Question

question 3
youre sending a gift package to your cousins for the holidays. you need to decide which shipping company to use: ups or fedex.
ups charges a flat fee of $7, plus $0.20 per pound. fedex charges a flat fee of $5, plus $0.30 per pound.
you weigh your package, calculate the shipping cost, and realize that ups and fedex will cost the same! how much does your package weigh, in pounds?

2 pts
question 4
4 + k
2(k + 3)
part a: use the drop - down menu to choose the expression that best represents the perimeter (p) of this rectangle.
p = select
part b: the perimeter of the rectangle is 56 inches. what is the value of k?
k = select

Explanation:

Question 3

Step1: Set up cost - equations

Let $x$ be the weight of the package in pounds. The cost of UPS is $C_{UPS}=7 + 0.2x$, and the cost of FedEx is $C_{FedEx}=5+0.3x$.

Step2: Set costs equal

Since $C_{UPS}=C_{FedEx}$, we have $7 + 0.2x=5 + 0.3x$.

Step3: Solve for $x$

Subtract $0.2x$ from both sides: $7=5 + 0.3x-0.2x$. Then $7 = 5+0.1x$. Subtract 5 from both sides: $0.1x=7 - 5=2$. Divide both sides by 0.1: $x=\frac{2}{0.1}=20$.

Question 4

Part A

Step1: Recall perimeter formula

The perimeter of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width. Here, $l = 2(k + 3)$ and $w=4 + k$.

Step2: Expand and simplify

$P=2((4 + k)+2(k + 3))=2(4 + k+2k + 6)=2(3k + 10)=6k + 20$.

Part B

Step1: Set up equation

Since $P = 56$, we have $6k+20 = 56$.

Step2: Solve for $k$

Subtract 20 from both sides: $6k=56 - 20=36$. Divide both sides by 6: $k=\frac{36}{6}=6$.

Answer:

Question 3

20

Question 4

Part A

$6k + 20$

Part B

6