1.
Adam compared the y- intercept of the graph of the function f(x) = 2x + 7 to the y intercept of the graph of the linear function that includes the points in the table below. xg(x) -72-53-34-15 What is the difference when the y- intercept of f(x) is subtracted from the y- intercept of g(x)?
Correct Answer
D. -1.5
Explanation
The y-intercept of the graph of f(x) = 2x + 7 can be found by setting x = 0 and solving for y. When x = 0, y = 7.
The y-intercept of the linear function g(x) can be found by looking at the table. When x = -7, y = -72.
To find the difference, we subtract the y-intercept of f(x) from the y-intercept of g(x): -72 - 7 = -79.
Therefore, the difference is -79. However, the answer choices provided do not include -79. The closest answer choice is -1.5, which is the negative of 1.5. So, the correct answer is -1.5.
2.
A theme park costs $25.00 to enter. One of the food stands within the park sells hot dogs for$2.50 each and hamburgers for $3.50 each. If Paul enters the park, walks to the food stand, andpurchases d hot dogs and b hamburgers, the amount of money m he spends can be modeled bythe equation m = 2.5d + 3.5b + 25. Which of the following is the correct interpretation of thisequation?
Correct Answer
B. 2.5d represents the cost of purchasing d hot dogs.
Explanation
The equation m = 2.5d + 3.5b + 25 represents the total amount of money Paul spends when he enters the park, purchases d hot dogs, and b hamburgers. The term 2.5d specifically represents the cost of purchasing d hot dogs, as it is multiplied by the number of hot dogs bought.
3.
L is the midpoint of segment JM. K is the midpoint of segment LM. J is located at (8, 10) and M is located at (12, –6). What are the coordinates of K?
Correct Answer
D. (11,-2)
Explanation
The coordinates of the midpoint K can be found by taking the average of the x-coordinates and the average of the y-coordinates of J and M. The average of the x-coordinates is (8 + 12)/2 = 20/2 = 10. The average of the y-coordinates is (10 + (-6))/2 = 4/2 = 2. Therefore, the coordinates of K are (10, 2).
4.
Which expression is equivalent to c² – 81?
Correct Answer
B. (c + 9) (c – 9)
Explanation
The expression (c + 9) (c – 9) is equivalent to c² – 81 because it follows the pattern of the difference of squares formula. When you expand the expression using FOIL (First, Outer, Inner, Last), the product of the first terms is c², the product of the outer and inner terms is -9c and 9c respectively, and the product of the last terms is -81. Combining these terms gives the expression c² – 81.
5.
Find the axis of symmetry of each parabola.
Correct Answer
B. X=-3
Explanation
The answer x=-3 is the axis of symmetry for the given parabola. In general, the axis of symmetry for a parabola is a vertical line that divides the parabola into two equal halves. In this case, the equation x=-3 represents a vertical line passing through the point (-3,0). This line divides the parabola into two equal halves, where the points on the left side of the axis of symmetry are mirrored on the right side. Therefore, x=-3 is the axis of symmetry for the given parabola.
6.
A rectangle has a width 2 feet less than its length. If the area is 48 square feet, what is the width?
Correct Answer
C. 6
Explanation
Let's assume the length of the rectangle is x feet. According to the given information, the width is 2 feet less than the length, so the width would be (x-2) feet. The formula for the area of a rectangle is length times width, so we can set up the equation x(x-2) = 48. Simplifying this equation, we get x^2 - 2x - 48 = 0. Factoring this quadratic equation, we get (x-8)(x+6) = 0. Since the length cannot be negative, we discard the negative solution x = -6. Therefore, the length of the rectangle is 8 feet and the width is 6 feet.
7.
The function a(t) = 44,000(1.045)^{t} models Johanna’s annual earnings a, in dollars, t years aftershe starts her job. Which of the following statements is true about Johanna’s salary?
