)=-1

Answer:

the numbers are 3 and 5

Step-by-step explanation:

x = first number

y = second number

a.        x+2 = y

b.        x^2 + y^2 = 34

Replace y from equation a into equation b:

x^2 + (x+2)^2 = 34

Expand it

x^2 + x^2 + 4x + 4 = 34

2*x^2 + 4x = 30

2x^2 + 4x - 30=0

solving x:

x = -5 and x =3 , it says it is a positive number, then it is x is 3

and the second number, y = x + 2

y = 5

Lets test it!

3^2 + 5^ 2 = 9 + 25 = 34

Answer:

C (-16, 3)

Step-by-step explanation:

[tex] 12 + 3 \leqslant - 3 \times - 16 \\ 15 \leqslant 48[/tex]

replace x and y

Answer:

c) (-16,3)

Step-by-step explanation:

Given: inequality [tex]12+\text{y}\leq -3\text{x}[/tex]

To Find: Which ordered pair is part of the solution set of the inequality

Solution:

Simplifying inequality,

[tex]12+\text{y}\leq -3\text{x}[/tex]

[tex]12}\leq -3\text{x}-\text{y[/tex]

now,

putting ordered pairs from options

a) [tex](3,-16)[/tex]

[tex]-3\times3-(-16)[/tex][tex]16-9=7[/tex]

as [tex]7<12[/tex], it does not satisfy inequality

b)  [tex](4,-1)[/tex]

[tex]-3\times4-(-1)[/tex][tex]1-12=-11[/tex]

as [tex]-11<12[/tex], it does not satisfy inequality

c)  [tex](-16,3)[/tex]

[tex]-3\times(-16)-(3)[/tex][tex]48-3=45[/tex]

as [tex]45>12[/tex], it satisfy inequality

d)  [tex](1,4)[/tex]

[tex]-3\times1-(4)[/tex][tex]-3-4=-7[/tex]

as [tex]-7<12[/tex], it does not satisfy inequality

So, from above only option c is part of the solution set of inequality.

Answer:

5 : 30

Step-by-step explanation:

Note that [tex]\frac{1}{2}[/tex] × 10 = 5

Thus 3 × 10 = 30

Hence

[tex]\frac{1}{2}[/tex] : 3 = 5 : 30

Ratios are used to relate quantities of different measurement

The ratio is given As

[tex]Ratio = \frac 12 : 3[/tex]

Represent the new numbers with  P1 and P2.

So, we have:

[tex]P1 : P2 = \frac 12 : 3[/tex]

The second number is 5 So, we have:

[tex]5 : P2 = \frac 12 : 3[/tex]

Multiply the ratio by 10

[tex]5 : P2 = \frac 12 \times 10: 3 \times 10[/tex]

[tex]5 : P2 = 5: 30[/tex]

By comparison

[tex]P2 = 30[/tex]

Hence, the ratio is equal to the ratio of 5 and

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Answer:

Step-by-step explanation:

/ -1/3 / = 1/3

Answer:

For the length of time less than 6 hours cost less to hire Hanks movers

Step-by-step explanation:

Let

x -----> the time in hours

y ----> the total cost in dollars

we know that

Acme movers

[tex]y=30x+150[/tex] ----> equation A

Hanks movers

[tex]y=55x[/tex] ----> equation B

Equate equation A and equation B and solve for x

[tex]55x=30x+150[/tex]

[tex]55x-30x=150[/tex]

[tex]25x=150[/tex]

[tex]x=6\ hours[/tex]

That means-----> For x= 6 hours The cost in both companies is the same

Verify

For x=6 hours

Acme movers

[tex]y=30(6)+150=\$330[/tex]

Hanks movers

[tex]y=55(6)=\$330[/tex]

If x < 6 hours ----> It cost less to hire Hanks movers

If x > 6 hours ----> It cost less to hire Acme movers

therefore

For the length of time less than 6 hours cost less to hire Hanks movers

Leonardo Da Vinci was a painter, sculptor, architect, engineer, scientist, philosopher, and a visionary. He was also commissioned to create a bronze statue nicknamed "Leonardo's Horse".

Answer:

Radius = Diameter / 2

Therefore Radius = 15 / 2 = 7.5 miles

Step-by-step explanation:

Answer:

Step-by-step explanation:

The two temperatures that will be located as shown in the vertical number line representing a thermometer will be:

4°C  and -4°C

Given that the vertical number line is to be used to represent a thermometer.

