MS. Cooper's Review Session Quiz

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.

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.

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).

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.

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.

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.

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The rate of change is the same for both functions because the difference between consecutive values of x for both functions remains constant.

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.

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.

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.

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.

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).

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.

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.