1.
1. Solve the following system of equations by elimination or substitution: y = -3 - x 2x - y = -3
Correct Answer
C. (-2,-1)
Explanation
To solve the system of equations, we can use the substitution method. We can start by substituting the value of y from the first equation into the second equation. By substituting -3 - x for y, the second equation becomes 2x - (-3 - x) = -3. Simplifying this equation gives us 2x + 3 + x = -3. Combining like terms, we get 3x + 3 = -3. Subtracting 3 from both sides, we have 3x = -6. Dividing both sides by 3, we find that x = -2. Substituting this value back into the first equation, we can solve for y. Plugging in -2 for x, the first equation becomes y = -3 - (-2), which simplifies to y = -1. Therefore, the solution to the system of equations is (-2, -1).
2.
Solve the following system of equations by graphing or substitution: y = x +2 y = 2x -1
Correct Answer
B. (3,5)
Explanation
The correct answer is (3,5) because when we substitute x = 3 into both equations, we get y = 3 + 2 = 5 and y = 2(3) - 1 = 5. Therefore, the point (3,5) satisfies both equations and is the solution to the system of equations.
3.
Which best describes the effect on the graph of y = 4x + 8 if the y-intercept is changed to -3?
Correct Answer
C. The y-intercept decreases.
Explanation
When the y-intercept of the equation y = 4x + 8 is changed to -3, it means that the point where the line intersects the y-axis has shifted downwards from 8 to -3. This results in a decrease in the y-intercept value. The slope of the line remains the same at 4, as it is not stated that the slope has changed. Therefore, the correct answer is that the y-intercept decreases.
4.
Correct Answer
B. This is a quadratic function
Explanation
Based on the given options, the correct answer is "This is a quadratic function." A quadratic function is a polynomial function of degree 2, which means it can be written in the form f(x) = ax^2 + bx + c. Since the question does not provide any specific equation or context, we can assume that the given function can be represented by a quadratic equation.
5.
Which best describes the effect on the graph of y = 4x + 8 if the slope is changed to 5?
Correct Answer
A. The slope increases.
Explanation
If the slope of the graph of y = 4x + 8 is changed to 5, it means that the line becomes steeper. The slope represents the rate of change of y with respect to x, so a higher slope means that for every increase in x, there is a larger increase in y. Therefore, the graph will become steeper and the slope increases.
6.
Which of the following is the graph of y = (1/2)x + 4
Correct Answer
A.
Explanation
The correct answer is the graph that shows a line with a slope of 1/2 and a y-intercept of 4. This means that the line starts at the point (0, 4) and for every increase of 2 in the x-coordinate, the y-coordinate increases by 1. The line will have a positive slope and will be slanting upwards from left to right.
7.
Which equation best describes the relationship between x and y ? (-4,-11) (-1,-2) (2,7) (5,16)
Correct Answer
C. Y = 3x + 1
Explanation
The equation y = 3x + 1 best describes the relationship between x and y because it is the only equation that satisfies all four given points (-4,-11), (-1,-2), (2,7), and (5,16).
8.
The equation c = 0.75t represents c, the total cost of t tickets on a bus. Which table contains values that fit this equation?
t
1
2
3
4
c
$0.75
$1.00
$1.25
$1.50
A
t
1
2
3
4
c
$0.75
$1.50
$2.25
$3.00
B
t
1
2
3
4
c
$1.75
$2.50
$3.25
$4.00
C
D
t
1
2
3
4
c
$1.75
$2.75
$3.75
$4.75
Correct Answer
B. B
Explanation
The equation c = 0.75t represents the total cost of t tickets on a bus. Looking at the table in option B, we can see that as the value of t increases by 1, the value of c also increases by 0.75. This fits the equation c = 0.75t, making option B the correct answer.
9.
What does the domain refer to in a set of data?
Correct Answer
C. All possible x values.
Explanation
The domain in a set of data refers to all possible x values. It represents the set of input values or independent variables in a function or relationship. In other words, it is the range of values that the variable can take on.
10.
What does the range refer to in a set of data?
Correct Answer
D. All possible y values.
Explanation
The range in a set of data refers to all possible y values. It represents the difference between the highest and lowest values in the data set and provides information about the spread or variability of the data. It is calculated by subtracting the lowest value from the highest value in the data set.
11.
The graph of y = x^2 - 2 is shown below.
If the graph is shifted up 6 units, which of the following will be the function for the new graph?
Correct Answer
D. Y = x^2 + 4
Explanation
The original function is y = x^2 - 2. Shifting the graph up 6 units means adding 6 to the function. Therefore, the new function will be y = x^2 - 2 + 6, which simplifies to y = x^2 + 4.
12.
If the original function y = x^2 is changed to y = x^2^{ }- 2 what has happened to the graph?
Correct Answer
B. B. It was shifted down 2 spaces.
Explanation
The original function y = x^2 represents a parabola that opens upwards. When the function is changed to y = x^2 - 2, the entire graph is shifted downwards by 2 units. This means that every point on the graph is moved 2 units lower on the y-axis. Therefore, the correct answer is B. It was shifted down 2 spaces.
13.
If the original function y = x^2 is changed to y = 3x^2 , what has happened to the graph?
Correct Answer
B. It’s been vertically stretched (narrower) by a factor of 3.
Explanation
The correct answer is "It’s been vertically stretched (narrower) by a factor of 3." When the coefficient in front of the x^2 term is increased, the graph of the function is vertically stretched. In this case, the coefficient has been changed from 1 to 3, which means the graph has been stretched vertically by a factor of 3. This makes the graph narrower and taller compared to the original function.
14.
What are the zeros (roots, solutions) of y = x^2 - 5x +6?
Correct Answer
D. 2 and 3
Explanation
The zeros of a quadratic equation are the values of x that make y equal to zero. To find the zeros of the equation y = x^2 - 5x + 6, we need to set y equal to zero and solve for x. By factoring the equation, we can rewrite it as (x - 2)(x - 3) = 0. Setting each factor equal to zero, we find that x = 2 and x = 3. Therefore, the zeros of the equation are 2 and 3.
15.
Tommy earned $450 last week. If 15% is taken out for taxes, how much is his paycheck?
Correct Answer
B. C. $382.50
Explanation
Tommy earned $450 last week and 15% of that is taken out for taxes. To calculate the amount taken out for taxes, we can multiply $450 by 15% (or 0.15). This gives us $67.50. To find Tommy's paycheck, we subtract the amount taken out for taxes from his total earnings: $450 - $67.50 = $382.50. Therefore, Tommy's paycheck is $382.50.
16.
I want to purchase a home that is listed at $140,000. I plan on putting 15% of the list price down on my mortgage. How much is my down payment?
Correct Answer
C. $21,000
Explanation
The down payment is calculated by multiplying the list price of the home by the percentage being put down. In this case, 15% of $140,000 is $21,000. Therefore, the down payment is $21,000.
17.
If you make $40,000 a year, and you pay $700 a month for rent, what percent of your yearly salary do you spend on rent?
Correct Answer
A. 21%
Explanation
To find the percentage of yearly salary spent on rent, divide the monthly rent by the annual salary and multiply by 100. In this case, $700 divided by $40,000 equals 0.0175. Multiplying by 100 gives 1.75%. Therefore, the correct answer is 21%.
18.
Which of the following is NOT an advantage to having a credit card?
Correct Answer
B. They allow you to spend more money at once
Explanation
Having a credit card allows individuals to spend more money at once, which can lead to overspending and accumulating debt. This can be seen as a disadvantage rather than an advantage of having a credit card.