C 957 | C957 Final Exam: Applied Algebra Updated
and Latest Questions and Correct Answers with
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1. A local gym charges a one-time registration fee of $50 and a monthly fee of $30. If a
member has paid a total of $410, which linear equation represents the number of months, m,
they have been a member?
A. 30m + 50 = 410
B. 50m + 30 = 410
C. 80m = 410
D. 30m - 50 = 410
Correct Answer: A
Explanation: To solve this problem, we must identify the fixed and variable costs. The $50
registration fee is a one-time constant, while the $30 monthly fee depends on the number
of months. Thus, the variable term is 30m and the constant is 50. Setting the sum of these
equal to the total cost gives us the correct equation. Therefore, 30m + 50 = 410 is the
accurate mathematical model for this scenario.
2. Solve the following linear inequality for x: 4(x - 3) + 2 > 14.
A. x < 6
B. x > 6
C. x > 3
D. x > 5
Correct Answer: B
Explanation: We begin by distributing the 4 into the parentheses to get 4x - 12 + 2 > 14.
Combining like terms results in the inequality 4x - 10 > 14. Next, we add 10 to both sides to
isolate the variable term, giving 4x > 24. Dividing both sides by 4 yields the solution x > 6.
This logical sequence of steps ensures that the inequality maintains its direction
throughout the process.
3. What is the y-intercept of the linear function f(x) = -2x + 7?
A. (-2, 0)
B. (0, 7)
C. (7, 0)
D. (0, -2)
,Correct Answer: B
Explanation: The y-intercept of a function occurs where the value of x is zero. Substituting
x = 0 into the equation f(x) = -2(0) + 7 simplifies the expression immediately. This leaves us
with f(0) = 7, which represents the y-coordinate of the intercept. In coordinate form, this
point is expressed as (0, 7). This confirms the starting point of the linear graph on the
vertical axis.
4. A car’s value depreciates according to the model V(t) = 25000(0.85)^t, where t is years.
What is the annual rate of depreciation?
A. 85%
B. 0.85%
C. 25%
D. 15%
Correct Answer: D
Explanation: In an exponential decay model of the form y = a(b)^t, the base b represents
the decay factor. The decay factor is calculated as 1 minus the rate of depreciation. Here,
the factor is 0.85, so we solve the equation 1 - r = 0.85. Subtracting 0.85 from 1 gives a rate
of 0.15, or 15%. This percentage represents the portion of value lost by the car each year.
5. Find the slope of the line passing through the points (2, 5) and (4, 13).
A. 4
B. 2
C. 8
D. 1/4
Correct Answer: A
Explanation: The slope of a line is defined as the change in y divided by the change in x.
Using the slope formula (y2 - y1) / (x2 - x1), we substitute the given points. This calculation
results in (13 - 5) / (4 - 2), which simplifies to . Further simplification yields a final
slope value of 4. This numerical value represents the constant rate of change for the linear
relationship.
6. Which of the following describes the end behavior of the polynomial function f(x) = -3x^4 +
2x^2 - 5?
A. As x approaches infinity, f(x) approaches negative infinity.
B. As x approaches infinity, f(x) approaches infinity.
C. As x approaches negative infinity, f(x) approaches infinity.
, D. The graph starts low and ends high.
Correct Answer: A
Explanation: The end behavior of a polynomial is determined by its leading term, which is
-3x^4. Since the degree is even, both ends of the graph will point in the same direction.
Because the leading coefficient is negative, the graph opens downward on both sides.
Therefore, as x goes to either positive or negative infinity, the function values decrease
without bound. This leads to the conclusion that f(x) approaches negative infinity in both
directions.
7. Solve the system of equations: 2x + y = 10 and x - y = 2.
A. (2, 6)
B. (3, 4)
C. (6, -2)
D. (4, 2)
Correct Answer: D
Explanation: This system can be solved efficiently using the elimination method by adding
the two equations together. Adding (2x + y) and (x - y) eliminates the y variable, resulting
in 3x = 12. Dividing by 3 gives the value x = 4. Substituting x = 4 back into the second
equation (4 - y = 2) allows us to solve for y. This step results in y = 2, making the final
solution point (4, 2).
8. What is the vertex of the quadratic function f(x) = (x - 3)^2 + 5?
A. (-3, 5)
B. (3, 5)
C. (3, -5)
D. (5, 3)
Correct Answer: B
Explanation: The given quadratic function is already written in vertex form, which is f(x) =
a(x - h)^2 + k. In this form, the vertex is represented by the coordinates (h, k). Looking at
the expression (x - 3)^2 + 5, we identify h as 3 and k as 5. It is important to remember that
the sign inside the parentheses is subtracted. Thus, the vertex of the parabola is located at
the point (3, 5).
9. A population of bacteria doubles every hour. If there are 100 bacteria initially, which
function models the population P after t hours?
