Exam 1: Equations and Graphs

Caitlin paints with watercolors on a sheet of paper 28 inches wide by 16 inches high. She then places this sheet on a mat so that a uniformly wide strip of the mat shows all around the picture. The perimeter of the mat is 112 inches. How wide is the strip of the mat showing around the picture?

Find all real solutions of the equation. $x ^ { 2 } - \sqrt { 29 } x + 1 = 0$

A jeweler has three small solid spheres made of gold, of radius 1 mm, 2 mm, and 3 mm. He decides to melt these down and make just one sphere out of them. What will the radius of this larger sphere be? Round the answer to one decimal place.

Solve the equation by completing the square. $x ^ { 2 } + 4 x - 9 / 4 = 0$

What quantity of a 50% acid solution must be mixed with a 20% solution to produce 300 mL of a 40% solution?

Solve the equation. $| x + 11 | = | 2 x + 5 |$

Solve the equation. $3 ( x + 11 ) + 1 = - 3 ( x + 5 ) + 7$

Solve the equation by factoring. $x ^ { 2 } = - 5 ( x - 100 )$

Solve the inequality. $\left| \frac { x + 5 } { 2 } \right| \geq 5$

Find all real solutions of the equation. $x ^ { 2 } - \sqrt { 29 } x + 1 = 0$

Solve the equation. $3 ( x + 11 ) + 1 = - 3 ( x + 5 ) + 7$

The average daily food consumption F of a herbivorous mammal with body weight x, where both F and x are measured in pounds, is given approximately by the equation $F = 0.4 x ^ { 3 / 4 }$ . Find the weight x of an elephant that consumes 400 lb of food per day.

Solve the inequality. Express the solution using interval notation. $| 4 x + 2 | \geq 2$

Find all real solutions of the equation $x ^ { 4 } = 16 x ^ { 2 }$

Solve the equation.3(x + 11) + 1 = - 3(x + 5) + 7

Solve the nonlinear inequality. $x ^ { 2 } + 3 x > 4$

Solve the inequality. $\left| \frac { x + 5 } { 2 } \right| \geq 5$

Solve the inequality. $| 7 x - 2 | < 4$

Solve the equation. $\frac { 7 } { x - 8 } + \frac { 7 } { x + 8 } = \frac { 154 } { x ^ { 2 } - 64 }$

Solve the equation for $h$ . $A = 2 \pi r h + 2 \pi r ^ { 2 }$