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 for the remaining parts: b. Equation: x = -2y + 6 Step 1: Substitute y=1, 2, 3 into the equation to find x. For y=1: x = -2(1) + 6 = -2 + 6 = 4 For y=2: x = -2(2) + 6 = -4 + 6 = 2 For y=3: x = -2(3) + 6 = -6 + 6 = 0 Step 2: Substitute y=4 into the equation to find m. m = -2(4) + 6 = -8 + 6 = -2 Step 3: Substitute y=5 into the equation to find x. For y=5: x = -2(5) + 6 = -10 + 6 = -4 Step 4: Substitute x=-174 into the equation to find n. -174 = -2n + 6 -174 - 6 = -2n -180 = -2n n = (-180)/(-2) = 90 Completed table for b: | y | 1 | 2 | 3 | 4 | 5 | 90 | |---|---|---|---|---|---|---| | x | 4 | 2 | 0 | -2 | -4 | -174 | The value of m is -2 and n is 90. d. Equation: y = x + 2 Step 1: Substitute x=2 into the equation to find y. y = 2 + 2 = 4 Step 2: Substitute y=5 into the equation to find n. 5 = n + 2 n = 5 - 2 = 3 Step 3: Substitute x=4, 5 into the equation to find y. For x=4: y = 4 + 2 = 6 For x=5: y = 5 + 2 = 7 Step 4: Substitute x=16 into the equation to find m. m = 16 + 2 = 18 Step 5: Substitute x=17 into the equation to find y. y = 17 + 2 = 19 Completed table for d: | x | 2 | 3 | 4 | 5 | 16 | 17 | |---|---|---|---|---|---|---| | y | 4 | 5 | 6 | 7 | 18 | 19 | The value of n is 3 and m is 18. f. Equation: q = 7p - 7 Step 1: Substitute p=1, 5 into the equation to find q. For p=1: q = 7(1) - 7 = 7 - 7 = 0 For p=5: q = 7(5) - 7 = 35 - 7 = 28 Step 2: Substitute p=10 into the equation to find m. m = 7(10) - 7 = 70 - 7 = 63 Step 3: Substitute p=20 into the equation to find q. q = 7(20) - 7 = 140 - 7 = 133 Step 4: Substitute q=168 into the equation to find n. 168 = 7n - 7 168 + 7 = 7n 175 = 7n n = (175)/(7) = 25 Step 5: Substitute p=100 into the equation to find q. q = 7(100) - 7 = 700 - 7 = 693 Completed table for f: | p | 1 | 5 | 10 | 20 | 25 | 100 | |---|---|---|---|---|---|---| | q | 0 | 28 | 63 | 133 | 168 | 693 | The value of m is 63 and n is 25. 2. What is the value of m and n? The rule is y = -7x + 2. Step 1: Find the value of m by substituting y=-145 into the equation. -145 = -7m + 2 -145 - 2 = -7m -147 = -7m m = (-147)/(-7) = 21 Step 2: Find the value of n by substituting x=60 into the equation. n = -7(60) + 2 n = -420 + 2 n = -418 The value of m is 21 and n is -418. That's 2 down. 3 left today — send the next one.