Math Problem Statement
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1Determine whether the values -1 and 7/3 are solutions to the quadratic equation 3x² - 4x – 4 = 3. A. Only x = 7/3 is a solution. B. Neither x = -1 nor x = 7/3 is a solution. C. Both x = -1 and x = 7/3 are solution. D. only x = -1 is a solution. 2Use the table to answer the question: X Substituted Evaluate True Statement? 12 24 36 48 When set off, a certain firework follows the path of the quadratic function h=25/36 x^2+16 2/3 x where: h = the height of the firework in feet x = the horizontal distance it travels in feet To determine how far the firework will travel before reaching the ground, determine which value of x in table is a solution to the equation 0= -25/36 x^2+16 2/3 x. A. 12 feet B. 36 feet C. 48 feet D. 24 feet 3Ariel is trying to determine if x = -3 is a solution to the quadratic equation -3x² - 9x = 0. Which explanation demonstrates the correct reasoning? A. Yes, x = -3 is a solution because substituting it back to the equation results in the following: x = -3 substituted: -3(-3)² - 9(-3) = 0 Evaluate: 54 = 0 True Statement? True B. No, x = -3 is NOT a solution because substituting it back into the equation results in the following: x = -3 SUBSTITUTED: -3(-3)² - 9(-3) = 0 EVALUATE: 54 ≠ 0 TRUE STATEMENT?: False C. x = -3 is a solution because substituting it back into the equation results in the following: x = -3 SUBSTITUTED: -3(-3)² - 9(-3) = 0 EVALUATE: 0 = 0 TRUE STATEMENT?: True D. No, x = -3 is NOT a solution because substituting it back into the equation results in the following: x = -3 SUBSTITUTED: -3(-3)² - 9(-3) = 0 EVALUATE: 54 ≠ 0 TRUE STATEMENT?: False 4Show how many solutions are in the solution set for the equation 3x² = 21. A. Two B. Zero C. One D. infinitely many 5Show how many solutions are in the solution set for 2(x – 5)² + 2 = 20. A. one B. infinitely many C. Zero D. two
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Factoring
Solving Quadratics
Square Roots
Formulas
Quadratic equation: ax^2 + bx + c = 0
Factoring: (x - r1)(x - r2) = 0
Square roots: x = ±√a
Theorems
Quadratic Formula
Zero Product Property
Suitable Grade Level
Grades 8-10
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