Chapter 1: Fundamentals

In this section we learned how to translate words into algebra. In this exercise we try to find real-world situations that could correspond to an algebraic equation. For instance, the equation $A=\frac{(x+y)}{2}$could model the average amount of money in two bank accounts, where $x$represents the amount in one account and $y$the amount in the other. Write a story that could correspond to the given equation, stating what the variables represent.

a) $C=20,000+4.50x$

b) $A=w(w+10)$

c)$C=10.50x+11.75y$

Factor the expression completely. Begin by factoring out the lowest power of each common factor.

$x^{-\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}+2x^{-\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}+x^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$

Find an equation of the circle that satisfies the given conditions.

Endpoints of a diameter are$P(-1,1)\mathrm{and}Q(5,9)$

Rationalize the numerator.

$\frac{\sqrt{r}+\sqrt{2}}{5}$

Find all real solutions of the equation.

$5=\sqrt{4x-3}$

Write a paragraph describing different real-world situations in which you would use natural numbers, integers, rational numbers, and irrational numbers. Give examples for each type of situation.

Use the scientific notation, the Laws of exponents, and a calculator to perform the indicated operations. State your answer rounded to the number of significant digits indicated by the given data.

$\frac{\left(0.0000162\right)\left(0.01582\right)}{(594,621,000)\left(0.0058\right)}$

Use the scientific notation, the Laws of exponents, and a calculator to perform the indicated operations. State your answer rounded to the number of significant digits indicated by the given data.

$\frac{{(3.542\times {10}^{-6})}^9}{{(5.05\times {10}^4)}^{12}}$

Solve the inequality $\left|x-4\right|\mathbf{<}\mathbf{0}\mathbf{.}\mathbf{02}$, express the solution using interval notation and graph the solution set on real number line.

The ancient Babylonians knew how to solve quadratic equations. Here is a problem from a cuneiform tablet found in a Babylonian school dating back to about 2000B.C.I have a reed, I know not its length. I broke from it one cubit, and it fittimes along the length of my field. I restored to the reed what I had broken off, and it fit 30times along the width of my field. The area of my field is 375square nindas. What was the original length of the reed? Solve this problem. Use the fact that 1ninda =cubits.