PLEASE I NEED HELP 20 POINTS Ben participated in a race. During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours. During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. What equation could you write to solve for the number of hours Ben ran during each half of the race? Let y represent the number of miles in half the race. Write two equations, one for the first half of the race and one for the second half. How could you transform these two equations to be the same as the original equation you wrote to solve for x? What do you think this means about solving for the variables in a situation represented by two equations?

y=5x+3

y=5.5x+2

Step-by-step explanation:

may also be written as  

5x+3 = 5.5x+2

subtract 2 from both sides

5x+3-2 = 5.5x+2-2

subtract 5x from both sides

5x-5x+3-2 = 5.5x+2-2-5x

3-2 = 5.5x-5x

1=0.5x

x = 2

y=5×2+3 = 13

5.5×2+2= 13

y = 13

When trying to solve for variables in a situation with two variables you can isolate one variable in one equation and replace it in the other equation.

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

d

step-by-step explanation:

given

y + 3 = - 4(x - 2) ← distribute the parenthesis

y + 3 = - 4x + 8 ( subtract 3 from both sides )

y = - 4x + 5 → d