Julio has found that his new car gets 36 miles to the gallon on the highway and 31 miles per gallon in the city. he recently drove 397 miles on 12 gallons of gasoline. how many miles did he drive on the highway? how many miles did he drive in the city?

Miles he drove on highway = 180 miles

Miles he drove in the city = 217 miles

Step-by-step explanation:

Lets assume that gallon used on highway = x

Miles driven on highway = y

(I) 36 miles per gallon on the highway.

36x = y    equation 1

(II) 31 miles per gallon in the city.He recently drove 397 miles on 12 gallons of gasoline

31(12-x)= 397-y    equation 2

372-31x= 397-y

Combine the constants:

-31x= 397-372-y

y-31x = 25

Now substitute the value of equation 1 in equation 2

y-31x=25

36x-31x=25

5x=25

Now divide both sides by 5

5x/5=25/5

x=5

Now substitute the value x=5 in equation 1

36x=y

36(5)=y

180= y

Now subtract the miles driven on highway from recently drove miles to get the miles driven in the city.

397-y = 389 - 180

= 217

Therefore,

Miles he drove on highway = 180 miles

Miles he drove in the city = 217 miles

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

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