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I need help with these make-up problems, i've been outta school for funerals and hospital visits, So i haven't been able to get any time or tutoring in class.

1. If a, b, and c are positive, and a divided by b is equal to b divided by c, then b is called the mean proportion, or geometric mean, between a and c. Find the mean proportion between the pair of numbers: 5 and 15. 5 3
 b = 3
b = 75  3 5


2. A public opinion poll found that out of a sample of 450 voters, 252 favored a school bond issue. If 20,000 people voted, how many are likely to vote for the bond measure? 15,714  11,200
1,120  10,100

3. The conductance of a wire varies directly as the square of the wire's diameter and inversely as its length. Fifty meters of wire with a diameter 2 mm has a conductance of 0.12 ohms. If a wire of the same material has length of 75 m and diameter of 2.5 mm, what is its conductance? 0.05 ohms  0.167 ohms
0.125 ohms  0.5 ohms

4. The length of a rectangle with constant area varies inversely as the width. When the length is 18, the width is 8. Find the length when the width is 9. 12  14
16  18


5. Divide using synthetic division:

3x3 - 2x2 + x + 4
 x + 1   
3x2 - 5x + 4  3x2 - 5x -  2  
x + 1

3x2 + 5x + 4  3x2 - 5x + 6 +  -2  
x + 1


6. Find a polynomial equation with integral coefficients that has the roots:

-2, -i, i

x3 + x + 2 = 0  x3 + 2x2 + 2 = 0
x3 + 2x2 + x + 2 = 0  x3 - 2x2 - x - 2 = 0

7. Find all the roots of the equation:

P(x) = 0.25x2 - 12x + 23

2, 46  2, 11
3, 4/5  -1, 7

8. Find all roots of the equation

3x2 - 11x - 4 = 0

-3, 4  3, 4
-1/3, 4  4

9. Find the midpoint of the segment joining the points:

(0.5,-1) and (-1,1)

(-2, 0)  (-0.25, 0)
(-0.5, 0)  (0.25, 0)


10. Choose the correct coordinates of the foci

x2 + 4y2 - 16 = 0

(12, 0) and (-12, 0)  (-2√3, 0) and (2√3, 0)
(-√12, 0) and (√12, 0)  (-4√3, 0) and (4√3, 0)

11. Identify the conic. Choose the conic and its center.

16x2 + 25y2 - 96x - 200y = -144

Ellipse (3, -4)  Ellipse (-3, 4)
Ellipse (3, 4)  Ellipse (-3, -4)

12. Identify the conic. Choose the conic and its center.

16x2 - 9y2 + 64x + 18y + 199 = 0

Hyperbola (-2, 1)  Hyperbola (1, -2)
Hyperbola (-2, -1)  Hyperbola (-1, 2)

13. Give the radius and the coordinates of the center of the circle:

(x - 1)2 + y2 = 144

center: (0, 0), radius: 12  center: (0, 0), radius: 72
center: (1, 0), radius: 12  center: (1, 0), radius: 72

14. Use the information to write an equation of the parabola:
Focus: (-8, 0), Directrix: x = 8

x2 = -8x  y2 = -8x
y2 = x/-2  y2 = -32x

15. Identify the conic section whose equation is given:
16x2 + 4y2 = 16

Circle  Parabola
Hyperbola  Ellipse

16. Choose the correct foci:

25x2 - 144y2 = 3600

(0, 13)  (5, 12)
(12, 5)  (13, 0)

17. Choose the real solutions of the system:

x2 + 2y2 = 12 and 3x2 - y2 = 8

(2,2) (-2,2) (2,-2) (-2,-2)  No real solution
(4,4) (-4,4) (4,-4) (-4,-4)  (-2,2) (2,2) (1,4) (2,4)

18. Choose the real solutions of the system:

x = y2 + -9 and x - 4y - 12 = 0

(0, 3); (40, -7)  (0, -3); (58, 7)
(0, -3); (40, 7)  (-3, 0); (40, 7)

19. Find the length of the legs of a right triangle having perimeter 56m if the hypotenuse is 25m. 12m and 14m  10.5m and 16m
17m and 20m  7m and 24m

20. Four squares, each with sides 4 cm long, are cut from the corners of a rectangular piece of cardboard having an area 560 cm2.  The flaps are then bent up to form an open box having volume 960 cm3.  Find the dimensions of the original piece of cardboard. 20 cm by 28 cm  22.4 cm by 25 cm
17.5 cm by 32 cm  22 cm by 26 cm

21. Find the dimensions of a rectangle with an area of 60 ft2 and a diagonal of 13 ft. 10 ft by 2 ft  20 ft by 3 ft
12 ft by 5 ft  32 ft by 4 ft

22. Find two negative numbers such that the sum of their squares is 170, and twice the square of the first minus three times the square of the second is 95. -12, -5  -11, -7
-24, -40  -2, -8

23. How many points do the graphs of y = x2 and xy = 27 have in common? 0  1
2  3

24. The lines with equations x = 2, x = 5, y = 7, and y = 3 form a rectangle. What is the area of this rectangle? 12  14
15  28


25. Solve the system:

z + 3x + y = 3

2x + 3y = 10

2y = 8

(-1, 2, 2)  (1, 4, 2)
(-1, 4, 2)  (-3, 2, 4)

26. Solve the system:

2x + 5y + 2z = -5

-3x + 3y + 5z = 2

x + 4y - z = 3

(-3, 1, -2)  (3, -1, -2)
(-3, 1, 2)  (-3, 1, 4)

27. Choose the correct exponential form for:

The cube root of (x to the sixth power times y to the negative four power)

x to the eighteenth power times y to the negative 12 power  x to the one half power times y to the negative three fourths power
x squared times y to the four thirds power  x squared times y to the negative four thirds power

28. Simplify:  

(The square root of 2 minus 1 to the 2 plus y power) all divided by (the square root of 2 minus 1 to the y power).

2
 3 - 2 2

1  3 + 2 2

_________________________________________________
Part 8-1
Select the best answer from the choices provided. (Each question is worth one point)

29. Express as a single logarithm: 4 ln 2 - ln 3 - 1  

4 ln  4 ln 4

ln 16/3e  ln 3/16e
__________________________________________________________
30. Solve: 3e2x + 2 = 50

ln 8  ln 0.25

ln 14  0.5ln 16

Answer
1. 5(3^1/2)  2. 11,200  3. 0.125  4. 16  5. 3x^2-5x+4  6. x^3+2x^2+x+2 = 0  7. 2,46
8. -1/3, 4  9. (-0.25,0)  10. [-2(3^1/2)] [2(3^1/2)]  11. ellipse (3,4)  
12. hyperbola (-2,1), +199 not correct   13. center (1,0) radius = 12  14. y^2 = -32x
15. ellipse   16. (+/-13,0)  17. (2,2)(-2,2)(2,-2)(-2,-2)  18. (0,-3)(40,7)
19. 7m and 24m  20. 20x28  21. 12ft, 5ft  22. -11,-7  23. 1  24. 12  25. (-1,4,2)
26. -3,1,-2  27. x^2y^-4/3 28. 1

Algebra

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