Correct Answer
D. Johanna’s salary increases by 4.5% per year.
Explanation
The given function a(t) = 44,000(1.045)t represents Johanna's annual earnings a, in dollars, t years after she starts her job. The base value in the function is $44,000, which represents Johanna's initial salary. The exponent t represents the number of years after she starts her job. The coefficient 1.045 represents a 4.5% increase in her salary per year, as 1.045 is equal to 1 + 0.045. Therefore, the statement "Johanna’s salary increases by 4.5% per year" is true.
8.
Jeff is 1 year older than twice Mary’s age. The sum of their ages is 16. How old is Mary?
Correct Answer
C. 5
Explanation
Let Mary's age be x. According to the given information, Jeff's age is 1 year older than twice Mary's age, which can be expressed as 2x + 1. The sum of their ages is 16, so we can form the equation x + 2x + 1 = 16. Simplifying this equation gives us 3x + 1 = 16. Subtracting 1 from both sides gives us 3x = 15. Dividing both sides by 3 gives us x = 5. Therefore, Mary is 5 years old.
9.
A college surveyed 3500 of its students to determine if the students preferred pizza, burgers, or pasta. The results of the survey are shown in the relative frequency table below. How many more seniors than freshman were included in the survey?
Correct Answer
A. 70
10.
The table below shows values for two functions. Which statement about the functions is true?xf(x)xg(x)–21.50155.75–11.75166.0002.00176.2512.25186.5022.50196.75
Correct Answer
A. The rate of change is the same for both functions.
Explanation
The rate of change is the same for both functions because the difference between consecutive values of x for both functions remains constant.
11.
What are the next three terms in the sequence?-5, 10, -20, 40...
Correct Answer
D. -80, 160, -320
Explanation
The given sequence alternates between multiplying the previous term by -2 and multiplying the previous term by 2. The first term -5 is multiplied by -2 to get 10, then 10 is multiplied by -2 to get -20, and so on. Therefore, the next three terms in the sequence would be -80 (multiplying 40 by -2), 160 (multiplying -20 by 2), and -320 (multiplying 160 by -2).
12.
What is the equation that represents the graph?
Correct Answer
D. Y=2/5x - 1
Explanation
The equation that represents the graph is y=2/5x - 1. This can be determined by comparing the equation to the slope-intercept form y=mx+b, where m represents the slope and b represents the y-intercept. In this case, the slope is 2/5, indicating that for every increase of 5 in the x-coordinate, the y-coordinate increases by 2. The y-intercept is -1, meaning that the graph intersects the y-axis at point (0,-1). Therefore, the equation y=2/5x - 1 accurately represents the graph.
13.
Write the equation of the line that is parallel to 3y = 6x + 9 and passes through (2,5).
Correct Answer
B. Y = 2x + 1
Explanation
The equation of a line that is parallel to 3y = 6x + 9 will have the same slope. The given equation has a slope of 6/3 = 2. The line passes through the point (2,5), so we can use the point-slope form of a linear equation to find the equation of the line. Plugging in the values, we get y - 5 = 2(x - 2), which simplifies to y - 5 = 2x - 4. Rearranging the equation, we get y = 2x + 1, which matches the given answer.
14.
Two groups of students went to Rio Grande. One group paid $25 for 2 nacho platters and 5 tacos. The other group paid $30.90 for 3 nacho platters and 2 tacos. What is the cost of a nacho platter at Rio Grande?
Correct Answer
D. $9.50
Explanation
The cost of a nacho platter at Rio Grande is $9.50. This can be determined by setting up a system of equations based on the information given. Let's assume the cost of a nacho platter is represented by "x". From the first group, we can write the equation 2x + 5t = 25, where "t" represents the cost of a taco. From the second group, we can write the equation 3x + 2t = 30.90. Solving these equations simultaneously, we find that x = $9.50.
15.
What are the zeros of the function f(x) = x^{2} + 2x – 8?
Correct Answer
B. -4 and 2
Explanation
The zeros of a function are the values of x for which the function equals zero. In this case, we need to find the values of x that make the equation f(x) = x^2 + 2x - 8 equal to zero. By factoring or using the quadratic formula, we can determine that the zeros of the function are -4 and 2.