A computer repair technician charges $50 per visit plus $30/h for house calls. a) Write an algebraic expression that describes the service charge for one household visit. b) Use your expression to find the total service charge for a 2.5-h repair job.

Find the value of x that satisfies the inequality.
${\displaystyle \left|\frac{3x+1}{2}\right|<1}$

Establish the conditions under which the equations
${\displaystyle ax+by+cz=q-r;bx+cy+az=r-p;cx+ay+bz=p-q}$,
are consistent. I am aware that by taking the system to echelon can get me the rank of the coefficient matrix and the augmented matrix. But that turns out to be a very cumbersome process and the terms in the echelon form are very big. Is there other ways to establish the conditions for consistency which are less cumbersome and time consuming?

A square is $\frac{1}{8}$ of a mile by $\frac{1}{8}$ of a mile. How many acres is this

Let ${\displaystyle f\left(x\right)=x^2+ax+b,a,b\in \mathbb{R}}$. If ${\displaystyle f\left(1\right)+f\left(2\right)+f\left(3\right)=0}$, then the nature of the roots of the equation ${\displaystyle f\left(x\right)=0}$ is
A) real
B) imaginary
C) real and distinct
D) equal roots

To solve: ${\displaystyle \frac{n+1}{8}-\frac{2-n}{3}=\frac{5}{6}}$

find the values of b such that the function has the given maximum or minimum value. $f(x)=-x^2+bx-75$, Maximum value: 25

If a,b,c are in Geometric Progression, then prove that the equations ${\displaystyle a{x}^2+2bx+c=0}$ and ${\displaystyle {dx}^2+2ex+f=0}$ have a common root
If ${\displaystyle \frac{d}{a},\frac{c}{b},\frac{f}{c}}$ are in an Arithmetic Progression
${\displaystyle b=\sqrt{ac}}$
${\displaystyle a{x}^2+2\sqrt{ac}x+c=0}$
${\displaystyle (\sqrt{a}x+\sqrt{c})(\sqrt{a}x+\sqrt{c})=0}$
${\displaystyle x=-\sqrt{\frac{c}{a}}}$
since both roots are roots are equal, both equations have the same roots. Therefore
${\displaystyle \frac{d}{a}=\frac{e}{b}=\frac{f}{c}}$
Why is this contradiction arising?