2(4x - 7) -1 = 11
8x - 14 -1 = 11
8x - 15 = 11
+ 15 + 15
8x = 26
/8 /8
x = 3. 25 ------> Rounded: 3.30
<h3>
Answer: 5 - 4i (choice A)</h3>
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Work Shown:
x = the other number
(5+4i)*x = 41
x = 41/(5+4i)
x = 41*(5-4i)/( (5+4i)*(5-4i) ) ..... see note below
x = 41*(5-4i)/( 41 )
x = (41/41)*(5-4i)
x = 5 - 4i
As a way to check, (5+4i)*(5-4i) = 5^2+4^2 = 25+16 = 41
The rule used is (a-bi)(a+bi) = a^2 + b^2
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Note: I multiplied top and bottom by (5-4i) to get rid of the imaginary term in the denominator.
We know that x = 30 + y, because the problem says that there are 30 more football players than basketball players.
Each group has 10 more members added: x + 10 and y + 10. We can write x + 10 as 30 + y + 10 or 40 + y.
The ratio (40 + y)/(y + 10) = 3/2. You can cross multiply to get:
80 + 2y = 3y + 30
Combine like terms to get:
y = 50 members on the basketball team. Since there are 30 more members on the football team, you just add 30 to 50 to get x = 80 members on the football team.
The largest integer is 144, and the other two numbers are 143 and 142.