A. P(t) = 100 + 2t
B. P(t) = 2(100)^t
and Latest Questions and Correct Answers with
Rationale - WGU
1. A local gym charges a one-time registration fee of $50 and a monthly fee of $30. If a
member has paid a total of $410, which linear equation represents the number of months, m,
they have been a member?
A. 30m + 50 = 410
B. 50m + 30 = 410
C. 80m = 410
D. 30m - 50 = 410
Correct Answer: A
Explanation: To solve this problem, we must identify the fixed and variable costs. The $50
registration fee is a one-time constant, while the $30 monthly fee depends on the number
of months. Thus, the variable term is 30m and the constant is 50. Setting the sum of these
equal to the total cost gives us the correct equation. Therefore, 30m + 50 = 410 is the
accurate mathematical model for this scenario.
2. Solve the following linear inequality for x: 4(x - 3) + 2 > 14.
A. x < 6
B. x > 6
C. x > 3
D. x > 5
Correct Answer: B
Explanation: We begin by distributing the 4 into the parentheses to get 4x - 12 + 2 > 14.
Combining like terms results in the inequality 4x - 10 > 14. Next, we add 10 to both sides to
isolate the variable term, giving 4x > 24. Dividing both sides by 4 yields the solution x > 6.
This logical sequence of steps ensures that the inequality maintains its direction
throughout the process.
3. What is the y-intercept of the linear function f(x) = -2x + 7?
A. (-2, 0)
B. (0, 7)
C. (7, 0)
D. (0, -2)
,Correct Answer: B
Explanation: The y-intercept of a function occurs where the value of x is zero. Substituting
x = 0 into the equation f(x) = -2(0) + 7 simplifies the expression immediately. This leaves us
with f(0) = 7, which represents the y-coordinate of the intercept. In coordinate form, this
point is expressed as (0, 7). This confirms the starting point of the linear graph on the
vertical axis.
4. A car’s value depreciates according to the model V(t) = 25000(0.85)^t, where t is years.
What is the annual rate of depreciation?
A. 85%
B. 0.85%
C. 25%
D. 15%
Correct Answer: D
Explanation: In an exponential decay model of the form y = a(b)^t, the base b represents
the decay factor. The decay factor is calculated as 1 minus the rate of depreciation. Here,
the factor is 0.85, so we solve the equation 1 - r = 0.85. Subtracting 0.85 from 1 gives a rate
of 0.15, or 15%. This percentage represents the portion of value lost by the car each year.
5. Find the slope of the line passing through the points (2, 5) and (4, 13).
A. 4
B. 2
C. 8
D. 1/4
Correct Answer: A
Explanation: The slope of a line is defined as the change in y divided by the change in x.
Using the slope formula (y2 - y1) / (x2 - x1), we substitute the given points. This calculation
results in (13 - 5) / (4 - 2), which simplifies to . Further simplification yields a final
slope value of 4. This numerical value represents the constant rate of change for the linear
relationship.
6. Which of the following describes the end behavior of the polynomial function f(x) = -3x^4 +
2x^2 - 5?
A. As x approaches infinity, f(x) approaches negative infinity.
B. As x approaches infinity, f(x) approaches infinity.
C. As x approaches negative infinity, f(x) approaches infinity.
, D. The graph starts low and ends high.
Correct Answer: A
Explanation: The end behavior of a polynomial is determined by its leading term, which is
-3x^4. Since the degree is even, both ends of the graph will point in the same direction.
Because the leading coefficient is negative, the graph opens downward on both sides.
Therefore, as x goes to either positive or negative infinity, the function values decrease
without bound. This leads to the conclusion that f(x) approaches negative infinity in both
directions.
7. Solve the system of equations: 2x + y = 10 and x - y = 2.
A. (2, 6)
B. (3, 4)
C. (6, -2)
D. (4, 2)
Correct Answer: D
Explanation: This system can be solved efficiently using the elimination method by adding
the two equations together. Adding (2x + y) and (x - y) eliminates the y variable, resulting
in 3x = 12. Dividing by 3 gives the value x = 4. Substituting x = 4 back into the second
equation (4 - y = 2) allows us to solve for y. This step results in y = 2, making the final
solution point (4, 2).
8. What is the vertex of the quadratic function f(x) = (x - 3)^2 + 5?
A. (-3, 5)
B. (3, 5)
C. (3, -5)
D. (5, 3)
Correct Answer: B
Explanation: The given quadratic function is already written in vertex form, which is f(x) =
a(x - h)^2 + k. In this form, the vertex is represented by the coordinates (h, k). Looking at
the expression (x - 3)^2 + 5, we identify h as 3 and k as 5. It is important to remember that
the sign inside the parentheses is subtracted. Thus, the vertex of the parabola is located at
the point (3, 5).
9. A population of bacteria doubles every hour. If there are 100 bacteria initially, which
function models the population P after t hours?
A. P(t) = 100 + 2t
B. P(t) = 2(100)^t
