Answer:
25/4 will have to be added to "complete the square"
Step-by-step explanation:
x² - 5x - 18 = 0
x² - 5x = 18
Find the half of the coefficient of x and square it
(5/2)² = 25/4
Add 25/4 to both sides to complete the square
x² - 5x + 25/4 = 18 + 25/4
x² - 5x + 25/4 = 18(4/4) + 25/4
x² - 5x + 25/4 = 72/4 + 25/4
x² - 5x + 25/4 = (72+25)/4
x² - 5x + 25/4 = 97/4
(x - 5/2)² = 97/4
Find the square root of both sides
√(x - 5/2)² = ±√97/4
x - 5/2 = √97/2
x = √97/2 + 5/2 or x = -√97/2 + 5/2
x = 7.42443 or -2.42443
Answer: 27
Step-by-step explanation:
The expression given is inside a cube root. This is a simplified version of a fractional exponent, 1/3.
We can take the expression outside of the radical to get this:
3 ^ 9 ^ (1/3)
When an exponent is raised to another exponent, multiply the exponents and keep the base the same:
3 ^ (9 * 1/3)
3 ^ 3
The expression is equal to 27.
Ruby's hours will represent x+6
Svetlana's hours will represent 4(x+6)
Issac will represent x.
The equation would read:
x+(x+6)+(4(x+6))=126
x+x+6+4x+24=126
6x+30=126
Subtract 30 from both sides.
6x=96
Divide 6 on both sides to get x by itself.
x=16
So:
Issac worked 16 hours
Ruby worked 22 hours
Svetlana worked 88 hours.
To check your answer, plug in the values:
16+22+88=126
126=126
Hope this helps.
Answer:
25
Step-by-step explanation:
20 books in 4 months is 5 books in 1 month.
20÷4=5
4÷4=1
1×5=5
5×5=25
Price decrease = 14.3% of $52,000 = 0.143*$52,000 = $7,436
Price of next model = $52,000-$7,436 = $44,564
