Identify the range of the function. A) (2, 8) B) [2, 8] C) (−5, 9) D) [−5, 9]

f(x) = (x-8)/(x+7) and g(x) = (-7x-8)/(x-1)

To confirm that f(x) and g(x) are inverses.

f(g(x)) = x

g(f(x)) = x

f(g(x)) = (((-7x-8)/(x-1))-8)/(((-7x-8)/(x-1))+7)

f(g(x)) = (-15x² -15x)/(-15x² - 15)

f(g(x)) = -15x/-15

f(g(x)) = x

g(f(x)) = (-7((x-8)/(x+7))-8)/(((x-8)/(x+7))-1)

g(f(x)) = (-15x² - 105x)/(-15x²- 105)

g(f(x)) = -105x/-105

g(f(x)) = x

f(x) and g(x) are inverses.

Answer:

12

Step-by-step explanation:

There would be 12 girl students in a class of 21 students.

"A proportion is a mathematical statement where two or more ratios are equivalent."

We have been given that, the ratio of girls to the total number of students in class is 4:7

We need to find the number of girl students if the class has 21 students in all.

Let 'n' represents the number of girl students.

⇒ [tex]\frac{4}{7} = \frac{n}{21}[/tex]

⇒ [tex]4\times 21 = n\times 7[/tex]                        ......................(cross product)

⇒ [tex]84 = n\times 7[/tex]

⇒ [tex]n=\frac{84}{7}[/tex]                                    ......................(Divide each side by 7)

⇒ [tex]n=12[/tex]

Hence, there would be 12 girls if class has 21 students in all.

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Answer:

x = - 9, x = - 4

Step-by-step explanation:

Set (x +)(x + 9) equal to zero, that is

(x + 4)(x + 9) = 0

Equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

x + 9 = 0 ⇒ x = - 9

Thus

x = - 9, x = - 4

Answer:

Yes.  It needs to be clear that it is on going.  So as long as it is evident that it repeats, you're good.

Step-by-step explanation:

Answer:

Coffees cost $2 each and bagels cost $4 each

Step-by-step explanation:

Let

Coffee=c

Bagels= b

2 coffees and 5 bagels for which he paid $24

2c + 5b= 24 (1)

he returned to buy 3 coffees and 4 bagels for

$22

3c + 4b = 22 (2)

2c + 5b= 24 (1)

3c + 4b = 22 (2)

Multiply (1) by 3 and (2) by 2

6c + 15b = 72 (3)

6c + 8b = 44 (4)

Subtract (4) from (3)

15b - 8b = 72 - 44

7b = 28

Divide both sides by 7

b= 28 / 7

= 4

b= $4

Substitute b=4 into (1)

2c + 5b= 24

2c + 5(4) = 24

2c + 20 = 24

2c = 24 - 20

2c = 4

Divide both sides by 2

c= 4 / 2

c= $2

Therefore,

Coffees cost $2 each and bagels cost $4 each

Answer:

I believe it would be "mean".

Step-by-step explanation:

Mean is an average of a set of numbers.

Answer:

12) [tex] y = -x - 5 [/tex]

Step-by-step explanation:

[tex] y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1) [/tex]

12) (0, -5), (-1, -4)

[tex] y - (-5) = \dfrac{-4 - (-5)}{-1 - 0}(x - 0) [/tex]

[tex] y + 5 = \dfrac{-4 + 5}{-1}(x) [/tex]

[tex] y + 5 = \dfrac{1}{-1}(x) [/tex]

[tex] y = -x - 5 [/tex]

Answer:

work is pictured and shown

Answer:

$513.34

Step-by-step explanation:

Mr. DeLuca used his debit card twice, each time for $27.50.  This is a total of $55 spent.

$27.50 × 2 = $55

You now have to subtract the money spent from his bank balance.

$568.34 - $55 = $513.34

$513.34 was left in his bank account.

