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3 years ago

What is the inverse of the function f(x)=1/4x-12

Mathematics

2 answers:

castortr0y [4]3 years ago

4 0

To find the inverse fountion interchange the veribles and solve for y.

icang [17]3 years ago

4 0

Answer:

$f^{-1}(x)=4x+48$ .

Step-by-step explanation:

We have been given a function $f(x)=\frac{1}{4}x-12$ . We are asked to find the inverse for our given function.

First of all, we will replace $f(x)$ by y as:

$y=\frac{1}{4}x-12$

Now, we will interchange x and y values as:

$x=\frac{1}{4}y-12$

Let us solve for y.

$x+12=\frac{1}{4}y-12+12$

$x+12=\frac{1}{4}y$

Switch sides:

$\frac{1}{4}y=x+12$

Multiply both sides by 4:

$4*\frac{1}{4}y=4(x+12)$

$y=4x+48$

Therefore, the required inverse function would be $f^{-1}(x)=4x+48$ .

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Look online for the growth of the trunk of a tree. Estimate how much time does it take for a water oak to grow one inch in diame

lana66690 [7]

Answer:

Explained

Step-by-step explanation:

The trunk of a tree grows in two different ways, first in height and second in diameter.Usually tree grows one ring per year in diameter. So, counting the number of rings we can determine the age of a tree. Both height and diameter growth does not occur at the same rate. Tree grows more in height than in their diameter. Mature trees usually grows 1 inch in diameter every year.

Water oak gains 24 inches in height every year and 1.5 inch growth in diameter annually, meaning if we divide 1.5 inches by 12 months we gets 0.125 inches growth monthly. So a water oak tree needs only 8 months to grow 1 inch in diameter.

4 0

4 years ago

Khan Academy math question. Just answer the picture

MrRissso [65]

Answer is 175
To start you need to work backwards from the mean so do 158*4 to give you the total of the revenue then simply minus what was given to get 175
Hope this helped

4 0

3 years ago

Giving 100 points.

Nitella [24]

Answer:

1. Cost per customer: 10 + x

Average number of customers: 16 - 2x

$\textsf{2.} \quad -2x^2-4x+160\geq 130$

3. $10, $11, $12 and $13

Step-by-step explanation:

Given information:

$10 = cost of buffet per customer
16 customers choose the buffet per hour
Every $1 increase in the cost of the buffet = loss of 2 customers per hour
$130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

Part 1

Cost per customer: 10 + x

Average number of customers: 16 - 2x

Part 2

The cost per customer multiplied by the number of customers needs to be at least $130. Therefore, we can use the expressions found in part 1 to write the inequality:

$(10 + x)(16 - 2x)\geq 130$

$\implies 160-20x+16x-2x^2\geq 130$

$\implies -2x^2-4x+160\geq 130$

Part 3

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

$\implies -2x^2-4x+160\geq 130$

$\implies -2x^2-4x+30\geq 0$

$\implies -2(x^2+2x-15)\geq 0$

$\implies x^2+2x-15\leq 0$

$\implies (x-3)(x+5)\leq 0$

Find the roots by equating to zero:

$\implies (x-3)(x+5)=0$

$x-3=0 \implies x=3$

$x+5=0 \implies x=-5$

Therefore, the roots are x = 3 and x = -5.

Test the roots by choosing a value between the roots and substituting it into the original inequality:

$\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144$

As 144 ≥ 130, the solution to the inequality is between the roots:

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an increase in cost. It does not confirm that if the cost is reduced (less than $10) the number of customers increases per hour.]

Cost per customer:

$x =0 \implies 10 + 0=\$10$

$x=3 \implies 10+3=\$13$

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

8 0

2 years ago

In 10 seconds, Lauren counts 5 vehicles passing by her house. At that rate, how many vehicles would pass by in one hour?

Anna007 [38]

6 x 60 x 5 would be the equation and all of that put together would be 1,800 vehicles would pass by in an hour.

7 0

4 years ago

Nevaeh went shopping for a new phone because of a discount sale. She multiplied the price of the phone by 0.95 to find the price

ella [17]

Answer:

95% off

Step-by-step explanation:

because the percent u times by the actual price is the percent u have off

3 0

3 years ago