# 4

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```					4.1

1. Simplify your answer, use a comma to separate the answers as needed

3/5 + ½ = 1/x 10/11

2. Simplify your answer, use a comma to separate the answers as needed

3/7v + 7/v = 1 52/7

3. Simplify your answer, use a comma to separate the answers as needed

4/(x+5) = 6/x -15

4. Simplify your answer, a comma to separate the answers as needed. Type an exact
answer, using radicals as needed.

(x-3)/(x+1) = (x+5)/(x+3)       -7/3

5. x=?

2/(x-1) + 3/(x+1)=3x/(x^2-1)         1/2

6. a=?

5-[(a-8)/(a+4)]=(a^2-4)/(a+4)          8

7. Solve. Simplify your answer; use a comma to separate the answers as needed

(2a-1)=(a+17)/(a+1)                     -3, 3

8. One dude does job for 5 hrs, another dude the same job for 4 hrs. How long will it
take them to do it together? 2 2/9 hours

9. One thing is 8 mph faster than another; it travels 310 miles in the same time it
takes another to travel 270 miles. What’s the speed of each?
54 mph, 62 mph

10. A thing travels 132 miles for a walk in one direction in snow. The return trip in
rain was finished at double the speed and took 3 hrs faster. Find the speed going.
22 mph

11. (Answered).

12. 2 lbs of muscle for every 7 lbs of body weight of an animal. For a 189 lbs animal,
how much of the weight is muscle? 54 lbs
13. 10cm^3 of a normal specimen of human blood contains 1.2 g of hemoglobin.
How many grams does 31 cm^3 of the same blood contain? 3.72 g

14. It is known that making 1 lb of honey requires 20,000 trips by bees to flowers to
gather nectar. How many lbs of honey would 25,000 trips produce?1.25 lbs

15. Last season, Rockies player got 80 hits in 200 times at bat. If he expects to bat
600 times in whole season with the same ratio, how many hits can the player
expect to have? 240 hits

16. Hat sizes are determined by measuring the circumference of one’s head in inches
or cm’s. Use ration and proportion to complete the following table.

Hat size                   Head Circumference              Head Circumference
(to nearest 1/5 inch)             (to nearest cm)
6 7/8                             21 3/5                          55

7¾                                24 2/5                               62

17. A sample of 129 firecrackers contained 9 duds. How many duds would you
expect in a sample of 1419 firecrackers? 99

18. For the pair of similar triangles, find the value for x.

X                                            G

Y                                 Z        F                                H

Between X Z is 12 and between G and H is 4.
(To solve this, some more data is required and is missing. Please clarify.)

19. Find the variation constant and an equation of variation where y varies directly as
x and y =40 when x =4. k = 10, y = 10x

20. The number N of aluminum cans used each year varies directly as the number of
people P using the cans. If 51 people use 14,484 cans in one year, how many cans
are used in a city which has population of 1,954,000? 554,936,000 cans

21. Hooke’s Law. The distance d when a spring is stretched by a hanging object
varies directly as the weight w of the object. If the distance is 30 cm when the
weight is 2 kg what is the distance when the weight is 7 kg? 105 cm
22. Find the variation constant and an equation of variation where y varies inversely
as x and y=10 when x=19. k = 190, y = 190/x

23. It takes 9 hrs for 5 cooks to prepare the food for a wedding rehearsal dinner. How
long will it take 8 cooks to prepare the dinner?

(a) What kind of variation applies to this situation: direct or inverse? Inverse
(b) Solve the problem. 5 5/8 hours

24. The stopping distance d of a car after the breaks are applied varies directly as the
square of the speed r. If a car traveling 70 mph can stop in 270 ft, how many feet
will it take the same car to stop when it is traveling 30mph? 49.59 ft

4(2).

