Complex Numbers
Simplify this equation:
(-10+3i) - (4+5i)
-14-2i
If Ben invest $4000 at 4% interest per year, how much additional money must he invest at 5.5% annual interest to ensure that the interest he receives each year is 4.5% of the total amount invest?
x=$2,000 @ 5.5%
A rectangular garden is 25 ft wide. If its area is 1125 ft^2, what is the length of the garden?
x=45 ft
((x+4)/(x-9))≥0
(-∞,-4] U (9,∞)
What amount of pure acid must be added to 300 mL of a 45% acid solution to produce a 70% acid solution?
x=250 mL
Simplify this equation:
(3+2i)(5-i)
17+7i
A rental company charges $30 a day and 40 cents a mile for renting a truck. Zach rents a truck for 3 days and his bill came to $209.20. How many miles did he drive?
x=298 miles
What amount of pure acid must be added to 300 mL of 40% acid solution to produce a 60% acid solution?
x=150mL
(x+4)(x-1)^2(x+2)<0
(-4,-2)
Evaluate the radical expression and express the results in the form a+bi=
√(-8) * √(-9)
=-6√(2)
Simplify the equation:
(3-5i)/(1-2i)
(13/5) + (i/5)
Phyllis invested $12,000, a portion earning a simple interest rate of 4.5% per year and the rest earning a rate of 4% per year. After 1 year the total interest earned on these investments was $525. How much money did she invest at each rate?
$9,000 @ 4.5%
$3,000 @4%
A rectangular building lot is 8ft longer than it is wide and has an area of 2900ft^2. Find the dimensions of the lot.
50x58 ft
x^2-3x-10≥0
(-∞,-2] U [5,∞)
Solve the linear inequality. Express the solution using interval notation:
1≤ 4x-7 < 9
[2,4)
Simplify:
i^17
i
A cell phone company charges a monthly fee of $10 for the first 1000 text messages and 10 cents for each additional text message. Miriam's bill for text messages for the month of June is $38.50. How many text messages did she send that month?
x= 1285 text messages
A rectangular bedroom is 2 ft longer than it is wide. Its area is 143 square feet. What is the width of the room?
x=11 ft
1≤ 4x-7 <9
[2,4)
A rectangular bedroom is 10 ft longer than it is wide. Its area 875 ft^2. What are the dimensions?
length= 35ft
width= 25ft
Simplify:
(x^2)+3x+6=0
(-3±i√(15))/2
If Katelyn invests $8500 at 4.3% interest per year, how much additional money must she invest at 5.5% annual interest to ensure that the interest she receives each year is 4.75% of the total amount invested?
x=$5100 @5.5%
What amount of a pure acid must be added to 300 mL of a 50% solution to produce a 60% acid solution?
x=75 mL
| 5x+2 | <4
(-6/5, 2/5)
A rental company charges $65 a day and 20 cents a mile for renting a truck. Michael rented a truck for 3 days, and his bill came to $275. How many miles did he drive?
x=400 miles