Travis made a business trip of 195.5 miles. He averaged

53 mph for the first part of the trip and

58 mph for the second part. If the trip took

3.5 hours, how long did he travel at each rate?

At 53 mph, he traveled for 1.5 hours

At 58 mph, he traveled for 2 hours

Step-by-step explanation:

Mathematically;

distance = speed * time

let the time for the first part of the trip be x hours and the second part be y hours

Total hours is 3.5

So therefore;

x + y = 3.5 ••••••••(i)

Now let’s work with the rate

53 mph for x hours = 53 * x = 53x miles

58 mph for y hours = 58 * y = 58y miles

Adding both;

53x + 58y = 195.5 miles ••••••••(ii)

We have two equations to solve simultaneously

From i, x = 3.5 - y

insert into ii

53(3.5-y) + 58y = 195.5

185.5 - 53y + 58y = 195.5

5y = 195.5-185.5

5y = 10

y = 10/5

y = 2 hours

x = 3.5 - y

x = 3.5 - 2

x = 1.5 hours

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2

a) 32pie square meters

step-by-step explanation: