Question

1. (4 pts) the length of a rectangle is 5 less than twice the width. if the perimeter of the rectangle is 146, find the length and width of the rectangle. length = ______ width = ______ 2. (3 pts) find three consecutive odd integers with a sum of 123. 3. (3 pts) solve the equation. 7(p + 3)+9 = 5(p - 2)-3p 4. (3 pts) what is the solution to the inequality -2(x + 2)<8 - x shown? 5. (3 pts) abby scored 87, 93, 96, and 89 on her first four math quizzes. what score does abby need to get on her fifth quiz to have an average of exactly 91 on her math quizzes? a. 90 b. 94 c. 98 d. 100 6. (3 pts) the cost for a pool membership for a family at a community pool is $350 plus $125 per month. a family paid a total of $1,350. how many months did the family use the pool? a. 8 b. 11 c. 12 d. 14 7. (2 pts) what value of r makes (2r + 3)/5=(4r - 3)/7 true? a. -2 b. -1 c. 2 d. 6 8. (3 pts) solve the literal equation (x + y)/3 = 5 for x. 9. (3 pts) what is the value of x in this equation: 1 - 3(x - 7)=6x + 4

Explanation:

1.

Step1: Define variables

Let the width of the rectangle be $w$. Then the length $l = 2w - 5$.

Step2: Use the perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 146$, so $146=2((2w - 5)+w)$.

Step3: Simplify the equation

First, simplify the right - hand side: $146=2(3w - 5)=6w-10$.

Step4: Solve for $w$

Add 10 to both sides: $146 + 10=6w$, so $156 = 6w$. Then $w=\frac{156}{6}=26$.

Step5: Solve for $l$

Substitute $w = 26$ into the length formula: $l=2w - 5=2\times26-5=52 - 5 = 47$.

Step1: Define the consecutive odd integers

Let the first odd integer be $n$. Then the next two consecutive odd integers are $n + 2$ and $n+4$.

Step2: Set up the equation

The sum of the three consecutive odd integers is $n+(n + 2)+(n + 4)=123$.

Step3: Simplify the equation

Combine like terms: $3n+6 = 123$.

Step4: Solve for $n$

Subtract 6 from both sides: $3n=123 - 6=117$. Then $n=\frac{117}{3}=39$.
The three consecutive odd integers are 39, 41, 43.

Step1: Expand the equation

$7(p + 3)+9=5(p - 2)-3p$. Expand to get $7p+21 + 9=5p-10-3p$.

Step2: Simplify both sides

$7p + 30=2p-10$.

Step3: Move the terms with $p$ to one side

Subtract $2p$ from both sides: $7p-2p+30=2p-2p - 10$, so $5p+30=-10$.

Step4: Move the constant to the other side

Subtract 30 from both sides: $5p=-10 - 30=-40$.

Step5: Solve for $p$

$p=\frac{-40}{5}=-8$.

Answer:

Length = 47, Width = 26

2.