1. What is the principle square root of 6400?       80

2. Find the square root that is a real number: √-81= Square root is not a real number

3. Find each function value, if it exist f(t)=√t^2+1, f(0)= 1

4. Find the following. Assume that variable can be any real number: √(a+3)^2=
|a + 3|

5. Simplify: 3√-27x^3      -3x

4
6.       10000   10

7.   4   (5a) ^4= 5a

8. Rewrite without exponents: x^1/3= 3x

9. Rewrite with rational exponents, simplify:   3   xy^2z x^(1/3) y^(2/3) z^(1/3)

10. Simplify completely: 8^-4/3 1/16

11. Use the laws of exponents to simplify: (6.5^5/4)/(6.5^6/7)= (6.5)^(11/28)

12. Rewrite using only rational positive exponents, simplify: (x^5/4)^-4/7=
1/[x^(5/7)]

13. Use rational exponents to simplify 6 x ^ 42 = x^-7

14. Use rational exponents to simplify:    x^6 y^8 = x^3 y^4
15. Use rational exponents to rewrite: x^1/6*y^1/5*z^1/3=      30
(x^5 y^6 z^10)

16. Simplify by factoring, an exact answer using radicals as needed: 108 x ^ 4 =
6x^2 3

17. Simplify by factoring, an exact answer using radicals as needed:      4
810 = 3 410

18. Multiply and simplify. Assume that all expressions represent nonnegative
numbers: 5x ^3 30 x 5x^2 6

19. Multiply and simplify by factoring. Assume that all expressions under radicals
represent nonnegative numbers: 3 y ^4 3 81y^5 = 81 y^4 y

20. Simplify by factoring. Assume that all expressions under radicals represent
nonnegative numbers: 4 48x^8 y ^10 = 2x^2 y^2 4(3y^2)

21. Simplify by factoring. Assume that all expressions under radicals represent
nonnegative numbers: 5 224x^17 y^20 = 2x^3 y^4 5(7x^2)

22. Multiply and simplify by factoring, an exact answer using radicals as needed:
80 * 90 = 602

23. Multiply and simplify by factoring. Assume that all expressions under radicals
represent nonnegative numbers: 5b ^3 55c ^ 4 = 5bc^2 (11b)

24. Divide. Then simplify by taking roots, if possible. Assume that all expressions
under radicals represent positive numbers: 15aa = 5
3

25. Divide. Then simplify by taking roots, if possible. Assume that all expressions
under radicals represent positive numbers: 3 32 a ^ 7b ^ 2 : 3 4a ^5b ^1 = 2a (2b)

26. Divide and simplify. Assume that all expressions under radicals represent
nonnegative numbers: 4 3x : 7 x 28(2187x^3)

27. Simplify by taking roots of the numerator and the denominator. Assume that all
243x^3
expressions under radicals represent positive numbers: 5         =
y ^ 20
(3/ y^4) 5(x^3)
28. Add or subtract. Simplify by collecting like radical items, if possible. Simplify,
type exact answer using radicals as needed: 6*√3-4*√3+7*√3= 93

29. Add. Simplify by collecting like radical terms if possible. Simplify to exact
answer: 7*√50+2*√18= 412

30. Add. Simplify by collecting like radical terms if possible, assuming that all
expressions under radicals represent nonnegative numbers, an exact answer using
radicals as needed: 2a +4* 8a ^3 = (1 + 8a) (2a)

31. Multiply, simplify, an exact answer using radicals as needed: √6*(9-10*√6)=
96 - 60

32. Multiply, simplify, an exact answer using radicals as needed:
3
a *( 3 3a ^ 2 + 3 81a ^ 2 )= 4a 33

33. Multiply, simplify, an exact answer using radicals as needed: (2+√5)(2-√5)= -1

34. Multiply. ( 5 4 - 5 2 )( 5 125 + 5 8 )= 5500 - 5250 + 2 - 516

35. Rationalize the dominator: (10*√3)/(3*√5)= (2/3) 15

36. Rationalize the dominator. Assume that all expressions under radicals represent
positive numbers: 3 3y ^4 : 3 6x ^ 4 = (y/ 2x^2) 3(4x^2 y)

37. Rationalize the dominator. Assume that all expressions under radicals represent
positive numbers: (2-√a)/(3+√a)= (6 - 5a + a)/(9 - a)

38. Rationalize the dominator. Assume that all expressions under radicals represent
positive numbers, an exact answer using radicals as needed: (√a-√b)/(√a+√b)=
[a + b - 2(ab)]/(a -- b).

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