Given the cubic trinomial equation x^3+2x^2+2x+1=0 , find the value of x^{1994}+x^{1997}+x^{2000}

Ms. Hobbes has a portfolio that includes $50,000 in stock, $75,000 in cash, and no other holdings. If she wishes to redistribute her holdings so that 80 percent of the portfolio is in cash, how many dollars of stock must she convert to cash?

If a remainder of 4 is obtained when x^3+2x^2-x-k is devided by x-2 , what is the value of k ?

What is the solution set to the equation 4+x^2=2x^2-5 ?

At a certain software company, the cost, C , of developing and producing a computer software program is related to the number of copies produced, x , by the equation C= 30000+2x . The company's total revenues, R , are related to the number of copies produced, x , by the equation R=6x-10000 . How many copies must the company produce so that the total revenue is equal to the cost?

In the figure, the length of AC is 3 times the length of CD . If B is the midpoint of AC , and the length of CD is 5, what is the length of BD ?

What is the solution set for the equation |2x-3| = 13 ?

Which of the ordered pairs is the solution to the equations

\begin{cases} x+2y=5 & \\ x-2y=9 & \end{cases}

If \dfrac{x+1}{2}+\dfrac{4x-1}{4}=5.5 , then x =

Jackie use 30 percentage of her monthly earnings for rent and 50 percentage of the remaining amount for food and transportation. If she spends $525 for food and transportation, how much does she pay for rent?

If a laser printer can print x pages per minute, how many minutes, in terms of x , would it take the laser printer to print a 100-page document?

If 2y^2+x-4 = 0 , and \dfrac{x}{2}=y^2 , then x =

Let ax+by=1 , bx+cy=1 , cx+ay=1 , and ac-b^2≠ 0. Prove the following expression is true:

a^2+b^2+c^2=ab+bc+ac

a,b, c satisfy the following equations if ac-b^2 ≠ 0.

ax+by=1 , bx+cy=1 , cx+ay=1

Prove: a^2+b^2+c^2=ab+bc+ac