Exam 1: Equations and Inequalities

Solve the problem. -The maximum number of volts, $E$ , that can be placed across a resistor is given by the formula $E = \sqrt { P R }$ , where $\mathrm { P }$ is the number of watts of power that the resistor can absorb and $\mathrm { R }$ is the resistance of the resistor in ohms. Solve this equation for $R$ . Use the result to determine the resistance of a resistor if $P$ is $\frac { 1 } { 2 }$ watts and $E$ is 10 volts.

Use the Discriminant to Determine the Number and Type of Solutions Compute the discriminant. Then determine the number and type of solutions for the given equation. - $x ^ { 2 } + 2 x + 1 = 0$

Solve Absolute Value Inequalities Solve the absolute value inequality. Other than $\phi ,$ use interval notation to express the solution set and graph the solution set on a number line. - $| x - 6 | \geq 0$

Solve the problem. -A car rental agency charges $175 per week plus $0.20 per mile to rent a car. How many miles can you travel in one week for $295?

Solve the problem. -Every Sunday, Jarod buys a loaf of fresh bread for his family from the corner bakery for $3.00. The local department store has a sale on breadmakers for $79. If the bread-making supplies cost $0.67 per week, for How many weeks would Jarod have to bake a loaf of bread at home before the breadmaker starts saving Him money?

Solve Linear Equations in One Variable - $( - 5 x + 5 ) + 1 = - 4 ( x + 7 )$

Solve the formula for the specified variable. - $I = \operatorname { Prt } \quad$ for $\mathrm { P }$

Recognize Identities, Conditional Equations, and Inconsistent Equations Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. - $\frac { 2 x } { x } = 2$

Perform Operations with Square Roots of Negative Numbers Perform the indicated operations and write the result in standard form. - $2 \sqrt { - 45 } + 5 \sqrt { - 20 }$

Solve Compound Inequalities Solve the compound inequality. Other than $\varnothing$ use interval notation to express the solution set and graph the solution set on a number line. - $- 7 \leq - 2 x + 5 < - 3$

Solve Equations Involving Absolute Value Solve the absolute value equation or indicate that the equation has no solution. - $| x | = 11$

Find all values of x satisfying the given conditions. - $y = \left( x ^ { 2 } - 2 x \right) ^ { 2 } - 11 \left( x ^ { 2 } - 2 x \right)$ and $y = - 24$

Solve Quadratic Equations Using the Quadratic Formula Solve the equation using the quadratic formula. - $3 x ^ { 2 } + 7 x + 8 = 0$

Find all values of x satisfying the given conditions. - $y _ { 1 } = 5 ( 3 x - 1 ) ^ { - 1 } , y _ { 2 } = 2 ( 3 x - 1 ) ^ { - 2 }$ , and $y _ { 1 }$ exceeds y 2 by 2

Solve Equations That Are Quadratic in Form Solve the equation by making an appropriate substitution. - $x - 12 \sqrt { x } + 35 = 0$

Solve Quadratic Equations by the Square Root Property Solve the equation by the square root property. - $( x - 11 ) ^ { 2 } = - 4$

Graph the equation. -y = -4

Interpret Information Given by Graphs The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -At what time was the temperature 79°?

Perform Operations with Square Roots of Negative Numbers Perform the indicated operations and write the result in standard form. - $\sqrt { - 16 } + \sqrt { - 64 }$

Recognize Identities, Conditional Equations, and Inconsistent Equations Determine whether the equation is an identity, a conditional equation, or an inconsistent equation. -16x + 15(x + 1)= 31(x + 1)- 16