Master Algebra 1 Word Problems with our Comprehensive Practice

Determine whether the given set of functions is linearly dependent or linearly independent on the interval ${\displaystyle (-\mathrm{\infty },\mathrm{\infty })}$
${\displaystyle f_1\left(x\right)=1+x,}$

$f_2\left(x\right)=x,$

$f_3\left(x\right)=x^2$

In order for the function to have the specified maximum or minimum value, find the values of b.
${\displaystyle f\left(x\right)=-x^2+bx-75}$ 
Maximum value: 25

$\text{If X is uniformly distributed over }(-1,1),\text{ find (a) }P|X|>\frac{1}{2}$
(b) the density function of the random variable |X|.

Let $A=\left[\begin{array}{ccc}4& 0& 5\\ -1& 3& 2\end{array}\right]$,
$B=\left[\begin{array}{ccc}1& 1& 1\\ 3& 5& 7\end{array}\right]$,
$C=\left[\begin{array}{cc}2& -3\\ 0& 1\end{array}\right]$
Find: ${\displaystyle 3A-B}$, and ${\displaystyle C\times B+A}$

Simplify.
$8\{[4(p-4)+19]-[2(3p-2)+5]\}$

Solve the system of equations by hand. $\{\begin{array}{l}-2x+y=5\\ -6x+3y=21\end{array}$

For $a,b\in Z$, let B(a,b) $\in$ M(2,Z) be defined by $B(a,b)=\left[\begin{array}{cc}a& 3b\\ b& a\end{array}\right]$.

Let $S=\{B(a,b);a,b\in Z\}\subseteq$ M(2,Z). Show that $S\cong Z\left[\sqrt{3}\right]=\{a+b\sqrt{3};a,b\in Z\}$

Find t so that $tx-3y=-4$ is perpendicular to the line $2x+2y=5$

Solve for the variable in given equation.
$2y+7$

Solve for the variable in given equation.
$8w-4=-60$

What is the ordered mpair that is the solution to the mfollowing systems of equations?
$y=7x-10$
$y=-3$

Jonah is solving the following system of equations.
$2x-5y=7$
$-2x+4y=-5$
Explain how to use the elimination method to solve the system of equations.
Give the solution.

Solve the following system of equations:
$5x-4y=-16$
$-2x-3y=-12$