Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. h(x) = 5x – 5 h(x) = 5x + 5

If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B

If Marguerite rents for 1 week, it will cost her the same at either company

h(x) = 5x - 5

Step-by-step explanation:

Marguerite wants to rent a carpet cleaner. Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. The following functions represent the rate structures of the two rental companies: x = the number of weeks Company A f(x) = 15(7x) Company B g(x) = 100x + 5 The function h(x) = f(x) – g(x) represents the difference between the two rate structures. Determine which statements about h(x) and about renting a carpet cleaner are true. Check all that apply. If Marguerite rents for 2 weeks, it will cost her more if she rents from Company B. If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B. If Marguerite rents for 1 week, it will cost her the same at either company. If Marguerite rents for 1 week, it will cost her more if she rents from Company A. h(x) = 5x – 5 h(x) = 5x + 5

Company A rents a carpet cleaner for $15 per day. Company B rents a carpet cleaner for $100 per week, with a one-time fee of $5. In one week there are 7 days, therefore in x weeks the cost of rentals are given below:

For company A: f(x) = 15(7x)

For company B: g(x) = 100x + 5  

h(x) = f(x) – g(x) represents the difference between the two rate structures.

h(x) = f(x) - g(x) = 15(7x) - (100x + 5)

h(x) = 105x - 100x - 5

h(x) = 5x - 5

If Marguerite rents for 2 weeks:

The cost for company A = 15(7x) = 15(7 × 2) = $210

The cost for company B = 100x + 5 = 100(2) + 5 = 200 + 5 = $205

If Marguerite rents for 2 weeks, it will cost her less if she rents from Company B

If Marguerite rents for 1 weeks:

The cost for company A = 15(7x) = 15(7 × 1) = $105

The cost for company B = 100x + 5 = 100(1) + 5 = 100 + 5 = $105

If Marguerite rents for 1 week, it will cost her the same at either company

x=-2

infinite number of lines, so there is an infinite number of equations.

step-by-step explanation:

there are an infinite number of line that passes through the point (-2,5)

x=-2   is one line that passes through the point

y = 5 is another line that passes through the point

(these two lines are perpendicular to each other).

since the number of   numbers are infinite and the slope is the ratio of two numbers,(change in y over change in x) we can have an infinite number of slopes.     our only condition is that it passes through the point (-2,5)