A. Use composition to prove whether or not the functions are inverses of each other. B. Express the domain of the compositions using interval notation.

Answer:

32 cups

Step-by-step explanation:

1 cup= 1/16 gallon

? cup= 2 gallon ( crisscross)

⇒[tex]\frac{2*1}{\frac{1}{16} }\\ \frac{2}{\frac{1}{16}} \\2*16=32 cups[/tex]

Answer:

-1/5+(√3)/20i   or   -0.2+0.05√3i

Step-by-step explanation:

  [tex]\dfrac{-8+\sqrt{-12}}{40}=-\dfrac{8}{40}+\dfrac{2\sqrt{3}i}{40}=\boxed{-\dfrac{1}{5}+\dfrac{1}{20}\sqrt{3}\,i=-0.2+0.05\sqrt{3}\,i}[/tex]

_____

Comment on answer form

Satisfying the input format requirements of a computer is always problematic. One never knows if fractions or decimals are preferred, whether radicals must be simplified, and so on. If no clues are offered by general instructions, other questions, or previous experience, then it might be useful to consult your instructor.

Answer:

V= 68.6 m/s

Step-by-step explanation:

height above the ground t seconds after it is dropped is 675-4.9t^2

For seven seconds

Height above ground= 675-4.9(7)²

height above ground= 675-240.1

Height above ground= 434.9 m

But it's dropped from a cliff and we need to find the distance traveled from the too of the cliff

Distance= 675-434.9.

Distance= 240.1

To determine it's speed

V²= U² +2gs

V= velocity we are looking for

U= initial velocity= 0

G= acceleration due to gravity= 9.8 m/s²

s= distance covered

V²= U² +2gs

V²= 0+2(9.8)(240.1)

V²= 4705.96

V= 68.6 m/s

Answer:

10i

Step-by-step explanation:

Step 1: Expand first 2

(1 + i)(2 + i)

2 + i + 2i + i²

2 + 3i + (-1)

1 + 3i

Step 2: Expand again

(1 + 3i)(3 + i)

3 + i + 9i + 3i²

3 + 10i + 3(-1)

3 + 10i - 3

10i

Answer:

x=3

Step-by-step explanation:

2/3x+15=17

first subtract 15 from both sides

2/3x=2

multiply by 3 to eliminate the fraction

2x=6

divide by 3

x=3

Answer:

x=3

Step-by-step explanation:

2/3x +15 = 17

2/3x = 17-15

2/3x = 2

x = 2  /  2/3

x = 2/1  *  3/2

x = 6/2

x = 3

Answer:

dx+9x+16d^2 dont know it it helps any but i tried

Step-by-step explanation:

Answer: Choice C)

(1/30)*(1/29)

Explanation:

Jack has a 1/30 chance of being picked since he is 1 person out of 30 total. After his name is picked, and not put back, there are 30-1 = 29 names left. The chances Jill is picked is 1/29. The two fractions are multiplied to get the overall probability both are picked.

Answer:

-2, b, a+c

Step-by-step explanation:

Answer:

All you have to do is switch A + C and B around. (basically if you wrote it out, it would look like this: -2, B, A + C.)

Answer:

Use a graphing calc.

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

For the third equation, m = 2

y = 2x + b

3 = 3(2) + b

3 = 6 + b

b = -3

y = 2x - 3

Answer:

Step-by-step explanation:

Formula for calculating the surface area of the box S = 2(LW+LH+WH) where

L is the length of the box

W is the width of the box

H is the height of the box

If the box is square based with dimension 4 * 4in, then L = W = 4in. substituting this values given into the formula we will have;

S = 2(4(4)+4H + 4H)

S = 2(16+8H)

S = 32+16H

Hence, The function that represents the surface area of this box as a

function of its height is S = 32+16H where H is the height of the box

Given H = 6.5in, to evaluate the function, we will substitute h = 6.5in into the modeled equation;

S = 32+16H

S = 32+16(6.5)

S = 32+106

S = 138in²

Hence the total surface area of the box is 138in²

Answer:

  30500 = 3.05·10^4

Step-by-step explanation:

Your calculator can do this for you. You may need to set the display to scientific notation, if that's the form of the answer you want.

__

This can be computed by converting both numbers to standard form:

  (5·10^2) +(3·10^4)

  = 500 +30000 = 30500 = 3.05·10^4

__

Addition of numbers in scientific notation in general requires that they have the same power of 10. It may be convenient to convert both numbers to the highest power of 10.

  5·10^2 + 3·10^4

  = 0.05·10^4 +3·10^4 . . . . now both have multipliers of 10^4

  = (0.05 +3)·10^4

  = 3.05·10^4

Answer:

See below.

Step-by-step explanation:

4)

So we have the expression:

[tex](-6n^{-3})^2[/tex]

We can use the power of a product property, where:

[tex](ab)^n=a^n\cdot b^n[/tex]

So:

[tex]=(-6)^2\cdot(n^{-3})^2[/tex]

For the left, -6 squared is the same as -6 times -6. This equals positive 36.

For the right, we can use the power of a power property. The property says that:

[tex](a^n)^k=a^{nk}[/tex]

So:

[tex](n^{-3})^2=n^{(-3)(2)}\\=n^{-6}[/tex]

So, all together, we have:

[tex]=(-6)^2\cdot(n^{-3})^2\\=36n^{-6}[/tex]

6)

We have the expression:

[tex]-\frac{3x^0}{x^4}[/tex]

First, note that anything to the zeroth power (except for 0) is 1, thus, x^0 is also 1. Simplify:

[tex]=-\frac{3}{x^4}[/tex]

And that's the simplest we can do :)

Notes for 6)

We can put the x^4 to the numerator. Recall that when you put an exponent to opposite side, you put a negative. In other words:

[tex]x^n=\frac{1}{x^{-n}}[/tex]

And vice versa:

[tex]\frac{1}{x^{-n}}=x^n[/tex]

So, we can write the above as:

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

However, traditionally, we want only positive exponents, so this wouldn't be correct.

