Emily's school is 4 miles away from her home. She goes by car to school and back. The car consumes 3 gallons of fuel during the 5 days Emily takes the car to school and back. How many miles can Emily travel per gallon of fuel? Round to the nearest tenth.

Answers

Answer 1

Answer: distance per day = 8 miles
3/1 = (8 X 5)/x
3x = 40
x=40/3
x = 13,3 miles

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Select the correct answer.The function f(x) is given by the table of values.

x 1 2 3 4
f(x) 1 8 27 64
If f(x) is shifted 4 units up to obtain g(x), which table of values represents the function g(x)?

x 5 6 7 8
g(x) 5 12 31 68

x 1 2 3 4
g(x) 5 12 31 68

x 5 6 7 8
g(x) 1 8 27 64

x 1 2 3 4
g(x) 4 32 108 256

Answers

The solution is Option B.

x = { 1 , 2 , 3 , 4 }

g(x) = { 5 , 12 , 31 , 68 }

The function g ( x ) = x³ + 4

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the function be represented as A

Now , the value of A is

when x = 1

f ( x ) = 1

when x = 2

f ( x ) = 8

when x = 3

f ( x ) = 27

when x = 4

f ( x ) = 64

So , the equation will be y = x³ be equation (1)

Now , f(x) is shifted 4 units up to obtain g(x)

So , Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Substituting the values in the equation , we get

when x = 1

g ( x ) = 1 + 4 = 5

when x = 2

g ( x ) = 8 + 4 = 12

when x = 3

g ( x ) = 27 + 4 = 31

when x = 4

g ( x ) = 64 + 4 = 68

Therefore , the function is g ( x ) = x³ + 4

Hence , the function is g ( x ) = x³ + 4

To learn more about transformation of a function click :

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Answer:

The second answer is correct.

Step-by-step explanation:

So g(x) = f(x) + 4

If f(x) = 1, 8, 27, and 64 then g(x) = 5, 12, 31, and 68.

Peggy works as a busperson and earns \$7.50/h. She also receives 9\% of the gratuities earned by all the staff. In one week she worked 35 hours and the gratuities totalled \$1936.80. What was Peggy's gross pay?

Answers

Answer: $ 436.81

Step-by-step explanation:

Given: Hourly rate for Peggy= $7.50

Also, she receives 9% of the gratuities earned by all the staff.

Total hours she worked = 35 hours

Total gratuities = $1936.80

Gross pay = (Hourly rate ) x (Number of hours worked)+ 9% of (Total gratuities )

= $ [(7.50 ×35)+(0.09 ×1936.80)]

= $ (262.5 +174.31)

= $ 436.81

Hence, her gross pay = $436.81

Simplify 5m - 13n - n + 4m.
9m - 14n
9m - 13
9m2 + 13n2
-5mn

Answers

9m-14n is what i got

9m-14n This was my anwser

The function q(w) = 3+5(w-1) represents the number of quarters in a bowl on week w. What does the value 5 represent in the situation?A. There were 5 quarters in the bowl on week 1.

B. The value of the quarters in the bowl on week 1 was &5.

C. Five quarters are added to the bowl every week

D. Quarters were added to his bowl for 5 weeks

Answers

the value of quarters in the bowl on week 1 was &5

Answer:

Five quarters are added to the bowl every week.

Step-by-step explanation:

Write a rule for the linear function in the table. x f(x) –3 –1 0 2 3 5 6 8 A. f(x) = x + 2 B. f(x) = 3x C. f(x) = x – 2 D. f(x) = x – 1

Answers

Answer:

The answer is A.

Step-by-step explanation:

In this kind of exercise the usual way to solve it is s kind of trial an error. We evaluate f(x) in the given values of x and check if it corresponds with the values of f(x) in the table. If only one of the calculations does not correspond we dismiss the function.

Let us start our analysis from D. to A.

D. In this case f(x) = x-1, then f(-3) = -3-1=-4, and the result does not correspond to the values of the table (recall f(-3)=-1).

C. The same idea: we have f(x)=x-2, then f(-3)=-3-2=-5, and the result does not correspond to the values of the table (recall f(-3)=-1).

B. Here f(x)=3x, then f(-3)=3*(-3)=-9, and the result does not correspond to the values of the table (recall f(-3)=-1).

A. Now f(x)=x+2, then f(-3)=-3+2=-1, and the result does correspond to the values of the table (recall f(-3)=-1). So, we need to check the next values of the table:

f(0)=0+2=2, f(3)=3+2=5 and f(6)=6+2=8.

As all the values are equal to those in the table, we conclude that A. is the correct answer.

If you notice:

x = -3, f(x) = -3 + 2 = -1

x = 0, f(x) = 0 + 2 = 2

x = 2, f(x) = 2 + 2 = 4

x = 3, f(x) = 3 + 2 = 5

And so on...

By observation: f(x) = x + 2. Option (A).

I hope this helps.

What is the simplified base for the function f(x) = 2(3√27(2x)?2
3
9
18