Please help me with #75. Thanks

At one gym, there is a $12 start-up fee, and after that each month at the gym costs $20. At another gym, it costs $4 to startup,

mart [117]

Answer:

In 4 months the cost of both gyms will be the same.

Step-by-step explanation:

At first we need to model the function to calculate the cost of the 2 gyms.

Slope-intercept equation of linear function

$f(x)=mx+b$

where

$m\rightarrow$ slope of line

$b\rightarrow$ y-intercept

Let linear function to calculate total cost of gym be:

$c(n)=mn+b$

where

$c\rightarrow$ total cost of gym

$m\rightarrow$ cost per month (slope)

$n\rightarrow$ number of months

$b\rightarrow$ start-up fee (y-intercept)

For Gym 1

$m=20$ , $b=12$

$c(n)=20n+12$

For Gym 2

$m=22$ , $b=4$

$c(n)=22n+4$

In order to find the number of months the cost of both gyms will be the same, we need to equate both functions and solve for number of months $(n)$

$20n+12=22n+4$

$\\\textrm{Subtracting 22n from both sides}\\20n-22n+12=22n-22n+4\\-2n+12=4\\\textrm{Subtracting 12 from both sides}\\-2n+12-12=4-12\\-2n=-8\\\textrm{Dividing both sides by -2}\\\frac{-2}{-2}n=\frac{-8}{-2}\\n=4\textrm{ months}$

So,

In 4 months the cost of both gyms will be the same.

5 0

3 years ago

What is the following simplified product? Assume x greater-than-or-equal-to 0

nlexa [21]

Answer:

$10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}$

Step-by-step explanation:

Remove perfect squares from under the radicals.

$(\sqrt{10x^4}-x\sqrt{5x^2})(2\sqrt{15x^4}+\sqrt{3x^3})\\\\=(\sqrt{10x^4})(2\sqrt{15x^4}) +(\sqrt{10x^4})(\sqrt{3x^3}) -(x\sqrt{5x^2})(2\sqrt{15x^4}) -(x\sqrt{5x^2})(\sqrt{3x^3})\\\\=2\sqrt{150x^8}+\sqrt{30x^7}-2x\sqrt{75x^6}-x\sqrt{15x^5}\\\\=\boxed{10x^4\sqrt{6}+x^3\sqrt{30x}-10x^4\sqrt{3}-x^3\sqrt{15x}}$

_____

The applicable rules of exponents are ...

(x^a)(x^b) = x^(a+b)

√(a^2) = a . . . . . . . for a > 0

(√a)(√b) = √(ab)

5 0

2 years ago

Read 2 more answers

A music school offers its students 8 different classes each semester. 4 of the classes are in music theory, 3 of the classes are

Bond [772]

Answer:

5

Step-by-step explanation:

8 0

2 years ago

Which ordered pair is a solution of the equation

alekssr [168]

Answer:

OPTION D: NEITHER

Step-by-step explanation:

The given equation is: 7x - 2y = - 5

To find a solution to this, we substitute the options and compare LHS and RHS.

OPTION A: (1, 5)

LHS = 7(1) - 2(5) = 7 - 10 = -3

RHS = - 5

LHS $\ne$ RHS.

So, this option is eliminated.

OPTION B: (-1, 1)

LHS = 7(-1) - 2(1) = -7 - 2 = - 9

RHS = - 5

Again, LHS $\ne$ RHS.

So, this Option is eliminated as well.

OPTION C: It says both A and B. Clearly, this is eliminated as well.

Therefore, the answer is: OPTION D: NEITHER.

NOTE: This is a two variable equation. So, we need a minimum of two equations to determine the solution. Since, only one equation is given here, we use the help of options.

8 0

3 years ago

Six values on the number line above are marked with letters. Which letters represent integers when the value on the number line

s344n2d4d5 [400]

Answer:

Here is your answer C

Step-by-step explanation:

4 0

2 years ago