Question

1. in a football game, the jaguars scored 21 more points than the colts did. together, the two teams scored a total of 55 points in the game. let j represent the points scored by the jaguars and c represent the points scored by the colts. which system of linear equations models the number of points scored by the jaguars and colts in this game? a. j + c = 21 j = 55 + c b. j = 21 + c j + c = 55 c. j - c = 21 j = 55 - c d. j = 21 - c j + c = 55 30. a trailer contains 500 pounds of mulch. agnes unloads the mulch from the trailer by filling a wheelbarrow with 25 pounds of mulch and then dumping the mulch from the wheelbarrow into a flowerbed. it takes agnes 4 minutes to fill the wheelbarrow and dump it in the flowerbed. which expression represents how much time it takes agnes to unload all of the mulch from the trailer using this process? a. (500 pounds) × 25 pounds / 1 wheelbarrow × 4 minutes / 1 wheelbarrow b. (500 pounds) × 1 wheelbarrow / 25 pounds × 4 minutes / 1 wheelbarrow c. (500 pounds) × 25 pounds / 1 wheelbarrow × 1 wheelbarrow / 4 minutes d. (500 pounds) × 1 wheelbarrow / 25 pounds × 1 wheelbarrow / 4 minutes 32. mr. howard is monitoring the growth of a bacteria culture. the function p(t) = 3,100(1.12)^t models the bacteria population t weeks after mr. howard begins monitoring the culture. what does p(4) represent in this context? a. 4 times the initial population of the bacteria culture b. the number of bacteria in the culture after 4 weeks of monitoring c. the number of weeks it takes the bacteria population to grow to 4 times its initial size d. 4 times the number of weeks since mr. howard began monitoring the bacterial culture 41. a cyclist pedals from the bottom to the top of a hill at a constant speed of 6 feet per second. during the climb, the distance from the cyclist to the top of the hill can be modeled by the formula d = b - 6c. for each quantity listed in the table, identify the variable in the formula which represents that quantity. select the correct circle in each row. quantity d b c the number of seconds since the cyclist began climbing the hill the total distance, in feet, from the bottom to the top of the hill the remaining distance, in feet, from the cyclist to the top of the hill

Explanation:

Question 29

Step1: Analyze the first condition

The Jaguars scored 21 more points than the Colts, so \( j = c + 21 \) (which can be rewritten as \( j - c = 21 \)).

Step2: Analyze the second condition

Together, the two teams scored a total of 55 points, so \( j + c = 55 \).
Looking at the options, option B has \( j = 21 + c \) (equivalent to \( j - c = 21 \)) and \( j + c = 55 \), which matches the two conditions.

Step1: Determine the number of wheelbarrows needed

To find the number of wheelbarrows, we need to divide the total pounds (500) by the pounds per wheelbarrow (25). This is represented by \( \frac{1\text{ wheelbarrow}}{25\text{ pounds}} \) (since we want to find how many wheelbarrows are in 500 pounds, we multiply 500 pounds by \( \frac{1\text{ wheelbarrow}}{25\text{ pounds}} \)).

Step2: Determine the time per wheelbarrow

Each wheelbarrow takes 4 minutes, so we multiply the number of wheelbarrows by \( \frac{4\text{ minutes}}{1\text{ wheelbarrow}} \).
Putting it together, the expression is \( (500\text{ pounds}) \times \frac{1\text{ wheelbarrow}}{25\text{ pounds}} \times \frac{4\text{ minutes}}{1\text{ wheelbarrow}} \), which is option B.

The function \( P(t)=3000(1.12)^t \) models the bacteria population \( t \) weeks after monitoring begins. When \( t = 4 \), \( P(4) \) represents the population (number of bacteria) after 4 weeks of monitoring. Option A is incorrect because it's not 4 times the initial population (the growth is exponential, not linear multiplication by 4). Option C is incorrect as \( P(t) \) is about population, not time to grow. Option D is incorrect as \( t = 4 \) is the number of weeks, not 4 times the weeks.

Answer:

B. \(

$$\begin{cases} j = 21 + c \\ j + c = 55 \end{cases}$$

\)

Question 30