1. = +
8t2 = 6t + 27
8t2 -6t – 27=0
b2 – 4ac = 36 + 864=900
t = (-6 ±)/ 16
t = (-6 + 30)/16 or (-6 -30)/16
t= 1.5 or -2.25
2. A = P ( 1 + r/q)nq for interest compounded q times a year.
P = &6000
r = 4%
n = 3 years
a) q = 2(semiannually)
A = P ( 1 + r/q)nq = 6000 (1 + 0.04/2)3(2) = $6756.97
b) q = 4(quarterly)
A = P ( 1 + r/q)nq = 6000 (1 + 0.04/4)3(4) = $6760.95
c) q= 12(monthly)
A = P ( 1 + r/q)nq = 6000 (1 + 0.04/12)3(12) = $6763.63
3.
The equation of the graph resembles y = 2x + 3
4. (6x + 8)2 is of form (a + b)2 = a2 + 2ab + b2
(6x + 8)2 = 36x2 + 96x +64
5. (x2 + 3x -10)/ (x-2)
x2 + 3x -10 = x2 + 5x -2x-10 = x(x +5) -2(x+5) = (x-2)(x+5)
(x2 + 3x -10)/ (x-2) = (x-2)(x+5)/ (x-2) = x+5
6.
Equation through (4, -5) and perpendicular to 4y = x-8
The equation 4y = x-8 can rewritten as y = 1/4x-2
The slope of the line m, m * ¼ = -1, implying that m = -4
Choosing a point (x, y)
= -4
y + 5 = -4(x-4) = -4x + 16
y = -4x + 16 -5 = -4x + 11
Therefore, f(x) = -4x + 11
7. x2 + 7x + 2 = 0
x = -7 ± (7 -8)1/2
The equation has no real roots
x = -7 ± (-1)1/2
x = -7 ± i
x = -7 +I, -7 – i
8. (5y2-7y +5) – (4y2-7y +2) = 5y2-7y +5 – 4y2 +7y -2
5y2– 4y2 -7y +7y +5 -2 = y2 + 3
9. -5=0
()2 =52
3x-2 =25
3x = 27
x=9
10. C(x) = (x-9)/(x2-25) =
The function is {xlx is a real number x ≠5
11. -17≤7x-10≤4
-17≤7x-10 and 7x-10≤4
-17 + 10 ≤7x
-7≤7x
-1≤x
7x-10≤4
7x≤4 +10
7x≤14
x≤2
Therefore, -1≤x ≤2
12. - =1
5t-2t = 6
3t =6
t = 2
13. = =
14. = = 4a2b3c3
15. 7x-2y =-42
-2y =-7x-42 rearranging the equation
y =x + 21 dividing by -2
The equation is in the form y= mx + C
The slope is 7/2 and the y intercept is 21
16. P α N
Let k be the constant of proportionality
P=kN
468,000=k(260,000)
k = 1.8
P=1.8N
N=344,000
P=1.8N=1.8* 344,000 = 619,200
The pollutants in city B is 619,200
17. = = =
18. – = =
= =
19. = =
20. (-8x3y6)(9x5y4) = -72x(3 +5)y(6 +4) = -72x8y10
21. D(x) = x
The proper dosage for a dog whose weight is 22 pounds is D(x)
D(22) = * 22 = 119.68 mg
22. Let the population be represented by p
P2006 = 30.2 million
P2001 =?
Percentage increase= 6.5%
Therefore, (P2006- P2001)/ P2001=6.5/100
(30.2- P2001)/ P2001 = 0.065
30.2 -P2001=0.065 P2001
30.2 = 1.065 P2001
P2001=30.2/1.065 = 28.3568 million
Rounded to the hundredth million
P2001=28.36 million
23. The equation passes through (0, 152000) and (5, 223350).
Let y be the median house prices in & and x be the years
a) Let (x, y) be an arbitrary point on the line
Then the equation of the line is given by
=
= =14270
y -152000 =14270x
y= 14270x + 152000
b) at year 2010 x = 9
y =14270 (9) + 152000 = $280430
The median house price at 2010 is $280430.
c) Every year the median price a house increases by &14270.
24. 2(x-3) + x = 3(x-3) + 3
4x -6 + x = 3x -9 + 3
5x -6 =3x -6
5x – 3x= 0
2x =0
x = 0
25. = ±3x
