12345 - Math Quiz - Grid questions 1 / 5 1. If 7y = 63, then y equals which of the following? Check To find the value of y: Divide both sides of the equation by 7: y = 63 / 7 y = 9 So, y equals 9. 2 / 5 2. Solve the quadratic equation x^2 - 6x - 16 = 0. Check Applying the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a For our equation, a = 1, b = -6, and c = -16: x = (6 ± √((-6)^2 - 4 * 1 * (-16))) / (2 * 1) x = (6 ± √(36 + 64)) / 2 x = (6 ± √100) / 2 x = (6 ± 10) / 2 x has two possible values: 8 and -2. 3 / 5 3. If the price of an item is increased by 10% and then decreased by 10%, what is the overall percentage change? Check Let the original price of the item be P. After increasing the price by 10%, the new price is 1.10P. After decreasing the price by 10%, we have 0.90(1.10P) = 0.99P. The overall percentage change is the difference between the new price (0.99P) and the original price (P) divided by the original price (P) times 100: [(0.99P - P) / P] * 100 = (-0.01P / P) * 100 = -1% The overall percentage change is a 1% decrease. 4 / 5 4. The function h is defined by h(x) = (x + 3)(x - 4)(x + 1). In the xy-plane, the graph of y = j(x) is the result of translating the graph of y = h(x) down 5 units. What is the value of j(2)? Check First, to find the value of j(2), we need to know the value of h(2) since j(x) is just h(x) translated down by 5 units. We substitute x in h(x) with 2 to get h(2) = (2 + 3)(2 - 4)(2 + 1) = 5 * -2 * 3 = -30. Since j(x) translates h(x) down by 5 units, j(2) = h(2) - 5 = -30 - 5 = -35. Therefore, the value of j(2) is -35. 5 / 5 5. . A rectangular garden is 12 meters long and 8 meters wide. If a sidewalk of uniform width is built around the garden, and the area of the sidewalk is equal to the area of the garden, what is the width of the sidewalk? Check Let's denote the width of the sidewalk as x meters. The dimensions of the garden with the sidewalk would then be (12 + 2x) meters in length and (8 + 2x) meters in width. The area of the garden is 12 * 8 = 96 square meters. According to the problem, the area of the sidewalk is also 96 square meters. The area of the garden plus the sidewalk can be calculated as: Area = (12 + 2x)(8 + 2x) We know that the area of the garden plus the sidewalk is equal to the sum of the areas of the garden and the sidewalk: (12 + 2x)(8 + 2x) = 96 + 96 Expanding the left side of the equation: 96 + 28x + 4x^2 = 192 Subtracting 192 from both sides: 4x^2 + 28x - 96 = 0 Dividing the entire equation by 4 to simplify it: x^2 + 7x - 24 = 0 Factoring the quadratic equation: (x + 9)(x - 2) = 0 The possible solutions for x are -9 and 2. Since the width of the sidewalk cannot be negative, the only valid solution is x = 2 meters. So, the width of the sidewalk is 2 meters. Your score is 0% Restart Quiz
