# Algebra

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1. Juanita has 180 feet of fencing that she intends to use to build a rectangular play area for her dog. She wants the play area to enclose at least 1800 square feet. What are the possible widths of the play area?

2. A bicycle maker sold 300 bicycles last year at a profit of \$300 each. The maker wants to increase the profit margin this year, but predicts that each \$20 increase in profit will reduce the number of bicycles sold by 10. How many \$20 increases in profit can the maker add in and expect to make a total profit of at least \$100,000?

3. The current in a circuit is amps (I), and the impedance is ohms (Z). What is the voltage? (Hint: use the formula

4. Write two complex numbers whose product is 10.

• Algebra - ,

I will do #5 for you
please show some ideas or work that you tried for the others

let the two numbers be a+bi and a-bi
then (a+bi)(a-bi)= 10
a^2 - b^2i^2 = 10

a^2 + b^2 = 10 .... because i^2 = -1

let a=1, then b^2 = 9
b = 3 or b= -3

so let's pick a=1 and b-3

two complex numbers whose product are 10 are
1 + 3i and 1-3i