homework 4

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1. If the hypotenuse of a right triangle is 6m and one side is 4m, what is the length of the other side?

2. Which of the following best describes imaginary numbers?

A. They are the values of expressions of the form for various real numbers a, as long as a ≠ 0.

B. They are not numbers, but are useful in solving equations.

C. They are the complex numbers.

D. They consist of two values, the principal imaginary number i and its negative –i.

3. Simplify .

4. Compute the value of .

5. Two children in nearby houses attempt to use walkie-talkies to communicate. The walkie-talkies reach one quarter of a mile (1320 feet). From one child's house to the other, the walk along the city sidewalks is as follows: Proceed 450 feet from the first house to the nearest corner, turn right 90° and proceed another 1050 feet. Are the children's houses within the 1320-foot range of one another? Choose the best answer.

A. Yes, because city blocks are much smaller than one quarter of a mile.

B. Yes, as the distance formula indicates.

C. No, because the distance is greater than 1320 feet.

D. No, but if the turn were to the left instead, they would be within range.

6. Choose the best description of the radical expression .

A. It can be simplified to –3.

B. It can be simplified to , but no further.

C. It is in simplified form.

D. It can be simplified, but the result is a complex number.

7. Which of these expressions simplifies to ?

8. Combine like radicals in .

9. Simplify .

10. Expand and simplify. Assume y ≥ 0.

11. Solve for x.

12. Solve for x.

A. 40

B. –41

C. 50

D. 4

13. Expand and simplify. Assume c ≥ 0 and d ≥ 0.

14. Simplify (6 − i)(2 + i).

A. 11 + 4i

B. 13 − 8i

C. 13 + 4i

D. 11 + 8i

15. Which of these expressions is in simplified form?

16. Solve for x.

A. x = 2

B. x = 4 or x = –4

C. x = 2 or x = 8

D. The two solutions for are complex numbers.

17. Which of these phrases best describes the standard deviation?

A. It is equal to the mean squared.

B. It is a measure of variability.

C. It is a radical expression using n variables.

D. It increases as more measurements are taken.

18. Rationalize the denominator of .

19. Simplify i23.

A. –1

B. 1

C. i

D. –i

20. What best describes the triangle whose corners are located at the points (1, 1), (2, 2), and (0, 16)?

A. It has area 22 square units.

B. It is isosceles.

C. None of the above.

D. It is a right triangle.

21. Which of these radical expressions simplifies to x?

22. Simplify by rationalizing the denominator.

23. Rationalize the denominator of assuming x ≥ 0 and y ≥ 0.

24. Simplify .

25. Simplify .