This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the questions: QUESTION 8 [FUNCTIONS AND RELATIONSHIPS] 8.1. Step 1: Substitute the input value x=9 into the given equation y = -x + 4. y = -(9) + 4 Step 2: Perform the subtraction. y = -9 + 4 y = -5 The output value is -5. 8.2. Step 1: To find a, substitute x=4 into the rule y = 2x + 1. a = 2(4) + 1 a = 8 + 1 a = 9 Step 2: To find b, substitute x=5 into the rule y = 2x + 1. b = 2(5) + 1 b = 10 + 1 b = 11 The values are a = 9 and b = 11. 8.3. Step 1: Examine the input and output values to find a pattern. Inputs: 2, 3, 8, 10 Outputs: 16, 22, 52, 64 Step 2: Test a linear relationship of the form y = mx + c. Using the first two pairs (2, 16) and (3, 22): For (2, 16): 16 = 2m + c (Equation 1) For (3, 22): 22 = 3m + c (Equation 2) Step 3: Subtract Equation 1 from Equation 2 to find m. (22 - 16) = (3m + c) - (2m + c) 6 = m Step 4: Substitute m=6 into Equation 1 to find c. 16 = 2(6) + c 16 = 12 + c c = 16 - 12 c = 4 Step 5: Formulate the rule and verify with other input-output pairs. The rule is y = 6x + 4. Check for x=8: y = 6(8) + 4 = 48 + 4 = 52 (Matches) Check for x=10: y = 6(10) + 4 = 60 + 4 = 64 (Matches) The rule is y = 6x + 4. QUESTION 9 [ALGEBRAIC EXPRESSIONS] 9.1. Given the expression: x^2 - 6x - 8 9.1.1. Step 1: Identify the terms in the expression. Terms are separated by addition or subtraction signs. The terms are x^2, -6x, and -8. There are 3 terms in the expression. 9.1.2. Step 1: Identify the term containing x. This is -6x. Step 2: The coefficient of x is the numerical factor multiplying x. The coefficient of x is -6. 9.1.3. Step 1: Identify the term that does not contain any variables. The constant term is -8. 9.1.4. Step 1: Identify the power of the variable in each term. For x^2, the power is 2. For -6x, the power is 1 (since x = x^1). For -8, the power is 0 (since x^0 = 1). Step 2: The degree of the expression is the highest power of the variable in any term. The highest power is 2. The degree of the expression is 2. 9.1.5. Step 1: Substitute x = -3 into the expression x^2 - 6x - 8. (-3)^2 - 6(-3) - 8 Step 2: Calculate the square of -3. (-3)^2 = (-3) × (-3) = 9 Step 3: Perform the multiplication. -6(-3) = 18 Step 4: Substitute these values back into the expression and perform the additions/subtractions. 9 + 18 - 8 27 - 8 19 The value of the expression if x = -3 is 19. Last free one today — make it count tomorrow, or type /upgrade for unlimited.