a membership at gym a costs $50 for 5 months. a membership at gym b down the street costs $40 for 3 months. you write two equations in the form of y = kx to try and figure out which membership would be cheaper for a year. what is the value of k for the cheaper membership?

Answer 1

Let's assume that gym A is cheaper for a year.
Equation 1 for gym A: y = 50/5 * x
Equation 2 for gym B: y = 40/3 * x

To find the value of k for the cheaper membership, we need to compare the rates of the two equations. In this case, we compare the values of 50/5 and 40/3.

50/5 = 10 and 40/3 ≈ 13.33

Since 10 is smaller than 13.33, the value of k for the cheaper membership is 10.

Answer 2

two equations are written to express how far a car can go when driving on different roads. on road 1, the car can go 60 miles in 2 hours. on road 2, the car can go 90 miles in 4 hours. write an equation where y is the distance in miles and x is the time in hours to represent the motion of the faster car.

Answer 3

To represent the motion of the faster car, we will use the information given for road 2.
Road 2:
Distance (y) = 90 miles
Time (x) = 4 hours

Using the formula for the equation of a line (y = kx), we can determine the value of k, representing the rate of speed of the car on road 2.
Plugging the values into the equation, we have:
90 = k * 4

To solve for k, we divide both sides of the equation by 4:
90/4 = k

Simplifying this, we find:
k = 22.5

Therefore, the equation representing the motion of the faster car on road 2 is:
y = 22.5x