Answer:
Which graph represents the solution set to this system of equations? –x + 2y = 6 and 4x + y = 3
On a coordinate plane, a line goes through (negative 1, negative 1) and (0, 3) and another line goes through (1, 4) and (2, 2).
On a coordinate plane, a line goes through (negative 4, 0) and (0, 4) and another line goes through (negative 1, 1) and (0, negative 3).
Step-by-step explanation:
Answer:
6.5e^(i·(-157.38°)) ≈ 6.5e^(-2.7468i)
Step-by-step explanation:
A suitable calculator can find the value of this ratio for you.
((2+3i)/(1-i))² = -6 -2.5i ≈ 6.5∠-157.38° ≈ 6.5e^(-2.7468i)
__
The second attachments shows the calculator set to radian mode for the angle measure.
The answer to the question
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..
