Answer:
Step-by-step explanation:
6) Let John's sister age be x
John's age = [tex]\frac{1}{2}x+7[/tex]
[tex]\frac{1}{2}x+7 = 35\\[/tex] {Subtract 7 from both sides}
[tex]\\\frac{1}{2}x=35-7\\\\\frac{1}{2}x=28\\\\x=28*2[/tex]
x = 56
His sister's age = 56 years
7) Longest side is hypotenuse. Use Pythagorean theorem.
hypotenuse² =base² + altituse²
15² = 12² + 9²
225 = 144 + 81
225 = 225
So, Pythagorean theorem is satisfied. So, 15cm , 12 cm ,9 cm will make a right angled triangle.
9) q = -1
7p + 5q -3 = 0
7p + 5*(-1) - 3 = 0
7p -5 - 3 = 0 {Combine like terms}
7p - 8= 0
7p = 8 {Divide both sides by 7}
p = 8/7
10) 8 - 3(x + 1) = 5 {Distributive property: a(b + c) = a*b + a*c}
8 - 3x - 3 = 5 {Combine like terms}
-3x + 5 = 5 {Subtract 5 from both sides}
-3x = 5 - 5
-3x = 0
x = 0
11) -20x⁴ - 7x³ + 5x² + 20 - ( 8x⁴ -7x² + 29x - 17)
= -20x⁴ - 7x³ + 5x² + 20 - 8x⁴ + 7x² - 29x + 17
= -20x⁴ - 8x⁴ - 7x³ + 5x² + 7x² - 29x + 20 + 17
= -28x⁴ -7x³ + 12x² - 29x + 37