Answer:

The Elegant Home Architects charges are less than Rock the House Digital Designs charges for hours worked more than 2.

If the number of hours worked is equal to 2 than both would charge the same and if the hours are less than 2 then  Rock the House Digital Designs  will be a better option .

Step-by-step explanation:

Let ℎ represent the number of hours for which the Johnson family hires the design firm.

Suppose the  Johnson family hires the design firm for ten hours so h= 10

Then the charges by the Rock the House Digital Designs will be

$ 500 + 50(10)= $ 500+ $500= $1000

And the charges for the services by Elegant Home Architects will be

$75.00(10) = $ 750

Therefore the Elegant Home Architects charges are less than Rock the House Digital Designs charges.

But if the number of hours worked is equal to 2 than both would charge the same and if the hours are less than 2 then  Rock the House Digital Designs  will be a better option .

Rock the House Digital Designs

For 2 hours

$ 500 + 50(2)= $300

For 1 Hour

$500 + 50 (1)= $ 550

Elegant Home Architects

For 2 hours

$75.00(2) = $ 300

For 1 Hour

$75.00(1) = $ 75

Answer:

p = -1

Step-by-step explanation:

Step 1: Write out equation

-5 - 8p = -3p

Step 2: Add 8p to both sides

-5 = 5p

Step 3: Divide both sides by 5

-1 = p

Step 4: Rewrite

p = -1

Answer:

P=-1

Step-by-step explanation:

-5-8p=-3p

+8p +8p

------------------

-5=5p then divide both sides by 5

P=-1

Answer:

w = y - x is the equation to find w

Where,

w = Weight of the liquid

x = Weight of the empty can

y = Weight of the can with liquid

Step-by-step explanation:

Let

Weight of the empty can = x

Weight of the liquid = w

Weight of the can with liquid = x + w = y

x= 30 grams

w = ?

y= 47.3 grams

y = x + w

w = y - x

= 47.3 - 30

= 17.3

w= 17.3 grams

Therefore, the weight of the liquid is 17 .3 grams

Answer:

5z

Step-by-step explanation:

Answer:

5z

Step-by-step explanation:

'The product of 5 and a number' would be 5 *  n.

Since the number in the question would be 'z', we will write it as '5 * z'.

However, the most ideal way to write this is '5z'. So,  "The product of 5 and a number z" would be '5z'.

Hope this helps.

Answer:

The order of the matrix D^T × (BE) is 2 × 4

Step-by-step explanation:

In the multiplication of matrix, the number of columns in the first matrix must be equal to the number of rows of the second matrix. The resulting matrix from the product will have the same number of rows as the first matrix and the same number of column as the second matrix. For example, given Matrix A of order (m × n) and Matrix Z of order ( n × k), the product of the two matrices will give a matrix ( say Y) of order (m × k).

AZ = Y

(m x n)(n x k) = (m x k)

Now, From the question,

The order of Matrix B is 4 × 5,

the order of the matrix D is 4 × 2

and the order of the matrix E is 5 × 4.

To determine the order of the matrix D^T × (BE)

First, will find the order of (BE)

Order of BE = (4 × 5) (5 × 4)

Order of BE = (4 × 4)

Hence, the order of matrix (BE) is 4 × 4.

Now, we will determine the order of matrix D^T

D^T means the transpose of matrix D.

The transpose of a matrix is defined as a new matrix whose rows are the columns of the original matrix and the columns of the new matrix are the rows of the original matrix. This means given Matrix A of order (m × n), the transpose of Matrix A (A^T) will have an order of (n × m).

The order of the matrix D is 4 × 2

Hence, the order of the transpose of matrix D (D^T) will be 2 × 4

Now, the order of the matrix D^T × (BE) will be

Order of the matrix D^T × (BE) = (2 × 4) × (4 × 4)

Order of the matrix D^T × (BE) = 2 × 4

Hence, the order of the matrix D^T × (BE) is 2 × 4.

