Master Algebra 1 Word Problems with our Comprehensive Practice

Write each of the following in radical form. For example, ${\displaystyle 3x^{\frac{2}{3}}=3\sqrt[3]{x^2}}$
${\displaystyle {(2x-3y)}^{\frac{1}{2}}}$

Whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) ${\displaystyle f\left(x\right)=-3x^2+7}$

c) $f(x)=\frac{x+1}{x+2}$
${\displaystyle d)f\left(x\right)=x^5+1}$

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers.
$3\sqrt[3]{4}(2\sqrt[3]{2}-6\sqrt[3]{4})$

Simplify the radical expressions.
$\sqrt[3]{54x{y}^{12}{z}^{14}}$

Perform the indicated operations and express answers in simplest radical form.
$\sqrt[3]{3}\sqrt[4]{3}$

Solve the following system of linear equations
$\{\begin{array}{l}-2x+3y-4z=8\\ 5x-3y+5z=-8\\ 7x-3y+3z=8\end{array}$

Simplify the radical expression by changing the expression to exponential form. Write the answer in radical form when appropriate. Assume that the variable represents positive real numbers.
$\sqrt{\sqrt[4]{a}}$

Foundations/Comprehension
1. Find the inverse $(A^{-1})$ of the following $3\times 3$ matrix, using either the row-operation method or the adjugate method (6 points):

$A=\left(\begin{array}{c}2\\ 3\\ 1\end{array}\begin{array}{c}1\\ 1\\ 3\end{array}\begin{array}{c}1\\ 1\\ 2\end{array}\right)$

The amount owed at the end of 5 years.
An amount of ${\displaystyle \mathrm{\$}3000}$ is loaned at a rate of $10\mathrm{\%}$compounded quarterly.

Beth intends to solve the following system of equations

$\{\begin{array}{l}5x+4y=13\\ 30x+by=50\end{array}$

The system contains the number b representing the age of Beth (in years). It turns out that Beth can by no means solve the system. How old is Beth?

Solve the following system of equations
$\{\begin{array}{l}x-2y=-4\\ -\frac{1}{2}x+y=2\end{array}$