Question

unit 1 post test year long (total 61 pts) name: 10. (3 pts) what is the solution to the inequality 4(x - 5) < 1/2(4x - 16)? a x < 6 b. x > 6 c. x < 3 d. x > 3 11. (2 pts) sergio wants to buy both chicken and ham to serve at a holiday dinner. chicken costs $4.29 per pound, and ham costs $6.99 per pound. the maximum amount sergio can spend is $88.00. if x represents the number of pounds of chicken sergio buys, and y represents the number of pounds of ham he buys, which inequality represents the situation? a. 4.29x + 6.99y ≥ 88.00 b. 4.29x + 6.99y > 88.00 c. 4.29x + 6.99y ≤ 88.00 d. 4.29x + 6.99y < 88.00 12. (2 pts) set up and solve the proportion. daren can read 7 pages of his book in 5 minutes. at that rate, how many pages can he read in 50 minutes? 13. (3 pts) which expression is equivalent to 5m - 3n, when m = 3x - 2 and n = 2x - 5? a. 9x + 5 b. 9x - 25 c. 21x - 25 d. 21x + 25 14. (3 pts) solve and graph the inequality below. 14 - 2x > - 2 15. (2 pts) the formula r = d/2 can be used to find the radius of a circle, r, given the diameter d. given r, which equation finds d? a. d = 2r b. d = r + 2 c. d = r - 2 d. d = r/2 16. (3 pts) pete earns $8.50 per hour plus tips. on tuesday, he received $16 in tips. how many hours did pete work if he earned a total of $50 on tuesday? a. 7 b. 6 c. 5 d. 4 17. (3 pts) solve and graph the inequality below on a number line. 8x + 1 < 41

Explanation:

10.

Step1: Expand both sides

Expand $4(x - 5)$ to get $4x-20$, and expand $\frac{1}{2}(4x - 16)$ to get $2x-8$. So the inequality becomes $4x-20<2x - 8$.

Step2: Move like - terms

Subtract $2x$ from both sides: $4x-2x-20<2x-2x - 8$, which simplifies to $2x-20<-8$. Then add 20 to both sides: $2x-20 + 20<-8 + 20$, resulting in $2x<12$.

Step3: Solve for x

Divide both sides by 2: $\frac{2x}{2}<\frac{12}{2}$, so $x < 6$.

The cost of chicken is $4.29 per pound and the number of pounds of chicken is $x$, so the cost of chicken is $4.29x$. The cost of ham is $6.99 per pound and the number of pounds of ham is $y$, so the cost of ham is $6.99y$. The maximum amount Sergio can spend is $88.00$. So the inequality representing the situation is $4.29x+6.99y\leq88.00$.

Step1: Set up the proportion

The proportion is $\frac{7}{5}=\frac{p}{50}$, where $p$ is the number of pages.

Step2: Cross - multiply

Cross - multiplying gives $5p=7\times50$, so $5p = 350$.

Step3: Solve for p

Divide both sides by 5: $\frac{5p}{5}=\frac{350}{5}$, so $p = 70$.

Answer:

A. $x<6$

11.