Algebra Word Problem Solutions

The speed of sound in air at 20 degree celsius is about 343 metre per second. How?

The sum of a number and it's additive inverse is always .
A. same as the number.
B. 0.0
C. 1

Prime factors of $231$.

75/100 divided by 3 for both 75 and 100 and reduce to lowest terms.

12: 20 can be expressed in the most straightforward way as

$2^{}{2}^{}isequalto?$

TV panels are being produced at two different factory plants.
5000 fewer panels than Plant B did. Two percent of the panels from Plant A and 4% of the panels from Plant B were defective. How many panels did Plant B produce, if the two plants together produced 1100 defective panels?

What is $\frac{4}{5}$ as an equivalent fraction?

Which of the following is the inverse of $y=6^x$
$$\begin{gathered} a.y={\log }_6<!--\; \; -->x \\ b.y={\log }_x<!--\; \; -->6 \\ c.y={\log }_{\frac{1}{6}}<!--\; \; -->x \\ d.y={\log }_6<!--\; \; -->6x \end{gathered}$$

Find the area enclosed by the curve $x=t^2-<!--\; -\; -->2t,y=\sqrt{t}$ and the y-axis.

Choose the function whose graph is gaven by:

Lina can mow a lawn in $45$ minutes. Nika takes twice as long to mow the same lawn. How long will it take to work together $(1)/(45)+(1)/(90)=(1)/(t)$

Uniformly cauchy sequences
A sequence of functions $f_n$ is said to be uniformly cauchy if
$\mathrm{\forall <!--\; \forall \; -->}\mathrm{\epsilon <!--\; \epsilon \; -->}>0\mathrm{\exists <!--\; \exists \; -->}N>0:\mathrm{\forall <!--\; \forall \; -->}z,\mathrm{\forall <!--\; \forall \; -->}r,s>N:|f_r(z)-<!--\; -\; -->f_s(z)|<\mathrm{\epsilon <!--\; \epsilon \; -->}$
How can I show that if a sequence is uniformly cauchy then $f_n$ converge uniformly to some funciton $f$? We can assume that the metric space is complete.

The local electronics store is offering a promotion "1-year: same as cash," meaning that you can buy a TV now, and wait a year to pay (with no interest). So, if you take home a $1,100 TV today, you will owe them $1,100 in one year. If your bank is offering 3.8% interest, what is the true cost of the TV to you today?
The true cost of the TV to you today is $______ (Round to the nearest cent.)

What's so special about characteristic 2?
I've often read about things which do not work in a field with a characteristic $2$, mainly things which have to do with factoring, or similar things. I'm not exactly sure why, but the only example of such a field I could think of is $\mathbb{Z}/2\mathbb{Z}$, which itself is an interesting field because it contains only the identity elements for the two groups, and naturally, it is a cyclic field. Do these properties lead to the fact that many things don't work if the charateristic is $2$
Any examples of things which break in such a field are also welcome.

$\mathrm{\Omega <!--\; \Omega \; -->}⊊<!--\; ⊊\; -->T$
What does it mean?

Which equation is equivalent to $$\begin{gathered} 6\cdot <!--\; \cdot \; -->e^{4x-<!--\; -\; -->2}=3 \\ {e}^{4x-<!--\; -\; -->2}=.5 \\ \ln <!--\; \; -->e^{4x-<!--\; -\; -->2}=\ln <!--\; \; -->(.5) \\ 4x-<!--\; -\; -->2=\ln <!--\; \; -->(.5) \\ 4x=\ln <!--\; \; -->(.5)+2 \\ x=(\ln <!--\; \; -->(.5)+2)/4 \\ x=0.3267 \\ x\approx <!--\; \approx \; -->0.327 \end{gathered}$$?
$3x+6y–3z=6$
$4x+12y–4z=12$
$2x+4y–2z=8$
$2x+3y–4z=12$

The system of equations sim, find missing
4x+5y=8
8x +_y=_

What is the solution to this equation? 6x=36