Answer:
x ≈ -7.73 , - 4.27
Step-by-step explanation:
x² + 12x + 33 = 0 ( subtract 33 from both sides )
x² + 12x = - 33
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(6)x + 36 = - 33 + 36
(x + 6)² = 3 ← take square root of both sides )
x + 6 = ± ( subtract 6 from both sides )
x = - 6 ±
Then
x = - 6 - ≈ - 7.73 ( to the nearest hundredth )
x = - 6 + ≈ - 4.27 ( to the nearest hundredth )
So 15 gallons of gas brought it from 1/8 full to 3/4 full.
Let's change 3/4 to the equivalent fraction 6/8 so that the denominators are the same. (3/4 = 6/8)
So 15 gallons of gas brought it from 1/8 to 6/8 Those 15 gallons must be 5/8 of the tank's capacity 6/8 - 1/8 = 5/8
So 15 is 5/8 of what number? (This will tell us the capacity of the whole tank)
15 = 5/8n
Divide both sides by 5/8 (remembering to multiply by the reciprocal 8/5)
15 ÷ 5/8 = 15 x 8/5 = 18
So the tank holds 24 gallons and (since it is 3/4 full or has 18 gallons) it needs 6 gallons to fill the tank.
Check - at first 1/8 full (1/8 of 24 = 3) So we started with 3 gallons. 15 gallons added to the 3 gallons is 18 gallons. Now the tank is 6/8 (3/4 full). The remaining 1/4 (2/8) of a tank is the difference between 18 and it's capacity (24 gallons) so it will need 6 gallons to fill it up..
Answer:
27
Step-by-step explanation:
First solve 3a - 9= 6
3a - 9 = 6 add 9
3a = 15 divide by 3
a = 5
Now that you know a is 5, put that in the other expression.
5a + 2
= 5(5) + 2
= 25 + 2
= 27
Answer:
1295 in^2
Step-by-step explanation:
A rectangle of length 37 in and width 35 in has area (37 in)(35 in) = 1295 in^2