Answer:

Grades to be scored in 3rd exam = 88

Step-by-step explanation:

Given that average of 3 numbers is 85.

First two numbers are 81 and 86.

To find:

3rd number so that average is 85

Solution:

Let the third number = [tex]x[/tex]

Formula for average is:

[tex]Average = \dfrac{Sum\ of\ numbers}{Total\ count\ of\ numbers}[/tex]

Here, sum of numbers = [tex]81+86+x =167+x[/tex]

Total count of numbers = 3

[tex]85 = \dfrac{167+x}{3}\\\Rightarrow x=255-167\\\Rightarrow \bold{x=88}[/tex]

Grades to be scored in 3rd exam = 88

Answer:

the value of the printer is going down over the years because it is getting older. all you need to do for this is label the x and y axis with the nbers on the graph and then fill it in

has ur teacher gone over how to fill in graphs yet?

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

This is basically just a ratio in disguise. Ratios can be represented as fractions, and we can write these ratios to be equal to each other.

[tex]\frac{x}{9} = \frac{8}{12}[/tex]

We can solve for x using the cross products property:

[tex]9\cdot8=72\\\\72\div12=6[/tex]

Hope this helped!

Answer:

x=6

Step-by-step explanation:

We can write ratios to solve

x          8

----- = -----------

9           12

Using cross products

12x = 8*9

12x = 72

Divide by 12

x = 72/12

x =6

Answer:

v > -1

Step-by-step explanation:

v satisfies both these inequalities:

(*) -17 + 4v < 10v - 11

(**) 10v - 11 < 11v + 6

(*) <=> -17 + 11 < 10v - 4v

<=> -6 < 6v or 6v > -6

<=> v > -1

(**) <=> -11 - 6 < 11v - 10v

<=> -17 < v or v > -17

Combine (*) and (**)

--> Solution for this inequality is v > -1

Answer:

19.25

Step-by-step explanation:

if it sells per pound you would just multiply by 7 because thats what your looking for

have a great day :)

Answer:

$19.25

Step-by-step explanation:

One lb of granola sells for $2.75. You are trying to find how much 7 pound costs. Multiply 2.75 with 7:

($2.75/1 lb of granola) x (7/7) = (2.75 * 7/7 lb of granola)

Simplify:

2.75 * 7 = 19.25

7 lbs of granola costs $19.25

~

Answer and Explanations

ACT score percentile help colleges compare students with one another, rather than just looking at everyone’s score. The  score range is between 1 and 36, the highest score that one can receive on the ACT is 36. Moreover, 36 is the perfect score.

The maximum ACT score (36) is that in 2018, only 3,741 students (out of millions of test-takers) scored a perfect 36 on the ACT.  The 99th percentile of test-takers includes those who earn 35 or 34 on the ACT. We can miss up to five questions on the ACT and still earn a 36. That is a reason why the maximum ACT score is 36 at the 100th percentile.

The ACT score report will provide more information about test-taking experience in the form of sub score. The higher the score,  you will get into the colleges of your choice.

The maximum ACT score is not at the 100th percentile. because the student cannot score more than himself as well as others whom scored the same.

Although your question lacks some data a general answer have been provided above

       For the maximum score ( 36) to be at the 100th percentile the individual who scores the maximum ACT score, must have scored higher than others and also him/herself in the data set.

Even if a student scores the highest score (36) it does not mean they have scored higher than others who had the same score ( 36 ) with them or him/her self.

Hence we can conclude that the maximum ACT score ( 36 ) cannot be at the 100th percentile because the student cannot score more than himself as well as others whom scored the same.

