The zeroes of <span>f(x) = x^5-12x^2+32x can be found by factoring,
</span><span>f(x) = x^5-12x^2+32x=(x-8)(x-4)
By the zero product theorem, (x-8)=0 or (x-4)=0 which means
x=8 or x=4.
So the zeroes of f(x) are S={4,8}</span>
Since the photo booth charges a $500 fee for two hours at the party and an additional 50 dollars per hour, we have:
50x+500=C
Where x is the hours stayed and C is the total cost. Since Cindy doesn't want to spend more than 700 dollars, we have:

So she spent an additional 4 hours on the rental.
Answer:
The solution of the system of equations is (11, 12)
Step-by-step explanation:
∵ The price of each student ticket is $x
∵ The price of each adult ticket is $y
∵ They sold 3 student tickets and 3 adult tickets for a total of $69
∴ 3x + 3y = 69 ⇒ (1)
∵ they sold 5 student tickets and 3 adults tickets for a total of $91
∴ 5x + 3y = 91 ⇒ (2)
Let us solve the system of equations using the elimination method
→ Subtract equation (1) from equation (2)
∵ (5x - 3x) + (3y - 3y) = (91 - 69)
∴ 2x + 0 = 22
∴ 2x = 22
→ Divide both sides by 2 to find x
∵ 
∴ x = 11
→ Substitute the value of x in equation (1) or (2) to find y
∵ 3(11) + 3y = 69
∴ 33 + 3y = 69
→ Subtract 33 from both sides
∵ 33 - 33 + 3y = 69 - 33
∴ 3y = 36
→ Divide both sides by 3
∵ 
∴ y = 12
∴ The solution of the system of equations is (11, 12)
143/7 + (11-9)
143/7 + 2
143/7 + 14/7
143+14/7
157/7
Alternative form 22 3/7