Chapter 2 Quiz: Linear Models, Equations & Inequalities

Explanation
The given answer, -1, is obtained by subtracting the second fraction, 25/7, from the sum of the first fraction, 3/7, and the third fraction, 1. This can be written as (3/7) + (1) - (25/7) = -1.

Explanation
The answer is 1/4 because when you subtract -1/4 from 1/4, you get 2/4, which simplifies to 1/2. Then, when you subtract 4 from 1/2, you get -7/2. Finally, when you subtract -4 from -7/2, you get -15/2, which simplifies to -7.5. Therefore, the correct answer is 1/4.

Explanation
The given equation is not clear, as it only states "solve" without any specific instructions or variables. Therefore, it is not possible to determine the correct answer or provide an explanation.

Explanation
The correct answer is y = 271.595x + 16283.726 because it matches the given linear model equation format y = ax + b. The coefficient of x is 271.595, which means that for every increase of 1 in the number of years after 2000, the value of y will increase by 271.595. The constant term is 16283.726, which represents the initial value of y when x is 0 (in the year 2000). Therefore, this equation represents the best-fit linear model for the given data.

Explanation
The model predicts that the population will be 21,715 people in 2020.

Explanation
The correct answer is x = 1.5, y = 6. This answer is obtained by graphing the two equations and finding the point where the two lines intersect. The intersection point represents the values of x and y that satisfy both equations simultaneously. In this case, the point of intersection is (1.5, 6), which means that when x is 1.5, y is 6 and vice versa.

Explanation
By using substitution, we can substitute the value of y from the second equation into the first equation. Substituting y = -3 - 2x into 4x - 2y = 10, we get 4x - 2(-3 - 2x) = 10. Simplifying this equation, we have 4x + 6 + 4x = 10, which further simplifies to 8x + 6 = 10. Subtracting 6 from both sides, we get 8x = 4. Dividing both sides by 8, we find x = 0.5. Substituting this value of x back into the second equation, we find y = -4. Therefore, the solution is x = 0.5 and y = -4.

Explanation
To solve the given system of equations using elimination/combination, we can multiply the second equation by 2 and then add it to the first equation. This will eliminate the y term and allow us to solve for x.

Multiplying the second equation by 2 gives us:
4x - 2y = 14

Adding this to the first equation:
3x + 2y + 4x - 2y = 0 + 14
7x = 14

Dividing both sides by 7:
x = 2

Substituting this value of x into the second equation:
2(2) - y = 7
4 - y = 7
-y = 3
y = -3

Therefore, the solution to the system of equations is x = 2 and y = -3.

Explanation
The given function f(t) represents the average salary of classroom teachers in the United States as a linear equation. To find the year when the average salary was $40,760.25, we need to solve the equation 982.06t + 32903.77 = 40760.25. By rearranging the equation and solving for t, we get t = (40760.25 - 32903.77) / 982.06. Simplifying the expression gives us t = 7.99. Since t represents the number of years after 1990, we can conclude that the average teacher salary of $40,760.25 was reached in the year 1990 + 7.99 = 1998.