Answer:
Problem 23) 
Problem 24) 
Step-by-step explanation:
step 1
Find the slope of the given line
The formula to calculate the slope between two points is equal to

we have

Substitute the values


step 2
Problem 23
we know that
If two lines are perpendicular then the product of its slopes is equal to minus 1
so

Find the slope of the line
we have

substitute in the equation and solve for m2


with the slope m2 and the point
find the equation of the line
Remember that
The equation of the line in slope intercept form is equal to

we have

-----> the given point is the y-intercept
substitute

step 3
Problem 24
we know that
If two lines are parallel, then its slopes are the same
so
with the slope m1 and the point
find the equation of the line
The equation of the line in slope intercept form is equal to

we have

-----> the given point is the y-intercept
substitute

It is 804.25
2 is in the tenths place and then 5 is hundredths place
Rearrange the first equation2x + y = 20take away 2x from both sidesy = 20 - 2x substitute this y value into the second equation6x - 5(20 - 2x) = 126x -100 +10x = 12add 100 to both sides6x + 10x = 11216x = 112divide both sides by 16 x = 7Substitute this x value into the first equation to get y.2(7) + y = 2014 + y = 20take away 14 from both sidesy = 6
So, y = 6 and x = 7
Answer:
3 gallons of gas
Step-by-step explanation:
First we need to create the ratio to build our answer off of.
This ratio would be 72:4, meaning 72 miles for every 4 gallons.
We can divide 72 by 4 to find the unit rate.
72 / 4 = 18
So, the unit rate is 18 miles for every 1 gallon.
Next we need to figure out how may gallons are needed to travel 54 miles.
We can divide 54 by 18 to receive 3.
This means that our ratio needed to answer the question is 3 times the unit rate.
Our new ratio is now: 54:m, m meaning miles.
To find the amount of miles, multiply the 3 we used later, to make this ratio 3 times the unit rate.
So, our final ratio is 54:3,
meaning that Hank will have used 3 gallons of gas after traveling 54 miles.
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