Exam 2: Linear Models, Equations, and Inequalities

Solve the equation for y. -A student earned scores of 85, 83, 90, 94, 88, and 84 on the first six tests in a biology class. What score is needed on the seventh test to produce an 86 average?

Translate the sentence to an algebraic inequality. -Correct Computers, Inc. finds that the cost to make $x$ laptop computers is $C = 2529 x + 128,651$ , while the revenue produced from them is $R = 4034 x$ ( $C$ and $R$ are in dollars). What is the smallest whole number of computers, $x$ , that must be sold for the company to show a profit?

Solve the inequality and draw a number line graph of the solution. - $- 5 ( 3 z + 15 ) < - 20 z - 45$

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate. - $\frac { x + 8 } { 5 } = \frac { 13 } { 10 } - \frac { x - 3 } { 4 }$

To find the number of units that gives break-even for the product, solve the equation R $\mathbf { R } = \mathbf { C }$ ound your answer to the nearest whole unit. -Suppose that the total annual consumption of salmon in a certain country is given by $y = 7.39 x + 727.1$ and that the total annual consumption of tuna in this country is given by $y = 1.99 x + 808.1$ , where consumption is measured in millions of pounds and $x$ is the number of years since 2010. Find the year in which consumption of salmon reaches consumption of tuna.

Solve the equation. - $\frac { 2 } { 5 } x - \frac { 1 } { 3 } x = 5$

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ . -

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ . -

Translate the sentence to an algebraic inequality. -During the first four months of the year, Jack earned $1180, $1170, $1460 and $1050. If Jack must have an average salary of at least $1180 in order to earn retirement benefits, what must Jack earn in the fifth month in Order to qualify for benefits?

Solve the equation using graphical methods. Round to the nearest thousandth when appropriate. - $- 4 x + 4 - 7 ( x + 1 ) = 3 x - 2$

Solve the system of equations by substitution, if a solution exists. - $\left\{ \begin{array} { l } 3 x + 5 y = 5 \\9 x = 10 + 15 y\end{array} \right.$

Construct a scatter plot of the data in the table. - x -10 -8 -5 -4 -2 2 4 6 8 9 y 1 -7 -2 4 4 -2 -3 5 -8 -4

Solve the system of equations by elimination, if a solution exists. - $\left\{ \begin{array} { l } x + 7 y = 5 \\- 4 x + 8 y = - 20\end{array} \right.$

Solve the system of equations by substitution, if a solution exists. - $\left\{ \begin{array} { l } 5 x + 9 y = 36 \\3 x + 5 y = 20\end{array} \right.$

Without graphing, determine whether the following data set is exactly linear, approximately linear or nonlinear. - 1 2 3 4 5 9 11 12 15 17

Solve the equation. - $\frac { r + 6 } { 5 } = \frac { r + 8 } { 7 }$

To find the number of units that gives break-even for the product, solve the equation R $\mathbf { R } = \mathbf { C }$ ound your answer to the nearest whole unit. -A certain product has supply and demand functions given b $p = 4 q + 29 \text { and } p = 254 - 11 q$ , respectively, where p is the price in dollars and q is the quantity supplied or demanded at price p. How many units are supplied And demanded at market equilibrium?

The graph of a certain function $y = f ( x )$ and the zero of that function is given. Using this graph, find a) the $x$ -intercept of the graph of $y = f ( x )$ and b) the solution to the equation $f ( x ) = 0$ . -

Translate the sentence to an algebraic inequality. -The formula for converting Fahrenheit temperature to Celsius is $C = \frac { 5 } { 9 } ( F - 32 )$ . If a bottle of prescription medicine is to be kept below 35° Celsius, how would you describe this warning using Fahrenheit temperature?

Find the linear function that is the best fit for the given data. Round decimal values to the nearest hundredth, if necessary. - x 2 4 6 8 10 y 15 37 60 75 94