Carole's car averages 13.2 mi/gal in city driving and 25.3 mi/gal in highway driving. If she drove a total of 396.0 mi on 19 gal
1 answer:
Answer:
7 gallons were used for city driving.
Step-by-step explanation:
I am going to solve this question by a system of equations.
I am going to say that:
x is the number of gallons driven in the city.
y is the number of gallons driven in the highway.
19 gal of gas
This means that
Carole's car averages 13.2 mi/gal in city driving and 25.3 mi/gal in highway driving. If she drove a total of 396.0 mi.
This means that
How many of the gallons (to the nearest gallon) were used for city driving?
This is x
From the first equation, i will have
Replacing in the second equation
7 gallons were used for city driving.
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Answer:
"complete the square" to put in vertex form
Step-by-step explanation:
It may be helpful to consider the square of a binomial:
(x +a)² = x² +2ax +a²
The expression x² +x +1 is in the standard form of the expression on the right above. Comparing the coefficients of x, we see ...
2a = 1
a = 1/2
That means we can write ...
(x +1/2)² = x² +x +1/4
But we need x² +x +1, so we need to add 3/4 to the binomial square in order to make the expressions equal:
_____
Another way to consider this is ...
x² +bx +c
= x² +2(b/2)x +(b/2)² +c -(b/2)² . . . . . . rewrite bx, add and subtract (b/2)²*
= (x +b/2)² +(c -(b/2)²)
for b=1, c=1, this becomes ...
x² +x +1 = (x +1/2)² +(1 -(1/2)²)
= (x +1/2)² +3/4
_____
* This process, "rewrite bx, add and subtract (b/2)²," is called "completing the square"—especially when written as (x-h)² +k, a parabola with vertex (h, k).