Exam 1: Equations, Inequalities, and Modeling

Solve the problem. -Median family income in Country X between 1990 and 1999 can be modeled by f(x) = 1174.6(x - 1990) + 35,265, where x is the year. Determine symbolically when the median income was $42,092.

Solve the problem. -How many liters of a 50% alcohol solution must be mixed with 40 liters of a 70% solution to get a 60% solution?

Find the equation of the line through the given pair of points. Solve it for y if possible. -(9, 10), (9, -1)

Solve the problem. -An office manager will spend a total of $20,000 on copiers at $2000 each and boxes of paper at $50 each. Write the number of copiers purchased, c, as a function of the number of boxes of paper purchased, b. Find and Interpret the slope. Hint: Start with standard form.

Use the method of your choice to find all real solutions of the equation. -x = 2 +

Graph the equation in the rectangular coordinate system. -4 - x = 3

Write an equation in standard form using only integers for the line described. -The line with slope , going through (0, 5)

Solve the problem. -Over the past two weeks, Jane earned $156 and $290 respectively, at her part time job. What must she earn in the third week to bring her three-week average earnings to $200 per week?

Use the y-intercept and slope to sketch the graph of the equation. -y = -7x

Find the perfect square trinomial whose first two terms are given. -

Write the solution set in interval notation. -

State the value of the discriminant and the number of real solutions. - = -6y - 2

Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers. -

Write an equation in slope-intercept form for the line shown. -

Find the product of the complex number and its conjugate. --7 + 3i

Find the center and radius of the circle. -

Find the equation of the line through the given pair of points. Solve it for y if possible. -(-5, -9), (-2, -1)

Use the appropriate formula to solve the problem. -Find the corresponding Celsius temperature for a temperature of 129°F. Round to the nearest tenth, if necessary.

Use the appropriate formula to solve the problem. -The length of a rectangular billboard is 7 inches more than the width. The perimeter of the billboard is 138 inches. Find the width of the billboard.

Perform the indicated operations and write the answer in the form a + bi, where a and b are real numbers. -(9 + 4i)(9 - 3i)