If 0 represents 0°C on the vertical number line, therefore:

Therefore, the two temperatures that will be located as shown in the vertical number line representing a thermometer will be:

4°C  and -4°C

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Answer: [tex]\frac{a}{b}= 18[/tex]

Step-by-step explanation:

You know that the quotient Colleen got when she divided an integer “a” by -6 was 6. This can be expressed as:

[tex]\frac{a}{-6}=6[/tex]

Then, you can find that integer solving for "a":

[tex]a=(6)(-6)\\\\a=-36[/tex]

The quotient Colleen got when she divided 6 by an integer “b” was -3. This can be expressed as:

[tex]\frac{6}{b}=-3[/tex]

Therefore, you can find that integer solving for "b":

[tex]6=(-3)(b)\\\\\frac{6}{-3}=b\\\\b=-2[/tex]

Knowing the values of "a" and "b", you can divide these integers in order to find the quotient between thenm

[tex]\frac{a}{b}=\frac{-36}{-2}}= 18[/tex]

Answer:

You know that the quotient Colleen got when she divided an integer “a” by -6 was 6.

Step-by-step explanation:

the other person is correct

Answer:

The answer is 4.5

Step-by-step explanation:

Solve for a:

3a +11 > 5

Subtract 11 from both sides:

3a >-6

Divide both sides by 3:

a > -6/3

a > -2

The Correct graph is the second one, because it has the dot on the -2 and the arrow points to the right

The 2 number line shows the solutions to the inequality 3a + 11 > 5 and the correct option is B.

The image shows two number lines, and asks which one shows the solutions to the inequality 3a + 11 > 5.

To solve this inequality, we can subtract 11 from both sides, and then divide both sides by 3. This gives us a simpler inequality: a > -2.

This means that all values of a that are greater than -2 are solutions to the inequality. On a number line, this can be represented by an open circle at -2, and an arrow pointing to the right.

The number line on the left of the image shows exactly this. Therefore, the number line on the left shows the solutions to the inequality 3a + 11 > 5.

The number line on the right of the image does not show the solutions to the inequality correctly. The open circle at -2 is missing, and the arrow points to the left, which is incorrect, since the solutions to the inequality are all values of a that are greater than -2, not less than -2.

Here is a more detailed explanation of the steps involved in solving the inequality:

1. Subtract 11 from both sides:

3a + 11 > 5

-11 - 11

3a > -6

2. Divide both sides by 3:

3a > -6

3 / 3

a > -6 / 3

3. Simplify:

a > -2

Therefore, the solution to the inequality is a > -2. On a number line, this can be represented by an open circle at -2, and an arrow pointing to the right.

The number line on the left of the image shows exactly this. Therefore, the 2 number line on the left shows the solutions to the inequality 3a + 11 > 5 and the correct option is B.

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Answer:

Step-by-step explanation:

The question says that you are multiplying 8 and something together. So to start with, it looks like this.

8*something.

Now you have to get 7 less a number which is 7 - x

So something is 7 - x

8(7 - x) is your answer.

Answer: The answer is -28

Step-by-step explanation:

Trust me

Final answer:

The integer representing the temperature drop of 28°, leaving the thermometer at 48°, is -28. The original temperature before the drop was 76°.

Explanation:

The integer that represents the number of degrees the temperature drops when the temperature drops 28° and the thermometer reads 48° afterwards is -28. To find this, we use the final temperature (48°) and add the temperature drop (28°) to determine the original temperature. However, since it is a temperature drop, we have to add a negative sign to the drop, making it -28°. Therefore, the original temperature was 48° + 28° = 76°. The decrease in temperature is represented by the negative integer -28°.

x + 8 = -7

move +8 to the other side

sign changes from +8 to -8

x+8-8= -7-8

x=-7-8

Answer:

x= -15

Answer:

x=-15

Step-by-step explanation:

Subtract 8

x-8+8=-7-8

x=-7-8

x=-15

Answer:

-42 + -43

-40 + -40=  -80

-2 + -3= -5

Answer:

each book costs $13

Step-by-step explanation:

Let the cost of each book be $x

cost of buying 8 books = $8x

It is given that with an original amount of $116, after buying 8 books, he had $12 left over. Hence,

$8x + $12 = $116   (dropping the $ signs)

8x + 12 = 116

8x = 116 - 12

8x = 104

x = 13  (each book costs $13)

Answer:

he possibly spent $13 on order to end up with $12 left.

Step-by-step explanation:

1) look. at the number 116 you can use a calculator.

2) if 14 only leaves you with nothing you take it away

3) add 13 + 8X that should give you 104

4). substract 116-104 your total should be $12

I hope I helped you.

