Homework section 1.2 college algebra

Written Assignment 1
2.5 points each

SECTION 1.1
For exercises 1 and 2 , simplify the given expressions.

1.

2.

For the following exercise, solve for the variable.

3.

For exercises for 4 and 5 , simplify the expressions.

4.

5.

6. During a recent storm clean up there is a mound of m tons of sand at the beach. Throughout the day 1,200 tons of sand are added to the mound. Two dump trucks come in and take 800 tons of sand each from the mound. At the end of the day, the mound has 2,400 tons of sand.

a. Write the equation that describes the situation.

b. Solve for m.

SECTION 1.2
Numeric
For exercises 7 and 8 , simplify the given expressions. Write answers with positive exponents.

7.

8.

For exercises 9 and 10 , write each expression with a single base. Do not simplify further. Write answers with positive exponents.

9.

10.

Technology
For the following exercise, use a graphing calculator or scientific calculator to simplify. Round the answer to the nearest thousandth.

11.

Extensions
For the following exercise, simplify the given expression. Write the answer with positive exponents.

12.

SECTION 1.3
Numeric
For exercises 13 and 14 , simplify each expression.

13.

14.

Algebraic
For exercises 15-17 , simplify each expression.

15.

16.

17.

Real-World Applications
18. A guy wire for a radio antenna tower runs from the ground diagonally to the top of the closest eye bolt to make a triangle. We can use the Pythagorean theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the eye bolt on the ground is 1,600 feet. The square of the height of the pylon is 6,400 feet. What is the length, c, of the guy wire? Give an exact answer in feet.

SECTION 1.4
Algebraic
For the following exercise, identify the degree of the polynomial.

19.

For the following exercise, find the sum.

20.

For exercises 21 and 22 , find the products.

21.

22.

For the following exercise, expand the binomial.

23.

For the following exercise, multiply the binomials.

24.

For the following exercise, multiply the polynomials.

25.

Real-World Applications
26. A real estate broker wants to purchase a plot of land for a subdivision development. The area of the plot can be described by the following expression: where x is measured in meters. Multiply the binomials to find the area of the plot in standard form.

SECTION 1.5
Algebraic
For the following exercise, find the greatest common factor.

27.

For the following exercise, factor by grouping.

28.

For exercises 29 and 30 , factor the polynomials.

29.

30.

For exercises 31 and 32 , factor the polynomials.

31.

32.

Real-World Applications
For the following exercise, consider this scenario:

33. Tammy has appointed a chairperson to lead a city restoration project. The first act is to plant a tree, flowers, and a statue in one of the city’s parks. The park is a rectangle with an area of , as shown in the following figure. The length and width of the park are perfect factors of the area.

a. Factor by grouping to find the length and width of the park.

b. A tree is to be placed in the center of the park with a rectangular flower garden around it. The area of the flower garden is . Factor the area to find the lengths of the sides of the flower garden.

c. At the southeast corner of the park, the city is going to install a statue. The area of the base of the fountain is . Factor the area to find the lengths of the sides of the statue.

SECTION 1.6
Algebraic
For the following exercise, simplify the rational expression.

34.

For the following exercise, multiply the rational expressions and express the product in simplest form.

35.

For the following exercise, divide the rational expressions.

36.

For the following exercise, subtract the rational expressions and then simplify.

37.

For the following exercise, simplify the rational expression.

38.

Real-World Applications
39. Brad is placing tile on his bathroom floor. The area of the floor is . The area of one tile is ) . To find the number of tiles needed, simplify the rational expression: .

40. The area of Sam’s driveway is . A container of blacktop sealer covers an area of . Divide the two areas and simplify to find how many containers of blacktop sealer Sam needs to resurface his driveway.