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Maria is deciding between two job offers. Company A offers her a base salary of $50,000 per year plus a 11% commision. Company B offers $58,000 per year plus 8.5% commision. Maria sets up the following equation to determine how much she must make for the salaries to be equal. Solve for x. 50000 + 0.11x = 58000 + 0.085x x = Ethan borrowed a book with 486 pages. On the first day, he read a certain number of pages. On the second day, he read twice as many pages as the first day. On the third day, he read six pages less than he did on the first day. The equation below represents the situation. How many pages did Ethan read on the first day? x + 2x + (x - 6) = 486 x = Two rectangular plots have the same area in square yards. What value of x (in yards) makes this statement true? 7(3x) = 9x 7(x+3) = 9x 7 + (x + 3) = x + 9 2(7 + x + 3) = 2(x + 9) Solve the following inequality. ≤ > < 9x ≤ (16x + 20) 3 4 x ≥ ? Solve the compound following inequality. -15 < 3x + 9 < 0 Solve for x. x = 10 x = 10 and x = -10 x = 10 and x = -14 x = -10 and x = 14 |4x - 8| + 12 = 60 What is the greatest solution for the absolute-value equation? Enter you answer in the space below. |4x - 3| - 6 = 31 Solve for x. x = u - k x = ku x = k + u x = k - u u = k - x Rewrite this equation to solve for the variable a. a = u = 3k a A function is given. Which graph represents the function? f(x) = x - 2 A B C D 1 3 An equation is shown. Identify the rate of change. -1 -3 6 1 y + 6 = -3(x - 1) An equation is shown. Identify the y-intercept. -3 3 -5 -15 3x - 5y = -15 For the linear function shown below, identify the x-intercept and y-intercept. x-intercept: y-intercept: 3x - 5y = -15 Identify the slope of the line that is perpendicular to the one shown in the graph. slope = 3 slope = -3 slope = ⅓ slope = -⅓ Identify the equation of the line that is parallel to the one shown in the graph. y = 2x - 2 y = 3x + 2 y = 2x + 3 y = -2x - 3 Identify a linear equation in slope-intercept form for a line perpendicular to the shown equation and passes through the point (-5, -9). y = -2x + 7 y = 2x + 7 y = 2x + 1 y = -2x + 1 y = x + 7 -1 2 A linear function is given. Which of the following are solutions of the equation? Select all that apply. (0, -4) (8, -8) (4, 6) (-10, 1) y + 7 = - (x - 6) 1 2 Find the value of x for the system of equations below. x = 4 x = 5 x = -5 x = 9 -4x + 9y = 9 x - 3y = -6 A new gym opened in town and started with 10 members. Each month, they gain 15 new members. This situation can be modeled using the equation M(x) = 10 + 15x, where M represents the total number of gym members and t represents the time in months. What is the rate of change? Find the solution for the systems of equations from the graph provided, which shows the equations h(x) and g(x). (3, 2) (2, 3) (-3, 2) (-4, 1) Ashely is making cupcakes for a bake sale. She bought two pounds of blueberries and six pounds of peaches and spent $19. Later, she went back to the store and bought another pound of blueberries and five more pounds of peaches and spent $15. Using the following equations, determine the cost of one pound of peaches. 2b + 6p = $19 b + 5p = $15 p = $ Solve the system of equations given below. Enter your answer in the form of an ordered pair. ( 2x + y = 19 x = y + 11 , ) Identify the constant percent rate of change for the exponential function. 0.06% 6% 20% 94% f(x) = 20(1 - 0.06)x Determine the y-intercept for the function. y = 6 (0.75)x is shown on the coordinate plane. Which of the following are true. Select all that apply. The graph of the exponential function The range of the function is y ≤ 0 There is an asymptote at y = 0 The function is negative over the interval -∞ < x < ∞ The function has an end behavior of: As x → -∞, y → 0; As x → ∞, y → -∞ f(x) = - • 2x 1 4 Which equation models exponential growth? y = 3 • 0.25x y = • (2)x y = 3 (1 - 0.2)x y = • (1 - 0.02)x 1 4 1 4 Identify the equation of the exponential function. y = 5 • (10)x y = 10 • (2)x y = 10 • (0.5)x y = 5 • (0.5)x You invest $725 in a savings account that applies 4.2% simple interest. Calculate the total amount of this investment after 15 years. $1,181.75 $11,331.75 $46,400.00 $45,675.00 9x - 12 21x2 - 12x 9x2 - 12x 9x2 + 6x Simplify: (15x2 - 3x) - (6x2 + 9x) -3n3 + 9n2 - 37n -35 -3n3 - 9n2 + 23n - 35 -3n3 - 21n2 + 23n +35 -3n3 + 14n - 35 Multiply: (n + 5)(-3n2 + 6n - 7) An expression is given. Which is equivalent? (w + 8)(w + 3) (w - 8)(w - 3) (w - 8)(w + 3) (w + 8)(w - 3) w2 - 5w - 24 An expression is given. Write an equivalent expression as the product of two binomials. x2 + 8x - 20 The data in the table of values models a quadratic function. Identify the vertex. x 5 6 7 8 9 -3 -4 -3 y 0 5 (5, -3) (6, -4) (8, 0) (9, 5) The data in the table of values models a quadratic function. Identify the x-intercepts. -12 -10 -8 -5 -4 x 16 -8 -5 y 0 0 The graph of a quadratic function is given. Identify its equation in vertex form. f(x) = (x - 6)2 - 10 f(x) = (x + 10)2 - 6 f(x) = (x + 8)2 - 4 f(x) = (x - 8)2 - 4 The graph of a quadratic function is given. Identify its equation in factored form. f(x) = (x + 2)(x + 12) f(x) = (x - 2)(x - 12) f(x) = (x - 7)(x - 25) f(x) = (x + 7)(x + 25) A quadratic equation is shown in factored form. Identify all solutions to the equation. -6, 5 6, -5 6, 5 -6, -5 (x - 6)(x + 5) = 0 Find all solutions for the equation, rounded to the nearest hundredth, if necessary. x = -2x2 + 3x + 7 = 0 x = Find the sum of (-b2 + 3b) + (-b + 3b2). 4 -2b2 -2b - 2b2 ? 2b4 + ? 2b ? Simplify: (15x2 - 3x) - (6x2 + 9x) 9x 12 11x2 9x2 ? - ? 6x 12x ? An expression is given. Which expression is equivalent? 3x(4x3 - 2x2 + 7x) 6x(2x2 - x + 4) 3x(4x2 - 2x + 7) 6(2x3 - x2 + 7x) 12x3 - 6x2 + 21x The graph of a quadratic function is given. Identify the domain and range. domain: -∞<x<∞ range: -4≤x<∞ domain: -∞<x<∞ range: -∞≤x<∞ domain: -10≤x≤-6 range: -4≤x<∞ domain: -8≤x<∞ range: -∞≤x<∞ An expression is given, where k ≠ 0. Find the quotient. -40k2 - 25k -5k |