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Answer:

fits under statistics category (also probability or math :\)

Answer:

[tex]\frac{1}{2}[/tex]

Step-by-step explanation:

9 - 4 = 5

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

Answer:

1/2

Step-by-step explanation:

4/10 = 2/5

9/10 - 2/5

LCD = 10

make the denominators the same as the LCD

9/10- 2x2 / 5x2

9/10 - 4/10

join the denominators

9-4/ 10

5/10 = simplify

=

1/2

The four color theorem-No more than 4 colors are required to color the regions map

Answer:

y+z=x

Step-by-step explanation:

we know that

The Exterior Angle Property of a Triangle states that the measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles

In this problem

Angle y and angle z are interior angles of triangle ABC and angle x is a exterior angle of triangle ABC

therefore

Applying the Exterior Angle Property of a Triangle

y+z=x

Hope This Helps!

Answer: (180 degrees − x = r)

Step-by-step explanation:

I took the test

Answer:

The correct option is;

16 inches

Step-by-step explanation:

The parameters of the motion given are;

The diameter, D of the bicycle = 16 inches;

The distance the bike moves (forward) after the screw punctures the tire = 56·π inches

We note that the circumference of the bicycle = π·D = π × 16 = 16·π inches

Therefore;

56·π inches/(16·π inches) = 3.5

Showing that the bicycle moves three and half complete turns (revolution) where after each complete turn, the screw starts from the bottom of the tire.

The height, h of the screw in the final half turn is given by the relation;

h = A×cos(Bx - C) + D

A = Amplitude of the motion = Diameter/2 = 16/2 = 8

P = The period of the motion 2·π/B

B·x = The angle described by the motion = Half of one revolution = π = 180°

C = Phase shift = π

D = The midline = Diameter/2 = 8 inches

Therefore;

h = 8×cos(π - π) + 8 = 16 inches

After the bike moves forward another 56·π inches the height of the screw = 16 inches.

Answer:

16 inches

Step-by-step explanation:

just took the assignment

Answer:

The correct answer is x = 6.

Step-by-step explanation:

To solve this problem, we first must recognize that DE + EF = DF.

From this information, we can set up the following equation when we substitute in the given values:

DE + EF = DF

(4x-1) + 9 = 9x - 22

Our first step is going to be to combine like terms on the left side of the equation.  This is modeled below:

4x - 1 + 9 = 9x - 22

4x + 8 = 9x - 22

Then, we should subtract 4x from both sides of the equation.

8 = 5x - 22

Now, we can add 22 to both sides of the equation.

30 = 5x

Finally, we can divide both sides by 5.

x = 6

Therefore, the correct answer is x = 6.

Hope this helps!

124.62 rounded to the nearest one is 125.

Rounding 124.62 to the nearest one is equivalent to finding the integer multiple of one nearest to 124.62.

" Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use. "

                  124 ≤ 124.62 ≤ 125

The distance from to 124.62 to 124 is = 124.62 - 124 = 0.62

The distance from to 124.62 to 125 is = 125 - 124.62 = 0.38

So, the rounded to the nearest whole number is 125.

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================================================

Explanation:

x is a variable or placeholder for a number. Think of it like a box.

1x = 1 box

2x = 2 boxes

and so on

9x = 9 boxes

5x = 5 boxes

9x+5x = 9 boxes + 5 boxes = 14 boxes = 14x

So that's one way to see how 9x+5x = 14x.

Or you could add the coefficients 9 and 5 to get 9+5 = 14. Then tack an x onto everything.

----------

The y terms are handled in a similar fashion.

-5y + 9y = 4y

which is the same as

9y - 5y = 4y

You could think of it like this

(9 yaks) - (5 yaks) = 4 yaks

So we started with 9 yaks and took away 5 of them to be left with 4 yaks.

----------

After getting the results 14x and 4y. We would then have the final answer 14x+4y

The x and y terms cannot be combined since they are not like terms. So we leave that expression as is.

Answer: mq  = 17

Step-by-step explanation:

If cm is 22   and cq  which is the whole distance,  then subtract the distance of  cm which is 22 from the distance of cq which is 39.

39 - 22 = 17