Answer:

Step-by-step explanation:50,897 is in standard form.

Expanded form is adding all your place values which is 50,000+800+90+7. There was a 0 in the thousand place so you do not add anything for that place value.

So (5×10,000) + (8×100) +(9×10)+(7×1) which is each number times it place value then add them all up.

Written form would be fifty thousand, eight hundred and ninety seven. So your answer is A, B, D

A function with direct variation is a linear function that passes through the origin (0, 0) and has a constant rate of change, the slope. Only the line passing through (negative 1, negative 4), (0, 0), and (1, 4) from the given options fulfills these conditions.

In Mathematics, a function with direct variation is a linear function that passes through the origin (0, 0).  It can be represented as the equation y = mx, where m is the slope of the line. The slope of the line determines if it is a direct variation. If it's a positive slope, y increases as x increases. If it's a negative slope, y decreases as x increases.

From the given options, only the coordinate plane with a line passing through (negative 1, negative 4), (0, 0), and (1, 4) represents a function with direct variation as it's a straight line passing through the origin.

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Answer:

(- 1, 9 )

Step-by-step explanation:

A translation of 3 units left, subtract 3 from the original x- coordinate

A translation of 1 unit up, add 1 to the original y- coordinate.

The rule is (x, y ) → (x - 3, y + 1 ), thus

(2, 8 ) → (2 - 3, 8 + 1 ) → (- 1, 9 )

The image point of (2,8) is (-1,9).

The term P', which is pronounced "P prime," is used to refer to the reflection of point P across the line, which is considered to be the "image" of point P.

Given point is (2,8).

And the translation is left 3 unit and up 1units of the point (2,8)

By increasing or decreasing the output or the input, you may change the direction of the function's graph to the right, left, up, or down. A function's output can be increased to shift the graph up. The graph is shifted downward when a function's output is subtracted from.

That means -3 and +1 respectively.

Now the image point of (2,8)

= (2-3, 8+1)

= (-1, 9)

Therefore, the image point is (-1,9).

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Final answer:

When Jonathan stops to tie his shoelaces four times, each adding 2 1/2 minutes, his jog takes an extra 10 minutes in total.

Explanation:

Jonathan stops to tie his shoelaces four times during his jog. Each time he stops, it adds 2 1/2 minutes to his total jog time. To find out how much longer his jog takes, we need to multiply the number of stops by the additional time per stop.

Let's calculate this step by step:

So, if Jonathan stops to tie his shoelaces four times, his jog will take an extra 10 minutes in total.

Answer:

Step-by-step explanation:

Rarely does the payroll office want to get involved in minor in-office expenses, such as coffee, donuts, or cupcakes. Perhaps more rarely, will a municipality impose a payroll tax.

However, it is quite common to see health insurance costs and Social Security taxes deducted from gross pay.

Answer: b. Z+5

Step-by-step explanation:

B. Z+5

Let’s say z was 9

The only equation that would work to find 5 more that 9 is 9+5

The number of boys in class is 9.

Let the number of boy = b and girls = g

We can create the following equations from the parameters

b + g = 27 ____(1)

g - 3 = 3(b - 4) ___ (2)

From (1)

g = 27 - b ___(3)

Substitute (3) into (2)

27 - b - 3 = 3(b - 4)

24 - b = 3b - 12

collect like terms

-b - 3b = -12 - 24

-4b = -36

b = 9

Hence, the number of boys is 9

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Answer:

Step-by-step explanation:

The formula of an area of a triangle:

[tex]A=\dfrac{1}{2}bh=\dfrac{bh}{2}[/tex]

b - base

h - height

We have b = 15, A = 200.

Substitute:

[tex]200=\dfrac{15h}{2}[/tex]

[tex]200=7.5h[/tex]              divide both sides by 7.5

[tex]\dfrac{200}{7.5}=\dfrac{7.5h}{7.5}[/tex]

[tex]h\approx26.7[/tex]

Answer:

[tex]cos^{4}[/tex] x

Step-by-step explanation:

Using the trigonometric identities

1 + tan²x = sec²x and 1 - sin²x = cos²x

secx = [tex]\frac{1}{cosx}[/tex]

Given

[tex]\frac{1-sin^2x}{1+tan^2x}[/tex]

= [tex]\frac{cos^2x}{sec^2x}[/tex]

= [tex]\frac{cos^2x}{\frac{1}{cos^2x} }[/tex]

= cos²x × cos²x

= [tex]cos^{4}[/tex] x