show all work

Name: College ID: Thomas Edison State College College Algebra (MAT-121-GS) Section no.: Semester and year: Written Assignment 3 Answer all assigned exercises, and show all work. 1. Solve each equation. (See section 1.1, Examples 1 and 2.) [10 points] a. b. c. d. 2. Solve each formula for the individual variable. Assume that the denominator is not 0 if variables appear in the denominator. (See section 1.1, Examples 4(a) and (b).) [7.5 points] a. for P (simple interest) b. for h (area of a trapezoid) c. for g (distance traveled by a falling object) 3. Simple interest (see section 1.1, Example 5)—Levada Qualls borrows $30,900 from her bank to open a florist shop. She agrees to repay the money in 18 months with simple annual interest of 5.5%. [2.5 points] a. How much must she pay the bank in 18 months? b. How much of the amount in part (a) is interest? 4. Convert to Celsius []. [5 points] a. 77°F b. 350°F 5. Perform mentally— If 120 L of an acid solution is 75% acid, how much pure acid is in the mixture? [2.5 points] 6. Solve (see section 1.2, Example 1)—The world’s largest ice cream cake, made at the Baxy ice cream factory in Beijing, China, on January 16, 2006, had a length 5.9 ft greater than its width. Its perimeter was 51 ft. What were the length and width of this 8-ton cake? (Sources: www.chinadaily.com.cn, www.foodmall.org). [2.5 points] 7. Which one or more of the following cannot be a correct equation to solve a geometry problem, if x represents the length of a rectangle? (Hint: Solve each equation and consider the solution.) [2.5 points] a. b. c. d. 8. Distance between cities (see section 1.2, Example 2)—On a vacation, Elwyn averaged 50 mph traveling from Denver to Minneapolis. Returning by a different route that covered the same number of miles, he averaged 55 mph. What is the distance between the two cities if his total traveling time was 32 hr? [2.5 points] 9. Speed of a plane (see section 1.2, Example 2)—Two planes leave Los Angeles at the same time. One heads south to San Diego, while the other heads north to San Francisco. The San Diego plane flies 50 mph slower than the San Francisco plane. In hr, the planes are 275 mi apart. What are their speeds? [2.5 points] 10. Alcohol mixture (see section 1.2, Example 3)—How many gallons of pure alcohol should be mixed with 20 gal of a 15% alcohol solution to obtain a mixture that is 25% alcohol? [2.5 points] 11. Cooking royalties (see section 1.2, Example 4)—Becky Schantz earned $48,000 from royalties on her cookbook. She paid a 28% income tax on these royalties. The balance was invested in two ways, some of it at 3.25% interest and some at 1.75%. The investments produced $904.80 interest per year. Find the amount invested at each rate. [2.5 points] 
 12. Determine whether each statement is true or false. If false, tell why. [7.5 points] a. No real number is a pure imaginary number. b. A number can be both real and complex. c. A complex number might not be a pure imaginary number. 13. Identify the number as real, complex, pure imaginary, or nonreal complex. (More than one of these descriptions may apply.) [5 points] a. b. 14. Find the sum or difference. Write the answer in standard form. (See section 1.3, Example 4.) [2.5 points] 15. Find each product. Write the answer in standard form. (See section 1.3, Example 5.) [10 points] a. b. c. d. 16. Find the quotient. Write the answer in standard form a + bi. (See section 1.3, Example 6.) [5 points] a. b. 17. Solve the equation by the zero-factor property. (See section 1.4, Example 1.) [5 points] a. b. 18. Solve the equation by completing the square. (See section 1.4, Examples 3 and 4.) [5 points] a. b. 19. Francesca claimed that the equation cannot be solved by the quadratic formula since there is no value for b. Is she correct? [2.5 points] 20. Solve each equation using the quadratic formula. (See section 1.4, Examples 5 and 6.) [7.5 points] a. b. c. 21. Solve the equation for the indicated variable. Assume no denominators are 0. (See section 1.4, Example 8.) [5 points] a. for r b. for t 22. Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions and whether they are rational, irrational, or nonreal complex. Do not solve the equation. (See section 1.4, Example 9.) [2.5 points]