PLEASE HELP I NEED TO GET THIS DONE LAST DAY: Paloma ran 3 3/4
miles around the school track. If each lap is 1/2 mile, how many laps did she run?

7 1/2

Step-by-step explanation:

. We are looking for the number, N, of laps. We are given the total distance ( in miles) for N laps that  Penelope ran. and we are given the total distance ( in miles) of one lap. The problem asks us to find N, (how many laps Penelope ran). We see that this is a division  problem ( how many 1/2 miles are there in 3 3/4 miles ) so we must solve:

3 3/4 ÷ 1/2 = (convert to improper fractions)

15/4 x 2/1 = (flip fraction and multiply)

15/2 (multiply and simplify)

7 1/2 (convert to mixed number)

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4