Exam 7: The Basic Concepts of Algebra

A triangle drawn on a map has sides of lengths 9.0 cm, 10 cm, and 13 cm. The shortest of the corresponding real-life distances is 106 km. Find the longest of the real-life distances. Round to the Nearest unit.

If x varies inversely as y2, and x = 2 when y = 10, find x when y = 2.

Translate the verbal phrase into a mathematical expression. Use x to represent the unknown number. -The ratio of a number and 13

Evaluate. - $2 ^ { 0 }$

Decide whether the statement translates into an expression or an equation. - $\frac { 8 } { 9 } \text { of a number }$

Solve the equation. - $2 m - 1 + 6 ( m + 1 ) = - 6 m - 3$

A plane flies 440 miles with the wind and 320 miles against the wind in the same length of time. If the speed of the wind is 30 mph, what is the speed of the plane in still air?

Solve the equation. - $\frac { x - 4 } { 6 } = \frac { x + 7 } { 4 }$

Evaluate the expression. - $\left( - \frac { 3 } { 4 } \right) ^ { - 3 }$

Decide whether the equation is "conditional," an "identity," or a "contradiction." Give its solution set. - $2 \mathrm { x } + 5 ( \mathrm { x } + 1 ) + 2 = 7 - 2 \mathrm { x }$

Decide whether the proportion is true or false. - $\frac { 7 } { 8 } = \frac { 63 } { 80 }$

Solve the equation. - $\frac { x } { 6 } - \frac { 7 } { 3 } = \frac { x - 5 } { 3 }$

Decide whether the statement translates into an expression or an equation. -The quotient of a number and 7 is 9.