Question

1 multiple answer 1 point
find the 2 factors of ( 6x^2 - 14x - 15 )
( (2x + 3) )
( (4x + 5) )
( (4x + 3) )
( (2x - 5) )
( (4x - 3) )
( (2x - 3) )
( (4x - 5) )
( (2x + 5) )

7 numeric 1 point
the cost function for a t - shirt sales school fundraiser is given by ( c = $72 + $3.52t ), where ( t ) is the number of t - shirts and ( c ) is the total cost the students had to pay for the t - shirts (including shipping and handling). the revenue is given by the function ( r=$15t ), where ( t ) is the number of t - shirts sold and ( r ) is the total revenue (money received for selling the t - shirts). how many t - shirts must be sold in order for the student to reach their goal of raising $820 to donate to the childrens hospital?
answer

10 numeric 1 point
a cannery processed 425 pounds of strawberries in 2.5 hours. the cannery processed 2150 pounds in 10 hours.
how many pounds of strawberries can be processed in 8 hours?
answer

Explanation:

Problem 1

Step1: Factor quadratic expression

We need two binomials $(ax+b)(cx+d)$ such that $ac=8$, $bd=-15$, and $ad+bc=-14$. Test factor pairs of 8 and -15:
For $a=2, c=4$, $b=3, d=-5$: $2*(-5)+4*3=-10+12=2$ (incorrect).
For $a=4, c=2$, $b=3, d=-5$: $4*(-5)+2*3=-20+6=-14$ (correct).
So $8x^2-14x-15=(4x+3)(2x-5)$

Step1: Define profit function

Profit $P = R - C$. Substitute given functions:
$P = 15t - (7t + 352)$

Step2: Simplify profit function

$P = 15t -7t -352 = 8t - 352$

Step3: Set profit to target

Set $P=800$ and solve for $t$:
$8t - 352 = 800$

Step4: Solve for t

Add 352 to both sides: $8t = 800 + 352 = 1152$
Divide by 8: $t = \frac{1152}{8}=144$

Step1: Find hourly processing rate

First rate: $\frac{425}{2.5}=170$ pounds/hour
Verify second rate: $\frac{2150}{10}=215$ pounds/hour. Use the consistent rate (second rate is the verified steady rate)

Step2: Calculate 8-hour output

Multiply hourly rate by 8: $215*8=1720$

Answer:

(4x + 3), (2x - 5)

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Problem 7