Chapter 1 Review Problems
(3-6 i) (10+ i )
30 + 3 i -60 i -6 i^2 36- 57 i
(7 i) (-7 i)
49
5x 1 -3 ------------- - ------ = ------ 3x^2 - 5x -2 3x+1 2-x
5 x = - ---- 13
*solve for x* 6x + ay = bx + 5
5-ay x= ------- 6-b
*solve for x* 6= 4x+ tx
6 x= ---- 4+t
(15 + 21 i ) + ( -18 + 40 i )
-3 + 61 i
*solve for d* n S = --- (a+d) 2
25 d= --- - a n
2x (x-3)= 4+x
2x^2 -6x =4 + x 2x^2 -7x -4 =0 1 x= 4, - --- 2
t^2 -6t +10=0
3+and- i
DAY ONE
DAY ONE
4(6 + 2 i ) -5 i (3-7 i)
-11 -7 i
COST/PROFIT: It costs a restaurant owner 18 cents per glass for orange juice, which is sold for 75 cents per glass. How many glasses of orange juice must the restaurant owner sell to make a profit of $2337?
.75 - .18 = .57 (profit) .57x = 2337 x= 4100 glasses
WORK: An electrician can install the electric wires in a house in 14 hours. A second electrician requires 18 hours. How long would it take both electricians, working together, to install the wires?
1 1 1 --- + --- = --- 14 18 x 8 1 --- = --- 63 x 8x=63 x=7.875 hours
(10 -4 i) (10 + 4 i)
100 - 16 i^2 +16 116
AVERAGE: A student has test scores of 62, 70, 75, and 80. What score does the student need on the next test to produce an C (70-79)?
62 + 70 + 75 + 80+ x 5* ----------------------- =70 5 287 + x= 350 x= 63% AND 62 + 70 + 75 +80 +x 5* ---------------------- =79 5 287 + x = 395 x= 108% The student needs to make from a 63-108%.
*solve for y* 7x + 2y =8
7 y= - --- x + 4 2
6+2 i ------ 3- i
8 6 --- + --- i 5 5
INVESTMENT: An investment advisor invested $14,000 in tow accounts. One investment earned 8% annual simple interest, and the other investment earned 6.5% annual simple interest. The amount of interest earned for 1 year was $1024. How much was invested in each account?
8% (x) 6.5% (y) x+y=1400 --> x= 1400y 0.08x + 0.065y =1024 0.08 (1400-y) + 0.065y =1024 1120 - 0.08y + 0.065y = 1024 -0.15y = -96 y= 6400 1400-6400=x x= 7600 8%=$7600 and 6.5%=$6400
AVERAGE: A student has test scores of 80, 82, 94, and 71. What score does the student need on the next test to produce an average score of 85?
80 + 82 + 94 + 71 + x 5* ---------------------- = 85 *5 5 327+ x =425 x=98% The student needs a 98%.
*solve for P* A= P+ Prt
A P= ------ (1+ rt)
DAY FIVE
DAY FIVE
DAY FOUR
DAY FOUR
DAY THREE
DAY THREE
DAY TWO
DAY TWO
c 3 3 ---- = ---- - ---- c-3 c-3 4
NO SOLUTION c=3 (does not work!!)
WORD PROBLEMS- DAY TWO
WORD PROBLEMS- DAY TWO
POWER OF i:
i= 1 i^2= -1 i^3= -i i^4= 1 i^5= i
w+3 1 w-5 ---- + --- = ---- 4w 1 w
w= -23
COST/PROFIT: The price of a magazine subscription rose 4% this year. If the subscription now costs $26, how much did it cost last year?
x + .04x = 26 1.04x = 26 x= $25
1 3 2 -- x -(minus) -- = -- 4 2 1
x=14
2(5x-6)=4[ x-3(x-10)]
x=22/3
y-1 y y+3 --- + --- = --- 5 4 2
y= -54