Final answer:
To solve each equation, isolate the variable on one side. Follow the given steps to find the values of the variables. Round to the nearest tenth, if necessary. 1) c = √234, rounded to the nearest tenth, 2) c = √314, rounded to the nearest tenth, 3) a = √10, rounded to the nearest tenth, 4) b = √20, rounded to the nearest tenth, 5) c = √114, rounded to the nearest tenth, 6) c = √194, rounded to the nearest tenth, 7) b = √70, rounded to the nearest tenth, 8) a = √20, rounded to the nearest tenth.
Step-by-step explanation:
To solve each equation for the variable, we need to isolate the variable on one side of the equation. Here are the steps for each equation:
1) 82+152=c²
Subtract 82 from both sides: 152 = c² - 82
Add 82 to both sides: 234 = c²
Take the square root of both sides: c = √234, rounded to the nearest tenth
2) 72+242=c²
Subtract 72 from both sides: 242 = c² - 72
Add 72 to both sides: 314 = c²
Take the square root of both sides: c = √314, rounded to the nearest tenth
3) a²+122=132
Subtract 122 from both sides: a² = 132 - 122
Simplify: a² = 10
Take the square root of both sides: a = √10, rounded to the nearest tenth
4) 32+b²=52
Subtract 32 from both sides: b² = 52 - 32
Simplify: b² = 20
Take the square root of both sides: b = √20, rounded to the nearest tenth
5) 52+62=c²
Add 52 and 62: 114 = c²
Take the square root of both sides: c = √114, rounded to the nearest tenth
6) 82+112=c²
Add 82 and 112: 194 = c²
Take the square root of both sides: c = √194, rounded to the nearest tenth
7) 112+b²=182
Subtract 112 from both sides: b² = 182 - 112
Simplify: b² = 70
Take the square root of both sides: b = √70, rounded to the nearest tenth
8) a²+102=122
Subtract 102 from both sides: a² = 122 - 102
Simplify: a² = 20
Take the square root of both sides: a = √20, rounded to the nearest tenth