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andrew-mc [135]
3 years ago
13

Claudia goes on a road trip; her car gets 24 miles per gallon (mpg) and gas costs $3.02 per gallon. Let n represent the number o

f miles Claudia has traveled since she started driving. Suppose Claudia has traveled 216 miles.
How many gallons of gasoline has Jacqueline used since she started driving?
What is the cost of the gasoline that Jacqueline has used since she started driving?
Write an expression in terms of n that represents the number of gallons of gasoline Jacqueline has used since she started driving.
Write an expression in terms of n that represents the cost of the gasoline that Jacqueline has used since she started driving.
Mathematics
1 answer:
blagie [28]3 years ago
7 0

Answer:

Step-by-step explanation:

Let n represent the number of miles Claudia has traveled since she started driving.

Claudia goes on a road trip; her car gets 24 miles per gallon (mpg).

The expression in terms of n that represents the number of gallons of gasoline Jacqueline has used since she started driving would be

n/24

Gas costs $3.02 per gallon. The expression in terms of n that represents the cost of the gasoline that Jacqueline has used since she started driving would be

n/24 × 3.02 = 3.02n/24

Suppose Claudia has traveled 216 miles, then the number of gallons of gasoline that Jacqueline has used since she started driving is

216 /24 = 9 gallons of gasoline.

The cost of the gasoline that Jacqueline used since she started driving is

(3.02 × 216)/24 = $27.18

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Step-by-step explanation:

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Okay so lets look at the equation given
a ^{2} + {b}^{2} = {c}^{2}
this is the Pythagorean theorem, this equation holds true to all right angle triangles.

for the "a" and "b" terms must be the two shortest lengths and "c" must be the longest length.
why? because "c" represents the hypotenuse in this theorem and the hypotenuse is by definition the longest side of a right triangle.

(side note: always draw a picture, it helps a lot if you doodle a bit to get an idea of what you are working with)

we are given three lengths : 3 , 4, and 5 (im ignoring the measurements for now)

we can look at it two ways with a picture and through algebra

try to draw a right triangle with the given info. you'll see there are only two cases were this is possible the picture above is one case where this is not possible

now we can look at this algebraically
a = 3 \\ b = 4 \\ c = 5
(but "a" and "b" can swap lengths)

now with the Pythagorean theorem we can see how this plays out
{a}^{2} + {b}^{2} = {c}^{2} \\ {3 }^{2} + {4}^{2} = {5 }^{2} \\ 9 + 16 = 25 \\ 25 = 25
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{4}^{2} + {3}^{2} = {5}^{2} \\ 16 + 9 = 25 \\ 25 = 25
now here's a case when we let 5 , our longest length , become a leg and let one our shorter lengths take the place of "c"

a = 5 \\ b = 3 \\ c = 4 \\ {5}^{2} + {3}^{2} = {4}^{2} \\ 25 + 9 = 16 \\ 34 = 16 \:
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hope this helped you out

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