The graph shows the average speed of two cars on the highway.

a. what does (2 , 120) repesent?

b. what does (1.5, 67.5) repesent?

c. what does the ratio of the y-coordinate to the x-coordinate for each pair of points on the graph repesent?

d. what does the slope of each line repesent?

e. which car is traveling faster? how can you tell from the graph?

The graph shows the average speed of two cars on the highway.

a. (2 , 120) shows that car A travels 120 miles in 2 hours.

b. (1.5, 67.5) shows that car B travels 67.5 miles in 1.5 hours.

c. ratio is : distance : time

d. Slope of car A = This is the unit speed of the car.

Slope of car B = This is the unit speed of car B.

e. Car A is travelling faster. If we compare (2,120) and (2,90) we can see that the car A travels 120 miles in 2 hours and car B travels 90 miles in 2 hours.

So, car A is travelling faster.

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

7.3

step-by-step explanation: