**MAT-121: COLLEGE ALGEBRA**

**Written Assignment 2**

2.5 points each

## SECTION 2.1

### Algebraic

For the following exercise, solve the equation for *y* in terms of *x*.

For the following exercise, find the distance between the two points. Simplify your answer, and write the exact answer in simplest radical form for an irrational answer.

- and

### Graphical

For exercises * 3 and 4*, plot the three points on the given coordinate plane. State whether the three points you plotted appear to be collinear (on the same line).

(Use a scale of 2 for each axis.)

- Name the quadrant in which the following points would be located. If the point is on an axis, name the axis.

### Numeric

For the following exercise, find and plot the *x*– and *y*-intercepts, and graph the straight line based on those two points.

For the following exercise, use the graph to the right.

- Find the distance between the two endpoints using the distance formula. Round to three decimal places.

(Use a scale of 1 for each axis.)

### Extensions

- A woman drove 15 miles directly east from her home, made a right turn at an intersection, and then traveled 8 miles south to her business. If a road was made directly from her home to her business, what would its distance be to the nearest tenth of a mile?

## SECTION 2.2

### Algebraic

For the following exercise, solve the equation for *x*.

For the following exercise, solve each rational equation for *x*. State all *x*-values that are excluded from the solution set.

For exercises * 10 and 11*, find the equation of the line using the point-slope formula. Write all the final equations using the slope-intercept form.

- with a slope of
- Perpendicular to and passes through the point (-1, 5)

### Graphical

For the following exercise, graph the pair of equations on the same axes, and state whether they are parallel, perpendicular, or neither.

- and

### Numeric

For the following exercise, find the slope of the line that passes through the given points.

- (-6, 5) and (8, 5)

### Real-World Applications

- If the profit equation for an ice cream vendor selling
*x*number of type one ice cream cone and*y*number of type two ice cream cone is , find the*y*value when .

## SECTION 2.3

### Real-World Applications

For the following exercise, use the information to find a linear algebraic equation that models the given information.

- Charles and Jamal are joking that their combined ages equal grandma’s age. If Charles is one and a half times Jamal’s age and grandma is 100 years old, what are Charles and Jamal’s ages?

For the following exercise, use this scenario:

- A truck rental agency offers two kinds of plans. Plan A charges $125/week plus $.18/miles driven. Plan B charges $150/week plus $.09/miles driven.
- Write the model equation for the cost of renting a truck for a week with plan A.
- Write the model equation for the cost of renting a truck for a week with plan B.
- Find the number of miles that would generate the same cost for both plans. Round up to the nearest mile.
- If Tom knows he has to travel 450 miles for a week, which plan should he choose?

- The slant height of a right circular cone is given by the formula , where
*r*is the radius of the base of the cone and*h*is the height of the cone. Solve the equation for*h*then determine the height of the cone if the slant height is 10 cm and the radius of the base is 6 cm?

## SECTION 2.4

### Algebraic

For the following exercise, evaluate the algebraic expressions.

- If evaluate
*y*given*x*= 2*i*.

### Graphical

For the following exercise, plot the complex numbers on a single complex plane.

- 4 + 6
*i***,**-8 – 4*i***,**-5 + 3*i***,**-4*i*, -5, 8 – 3*i*

### Numeric

For exercises * 20 and 21*, perform the indicated operation and express the result as a simplified complex number.

- (-5 – 7
*i*)(-3 + 5*i*)

## SECTION 2.5

### Algebraic

For the following exercise, solve the quadratic equation by factoring.

For the following exercise, solve the quadratic equation by using the square root property. Simplify any radical solution to lowest terms.

For the following exercise, solve the quadratic equation by completing the square. **Show each step.**

For the following exercise, determine the discriminant, and then state how many solutions there are and the nature of the solutions.** Do not solve.**

For the following exercise, solve the quadratic equation by using the quadratic formula. If the solutions are not real, state **No Real Solution**. Simplify radicals to lowest terms.

### Extensions

- A company’s stock had a price given as , where t is the time in months from 2009 to 2011 ( t = 1 is January 2009). Find the two months in which the price of the stock was $25.

### Real-World Applications

- A formula for the normal systolic blood pressure for a man of age
*A*, measured in mmHg, is given as. Find the age to the nearest tenth of a year of a man whose normal blood pressure measures 130 mmHg.

## SECTION 2.6

### Algebraic

For the following exercise, solve the rational exponent equation. Use factoring where necessary.

For the following exercise, solve the following polynomial equation by grouping and factoring. Make sure to find any complex solutions.

For the following exercise, solve the radical equation. Be sure to check all solutions to eliminate extraneous solutions.

For the following exercise, solve the equation involving absolute value.

For the following exercise, solve the equation by identifying the quadratic form. Use a substitute variable and find all real solutions by factoring. Find all real and complex solutions. **Show all work.**

### Real-World Applications

For the following exercise, the slant height of a right circular cone is given by the formula , where *r* is the radius of the base of the cone and *h* is the height of the cone.

- What is the radius of the cone if the slant height is 200 cm and the height of the cone is 150 cm?

## SECTION 2.7

### Algebraic

For the following exercise, solve the inequality. Write your final answer in interval notation.

For the following exercise, solve the inequality involving absolute value. Write your final answer in interval notation.

- | | > 11

For the following exercise, solve the compound inequality. Express your answer using inequality signs, and then write your answer using interval notation.

### Numeric

For the following exercise, write the set in interval notation.

For the following exercise, write the interval in set-builder notation.

### Real-World Applications

- A car rental package costs $70/week, with an additional charge of $0.15/mile beyond 200 miles. The cost formula would be. If you have to keep your bill lower than $125, what is the maximum distance (in miles) beyond 200 miles you can drive?