THEOREM:
- h² = p² + b² where h is hypotenuse, b is base and p is perpendicular.
ANSWER:
[3] By pythagorean theorem,
- x² = 14² + 9²
- x² = 196 + 81
- x² = 277
- x = √277
- x = 16.64 rounded.
[4] By pythagorean theorem,
- x² = 32² + 24²
- x² = 1024 + 576
- x² = 1600
- x = √1600
- x = 40.
[5] By pythagorean theorem,
- (2x)² = 21² – 12.6²
- 4x² = 441 – 158.76
- 4x² = 284.24
- x² = 284.24/4 = 70.56
- x = √70.56
- x = 8.4
[6] By tangent property,
- 7x – 29 = 2x + 16
- 7x – 2x = 16 + 29
- 5x = 45
- x = 9.
So, WX = 7(9) – 29 = 63 – 29
Simplifying
j = (2j + 3)
Reorder the terms:
j = (3 + 2j)
Remove parenthesis around (3 + 2j)
j = 3 + 2j
Solving
j = 3 + 2j
Solving for variable 'j'.
Move all terms containing j to the left, all other terms to the right.
Add '-2j' to each side of the equation.
j + -2j = 3 + 2j + -2j
Combine like terms: j + -2j = -1j
-1j = 3 + 2j + -2j
Combine like terms: 2j + -2j = 0
-1j = 3 + 0
-1j = 3
Divide each side by '-1'.
j = -3
Simplifying
j = -3
Yesthe value of 4 in 46,395 36 times the value of 4 in 14,906
1.59, 1.95, 9.15, 9.5, 15.9