Answer:

Step-by-step explanation:

x^m×x^n=x^{m+n}

x^m÷x^n=x^{m-n}

[tex]\frac{1}{x^m} =x^{-m}\\x^{-n}=\frac{1}{x^n} \\(xyz)^m=x^m\times y^m \times z^m \\(x^m)^n=x^{mn}[/tex]

[tex]x^0=1[/tex]

Answer:

[tex]0[/tex]

Step-by-step explanation:

[tex] \frac{1}{3}m - 1 - \frac{1}{2}n = \frac{1}{3}(21) - 1 - \frac{1}{2}(12) = 7 - 1 - 6 = 6 - 6 = 0[/tex]

Answer:

0

Step-by-step explanation:

1/3m - 1 - 1/2n
= 1/3(21) -1 1/2(12)
= 7 - 1 - 6
= 0

Answer:

9

Step-by-step explanation:

Working backwards, the blank box between the 7 and 4 at the end must be 9 in order for the three digits to equal 20.  Then we see the pattern of 947 repeated.  The whole number would be 94794794794794.  That way, any three consecutive numbers would be 20.  The number in the box marked a would be 9.

Answer:

1/2

Step-by-step explanation:

Answer:

Mrs Taylor should buy 45.5 yards of fabric ( 45.5364 actually but rounded to the nearest tenth)

Step-by-step explanation:

Here in this question, we are interested in calculating the total yards of fabric that Mrs Taylor should buy.

From the question, we are made to know that one uniform requires 26 inch of fabrics and she wants to make a total of 63 uniforms

The total inches of fabric needed is thus; 26 * 63 = 1,638 inches of Fabrics

But we want our answer in yards.

Mathematically;

1 inch = 0.0278 yard

1638 inches = x yard

x = 1638 * 0.0278 = 45.5364 yards which is approximately 45.5yards

Answer: you end up at (2,2)

Step-by-step explanation:

Answer:

2,2

Step-by-step explanation:

go down to the bottom right corner (5,-5)

move over left 3 boxes

and then up 7 boxes

hope this helps :P

Answer:

p=2

Step-by-step explanation:

so how to find this u take the five and three and u subtract them both and whatever is left over that is your answer

Answer:

1

Step-by-step explanation:

To find the answer of a negative and a positive, you subtract and then keep the symbol of the bigger number.  So in the equation 1-8 you subtract 1 from 8, then keep the symbol of the 8 (which is a negative) since it is the bigger number.  1 minus 8 is 7, and the symbol is negative, so the answer is -7.  This makes K=1.

Answer:

Step-by-step explanation:

[tex]4x+6-11\\\\\mathrm{Add/Subtract\:the\:numbers:}\:6-11=-5\\=4x-5[/tex]

Answer:

$176.50

Step-by-step explanation:

Take each room type and multiply the number of rooms by the price of the room. Add the total for prices and add the total for the number of rooms. Divide the total prices by the total number of rooms.

Type of room   Number Cost    Total

Double queen 140      $200.00   $28,000.00  

King                  160       $150.00   $24,000.00  

Junior Suite          220      $100.00   $22,000.00  

Full business          285 $50.00    $14,250.00  

                                $500.00    $88,250.00  

Average cos per room                    $176.50  

Answer:

these are the ten numbers :

0 8 2 6 9 2 0 8 0 0

Answer:

Step-by-step explanation:

To combine integers with different signs find their absolute values then subtract the smaller absolute value from the larger one. Give the sum the sign of the number with the largest absolute value.

Answer:

Step-by-step explanation:

[tex]3+g = \frac{a}{3h} \\\\Cross\:Multiply\\\\3h(3+g) = a\\9h +3gh = a\\\\a = 3gh+9h[/tex]

Answer:

Max is 9 ft above Brett

Step-by-step explanation:

Brett is 34 feet below the surface  = -34

Max is 25 feet below the surface = -25

Subtract the heights

-25 - -34

-25 +34

9

Max is 9 ft above Brett

Answer:

n = 2.5

Step-by-step explanation:

We need to isolate n by first moving it to one side.

11n = 13n - 5

11n - 13n = -5

-2n = -5

n = -5/-2

n = 2.5

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Answer:

n = 5/2

Step-by-step explanation:

5 + 11n = 13n

5 = 13n - 11n

5 = 2n

n = 5/2

Check:

5 + 11*5/2 = 13*5/2

10/2 +  55/2 = 65/2

Answer:

yes

Step-by-step explanation:

Answer:

  yes

Step-by-step explanation:

The standard form of a polynomial has the exponents decreasing left to right. Here, the exponents are 4, 3, 1, 0, so are decreasing left to right. The expression is in standard form.

Answer:

5

Step-by-step explanation:

6n -12 -8=22+8-4n

6n-20=30-4n

6n=50 -4n

10n = 50

5

Answer: -506.5 or -253.25

Step-by-step explanation:

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Hi my lil bunny!

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

[tex]\frac{1}{2}-3\ \left(12\ +\ 1\right)^2[/tex]

[tex]= \frac{1}{2}-3 (13^2)[/tex]

[tex]= \frac{1}{2} - (3) (169)[/tex]

[tex]= \frac{1}{2} - 507[/tex]

[tex]= \frac{-1013}{2}[/tex]

❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙

●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●

Have a great day/night!

❀*May*❀

Answer:

  4.54

Step-by-step explanation:

The 4th digit (6) is greater than 4, so the 3rd digit (3) is increased by 1 before you drop the remaining digits:

  4.54