|
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 = { , } |4x - 8| + 12 = 60 What is the greatest solution for the absolute-value equation? Enter your 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 = 3x + 2 y = 3x - 3 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, 0) 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 - 6x 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 - 7x + 10 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≤y<∞ domain: -∞<x<∞ range: -∞≤y<∞ domain: -10≤x≤-6 range: -4≤y<∞ domain: -8≤x<∞ range: -∞≤y<∞ An expression is given, where k ≠ 0. Find the quotient. -40k2 - 25k -5k Evaluate the expression using the laws of exponents. (16) 5 4 Evaluate the expression using the laws of exponents. (-27) 2 3 Rewrite the polynomial by filling in the boxes. ( x + ) x2 - 9x + 20 ( x + ) What is the sum of (2x3 + 4x) and (3x3 +5x)? 14x8 14x6 5x6 + 9x2 5x3 + 9x An equation is shown. Identify the rate of change. y + 4 = -5 (x - 2) Polly purchased softball equipment and uniforms for a total cost of $1,836. The equipment cost $612, and the uniforms cost $25.50 each. Which equation could be used to find out how many uniforms the school purchased? x/1836 = 612(25.50) 1836 = 612x + 25.50 1836 = 612 + 25.50x 1836/25.50 + x = 612 Write an equation for the given words. 7 less than 15 times a number is 80. 7 - 15n = 80 7 - 15 + n = 80 15n - 7 = 80 7(15 - n) = 80 Solve the equation below. -14x + 7 = -6x - 89 x= Jon and Sara are planting pine trees as a summer job. Jon planted 60 trees and is planting at a rate of 20 trees per day. Sara has planted 96 trees and is planting at a rate of 11 trees per day. Given the equation below, in how many days will they have planted the same number of trees? 60 + 20d = 96 + 11d days Solve the equation below. n + 3 = -3 + n - 2 + 6 no solution 8 -10 All Real Numbers The figures below have the same perimeter. Remember, perimeter means the distance around. What is the value of x? x 2x+4 2x+4 x = x 6x 2x-8 2x-8 Which inequality represents the stated situation: A theater is made to receive no more than 750 spectators. s≥750 s≤750 s<750 s=750 0 2 -2 4 -4 6 -6 8 -8 Write the equation of the inequality shown on the graph below. x≤3 x≥3 x<3 x>3 x 0 2 -2 4 -4 6 -6 8 -8 11. Write the equation of the inequality shown on the graph. x≤2 x≥2 x<2 x>2 x 7. Harry has to invite at least 15 people to his birthday party at Lost City so that he gets the party rate. He already has 7 friends in mind. How many more must he invite? Choose the inequality below that best represents this situation. f + 7 ≥15 7 - f ≥ 15 15 + 7 > f 15 - f < 8 Write an inequality for the words below. The difference of a number and 4 is at least 22. m - 4 < 22 m - 4 > 22 m - 4 ≥ 22 m - 4 ≤ 22 Solve the inequality. 6x > -24 x > -4 x < -4 x < 4 x > 4 A local elementary school is having their annual carnival. Emily was given $14 by her grandma to spend. She wants to buy as many tickets as possible with her money. If each ticket is $1.25, how many tickets can she buy? 0 - 11 tickets 0 - 10 tickets 0 - 12 tickets 0 - 13 tickets Solve the inequality below. m < -6 m < -9.6 -5m + 9 > 39 m > -9.6 m > -6 Henry needs a minimum of $185 to attend a summer camp. He has $75 already saved and plans to save $20 per month. Which inequality below represents this situation? 75 + 20m ≥ 185 75 + 20m ≤ 185 75 - 20m ≥ 185 75 - 20m ≤ 185 Solve the equation below. h = 4 + 2.2h = -3.7 Ms. Morris joined a local gym. They charged her a $50 sign-up fee plus $45 per month. If she paid a total of $455, how many months, m, was she a member at the gym? Which equation represents this situation? 50 + 45m = 455 50m + 45 = 455 50 - 45m = 455 455 + 45m = 50 Write an equation for the sentence below. The sum of three times a number and 16is the same as 54. 3n - 16 = 54 3n + 16 = 54 3n = 16 + 54 3(n + 16) = 54 Solve the equation below. -3x - 10 = -7(x + 6) x = Solve the equation below. 2 (x - 9) = 2 (x + 5) no solution 1 -10 All Real Numbers Move-A-long moving company charges $200 a day plus $21 per hour. Take-U-There moving companycharges $270 plus $16 per hour. Using the equationbelow, how long is a job that costs the same no matterwhich company is used? 200 + 21h = 270 + 16h hours The difference of 7 times a number and 17 is equal to the sum of 4 times that number and 1. Find the number. Which inequality represents the stated situation: Minimum Speed: 25 mph. s≤25 mph s<25 mph s>25 mph s≥25 mph 0 2 -2 4 -4 6 -6 8 -8 Write the equation of the inequality shown on the graph below. x x≤-3 x≥-3 x<-3 x>-3 Carlos has $15 to spend on his sister for her birthday. If he already bought a toy for $5.50, which inequality below represents this situation? 5.50 + x ≤ 15 5.50 + x > 15 5.50 - x < 15 5.50 - x ≤ 15 Write an inequality for the words below. The sum of 4 and a number is at most 22. m + 4 < 22 m + 4 > 22 m + 4 ≥ 22 m + 4 ≤ 22 Solve the inequality. -5b ≤ -35 b ≤ 7 b ≥ 7 b ≤ -7 b ≥ -7 0 2 -2 4 -4 6 -6 8 -8 Which inequality has the solution shown in the graph? -2x ≤ 4 -2x ≤ -4 -2x ≥ -4 -2x ≥ 4 Solve the inequality below. x < 52 < -4(x - 4) A water tank holds 55 gallons of water. There is 25 gallons of water in the tank and it is being filled at a rate of 7 gallons per hour. How long can the water tank be left unattended before the water overflows? Choose the correct inequality. 25 + 7h < 55 7h - 25 > 55 25 + 7h ≤ 55 Choose all the factors for the given polynomial. 6 6x x+6 x-6 6x3-18x2-108x 3 3x x+3 x-3 Which of the following ordered pairs is not a solution to the linear function on the given graph? (-1, -5) (0, -2) (2, 4) (5, 7) An inequality is shown. What is the solution set for x? {x | x ≤ 6} {x | x ≤ -6} {x | x ≥ 6} {x | x ≥ -6} -3x + 7 ≥ -x - 5 Fill in the boxes to complete the equation in vertex form. f(x) = (x + )2 + The equation T(x) = 3(x-4)(x-8) models the temperatures recorded yesterday, where x is the number of hours after midnight and T is the temperature in degrees Celcius. Find the zeros of the function. x = 12 hours x = 24 hours x = 12 and 24 hours x = 4 and 8 hours Four functions are given in the table. Place a check in the correct box to identify each function type. j(x) = x f(x) = |x + 3| g(x) = x3 h(x) = 5x - 6 absolute value absolute value absolute value absolute value linear linear linear linear cubic cubic cubic cubic f(x) = 0.5 ∙ 10x h(x) = 4 ∙ 0.5x f(t) = 0.25 ∙ 1.5t g(x) = 3(0.2)x f(x) = 3(4)x h(t) = 0.5 ∙ 1.1t Growth Growth Growth Growth Growth Growth Decay Decay Decay Decay Decay Decay |