The function F (t) = -16t^{2} + 64t + 5 represents the height (in feet) of a pumpkin t seconds after being launched from a catapult. What is the maximum height of the pumpkin as it flies through the air? Enter your answer as a number without units.

69

Step-by-step explanation:

-16t^2 +64t +5

= -16t(t-4) +5

so since t can't be negative then t-4<0 with t positive

so t =2

-16(2) × -2 +5 = 64+5 = 69

a) at most means it can cost $12 or less

so the inequality sign would be ≤

you would then need to multiply the number of toppings by the 0.35 for each one and add it to the cost of the cheese pizza.

the equation would be 9.99 + 0.35x ≤ 12

b) using the above equation:

9.99 + 0.35x ≤ 12

subtract 9.99 from each side:

0.35x ≤2.01

divide both sides by 0.35:

x ≤ 2.01 / 0.35

x ≤5.74

at most you could have 5 toppings.

the 5 topping pizza would cost: 0.35 x 5 = 1.75 + 9.99 = $11.74