Question 2* 2 points
A family is traveling from their home to a vacation resort hotel. The table below shows their distance from home as a function of
time.
Time (hrs)
0
2.
5
7
Distance (mi)0
140
375
480
Determine the average rate of change between hour 2 and hour 7, including units.

The average rate of change between these times is 68 miles per hour

Step-by-step explanation:

Here, we are to determine the average rate of change between hour 2 and hour 7

The distance traveled at hour 2 is 140 miles

The distance traveled at hour 7 is 480 miles

So we can say we have two points and we want to know the rate of change between these points

Mathematically, we can represent the rate of change as Δ

Thus, between the two different times, we have;

Δ = (D7-D2)/(T7-T2)

where (T7,D7) = (7,480) and (T2,D2) = (2,140) represents the time and distance at hour 2 and hour 7 respectively

Now inputing the values into the equation, we have;

Δ = (480-140)/(7-2) = 340/5 = 68 miles/hour

i think it is 18

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.