Marion is observing the velocity of a cyclist at different times. after two hours, the velocity is 18km/h. after four hours, the velocity of the cyclist is 4km/h.
part a: write an equation in two variables in the standard form that can be used to describe the velocity of the cyclist at different times. show your work and define the variables used.
part b: how can you graph the equations obtained in part a for the first 8 hours?

To solve this problem, we assume that velocity is a linear function of time:
v(t) = m t + b
where
v = velocity

t = time

m = slope of line

b = y-intercept of line equation

When t = 2 hours, v = 18 km/h, therefore:
2 m + b = 18         (1)

When t = 4 hours,  v = 4 km/h, therefore
4 m + b = 4          (2)

Subtract (1) from (2) to obtain
4 m – 2 m = 4 - 18
2 m = -14
m = -7

From (1), calculate for b:
b = 18 – 2(-7) = 32

Part A. The equation in standard form is therefore:
v = -7 t + 32

Part B. To graph the equation for the first 8 hours, we create a table as shown below. Assign values of t from 0 to 8 hours then calculate the corresponding velocity.

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it