Master Algebra 1 Word Problems with our Comprehensive Practice

Mr. White can travel for 6 hours while taking 3 breaks of 10 minutes each. Once, he had to travel for 36 hours and how many minutes in breaks did he take?

Find the slope of the line perpendicular to ${\displaystyle y=\frac{7}{12}x-2}$

Why is linear interpolation and extrapolation not useful in making predictions?

For which α does the integral $$\underset{2}{\overset{+\mathrm{\infty <!--\; \infty \; -->}}{\int <!--\; \int \; -->}}\frac{e^{\mathrm{\alpha <!--\; \alpha \; -->}x}}{(x-<!--\; -\; -->1{)}^{\mathrm{\alpha <!--\; \alpha \; -->}}\ln <!--\; \; -->x}\mathrm{d}x$$ converge?
For which values of $\mathrm{\alpha <!--\; \alpha \; -->}$ does the integral
$$\underset{2}{\overset{+\mathrm{\infty <!--\; \infty \; -->}}{\int <!--\; \int \; -->}}\frac{e^{\mathrm{\alpha <!--\; \alpha \; -->}x}}{(x-<!--\; -\; -->1{)}^{\mathrm{\alpha <!--\; \alpha \; -->}}\ln <!--\; \; -->x}\mathrm{d}x$$
converge?
I'm lost here.
For simplicity, let us denote the above integral as $I_1$
I was able to prove (I noticed that it's kind of standard exercise though) that:
$$I_2=\underset{2}{\overset{+\mathrm{\infty <!--\; \infty \; -->}}{\int <!--\; \int \; -->}}\frac{1}{(x-<!--\; -\; -->1{)}^{\mathrm{\alpha <!--\; \alpha \; -->}}{\ln }^{\mathrm{\beta <!--\; \beta \; -->}}<!--\; \; -->x}$$
I2 converges for $\mathrm{\alpha <!--\; \alpha \; -->}>1$ and $\mathrm{\forall <!--\; \forall \; -->}\mathrm{\beta <!--\; \beta \; -->}$.
converges for $\mathrm{\alpha <!--\; \alpha \; -->}=1$ and $\mathrm{\beta <!--\; \beta \; -->}>1$. For $\mathrm{\beta <!--\; \beta \; -->}\le <!--\; \le \; -->1$ it diverges.
diverges for $\mathrm{\alpha <!--\; \alpha \; -->}<1$ and $\mathrm{\forall <!--\; \forall \; -->}\mathrm{\beta <!--\; \beta \; -->}$.
So my strategy was to use $I_2$ to prove the converges/divergence of $I_1$, by means of inequalities, but I get nothing from this.
For instance I did the following:
For $\mathrm{\alpha <!--\; \alpha \; -->}>1$ we have that
$$0<\underset{2}{\overset{+\mathrm{\infty <!--\; \infty \; -->}}{\int <!--\; \int \; -->}}\frac{\mathrm{d}x}{x^{\mathrm{\alpha <!--\; \alpha \; -->}}\ln <!--\; \; -->x}\le <!--\; \le \; -->\underset{2}{\overset{+\mathrm{\infty <!--\; \infty \; -->}}{\int <!--\; \int \; -->}}\frac{e^{\mathrm{\alpha <!--\; \alpha \; -->}x}}{(x-<!--\; -\; -->1{)}^{\mathrm{\alpha <!--\; \alpha \; -->}}\ln <!--\; \; -->x}\mathrm{d}x$$
That is, for $\mathrm{\beta <!--\; \beta \; -->}=1$
$$0<I_2\le <!--\; \le \; -->I_1$$
From 1. we know that $I_2$ converges, but this doesn't tell us anything about the convergence of $I_1$.
The answer given by my textbook is that $I_1$ converges for $\mathrm{\alpha <!--\; \alpha \; -->}<0$, but I don't know how to arrive at that conclusion.

Find the equation of the line perpendicular to the line y=5 and passing through (5,4)

An ice cream company reported a net profit of $24,000 in 2002 and a net loss of $11,000 in 2003. How much did the company‘s profits change from 2002 to 2003?

Find the second and third terms of an arithmetic sequence be if the first term is 6 and the fourth is 33

One pump can fill a water tank in 40 minutes and another pump takes 30 minutes? How long will it take to fill the water tank if both pumps work together?

How do you find ${\displaystyle a_{10}}$ given ${\displaystyle a_n=\frac{2^n}{n!}}$?

Find answers of this system of equations in reals
$$\{\begin{array}{c}x+3y=4y^3\\ y+3z=4z^3\\ z+3x=4x^3\end{array}$$

How do you create a line of best fit?

Write the first six terms of the sequence ${\displaystyle a_n=n^3-1}$

Find the slope perpendicular to 2y=10

Given:
$\begin{array}{}\text{(1)}& A=\left[\begin{array}{ccc}{q}_1& q_2& q_3\\ q_4& q_5& q_6\\ q_7& q_8& q_9\end{array}\right]\end{array}$
$$A$$ is a matrix with determinant 1,orthogonal , invertible and not necessary that all $q_i$s are equal. All entries of the A are constants cant alter
$\begin{array}{}\text{(2)}& C=\left[\begin{array}{ccc}{p}_1& p_2& p_3\\ p_4& p_5& p_6\\ p_7& p_8& p_9\end{array}\right]\end{array}$
$$C$$ is a matrix which is non-invertible and not necessary that all $p_i$s are equal. All entries of the $$C$$ are constants cant alter
$\begin{array}{}\text{(3)}& B=\left(\begin{array}{ccc}0& -<!--\; -\; -->z& y\\ z& 0& -<!--\; -\; -->x\\ -<!--\; -\; -->y& x& 0\end{array}\right)\end{array}$
$$B$$ is a matrix which is non-invertible. It is the varible matrix,and the variables are $$x,y,z$$
If we have the equation
$\begin{array}{}\text{(4)}& A=BC\end{array}$
Can we find the solutions of $$x,y,z$$ interms of constants $p_i$s and $q_i$s ?

Determine if 5y+3x=1 is parallel, perpendicular to neither to the line y+10x=−3

How much did each sell if Nancys sales last week were $140 less than three times Andrea's sales and together they sold $940.

David works moving lawns and babysitting. He earns $7.10 an hour for mowing and $6.80 an hour for babysitting. So how much will he earn for 1 hour of mowing and 5 hours of babysitting?

Find the slope perpendicular to (-7,2) and (5,-12)

How do you write the first five terms of the sequence defined recursively ${\displaystyle a_1=28,a_{k+1}=a_k-4}$?