Question

1. bill is building boxes of different sizes. the supplies are limited. he restricts the volume of each box to at most 3.5 ft³ and the base area to exactly 2.5 ft². an inequality that represents the range of possible box heights, h, is ft < h ≤ ft. 9. which graph shows the solution to the inequality 25 ≤ 2x + 5 ≤ 35? a graph with open circles at 40 and 60, line between b graph with closed circles at 40 and 60, line between c graph with open circles at 10 and 15, line between d graph with closed circles, line between (partial)

Explanation:

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Q8 Step1: Recall volume formula

Volume $V = \text{Base Area} \times h$

Q8 Step2: Substitute known values

$V = 2.5h$

Q8 Step3: Apply volume limit

$2.5h \leq 3.5$

Q8 Step4: Solve for maximum $h$

$h \leq \frac{3.5}{2.5} = 1.4$

Q8 Step5: Define minimum height

Height must be positive: $h > 0$

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Q9 Step1: Subtract 5 from all parts

$25 - 5 \leq 2x + 5 - 5 \leq 35 - 5$
$20 \leq 2x \leq 30$

Q9 Step2: Divide by 2 on all parts

$\frac{20}{2} \leq \frac{2x}{2} \leq \frac{30}{2}$
$10 \leq x \leq 15$

Q9 Step3: Match to graph

Closed dots at 10 and 15, shading between them (Option D)

Answer:

For Q8: $0$ ft $< h \leq 1.4$ ft
For Q9: D. (The graph with closed dots at 10 and 15, shading between them)