Outcome 13 Solving Rational Equations

Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours to paint a similar sized house. How long would it take the two painters together to paint the house? Check all that apply

• $\frac{1}{12}+\frac{1}{8}=\frac{1}{t}$

• $\frac{1}{12\ }+\frac{1}{t}=\frac{1}{8}$

• $t=\frac{24}{5\ }hours$

• $t=\ \frac{21}{5\ }hours$

Suppose John can mow a lawn in 12hours, Jill can mow the same lawn in 6 hours. How long does it take Bill to mow the lawn if John, Jill and Bill can mow the lawn together in 2 hours. Check all that apply.

• $\frac{1}{12}+\frac{1}{6}+\frac{1}{b}=\frac{1}{2}$

• $\frac{1}{12}+\frac{1}{6}+\frac{1}{2}=\frac{1}{b}$

• Bill can mow the lawn in 4 hours.

• Bill can mow the lawn in 1 hour and 20 minutes. (1.333 hours)

A water tanks is being emptied by two drains and can be emptied in 55 minutes. One drain can empty the tank in 80 minutes. Check the true statements about the drains.

• $\frac{1}{55}=\frac{1}{80}+\frac{1}{x}$

• $\frac{1}{55\ }+\frac{1}{80}=\frac{1}{x}$

• The second pipe can drain the pool in 176 minutes

• The second pipe can drain the pool in 33 minutes

It takes Alice 5 hours to mow a 3 acre plot of land. John can mow the same 3 acre plot of land in 8 hours. Check all that applies in relation to Alice and John mowing the land together

• $\frac{3}{5}+\frac{3}{8}=\frac{3}{x}$

• $\frac{1}{5}+\frac{1}{8}=\frac{1}{x}$

• It will take approximately 3 hours to mow the land

• $\frac{1}{8}+\frac{1}{x}=\frac{1}{5}$

• It will take approximately 13 hours to mow the land

The volume of a sphere is  $11,494\ cm^3$  . What is the surface area of the sphere?

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mattdoesmath

Video:
Surface Area of Sphere from Volume.

•  $2,463\ cm^2$  

•  $2,464\ cm^2$  

•  $2,465\ cm^2$  

•  $2,466\ cm^2$  

What is the volume of a sphere that has a surface area of  $530.93\ cm^2$  ?

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Mattdoesmath


Video:
Volume of a sphere from surface area

•  $1148\ cm^3$  

•  $1150\ cm^3$  

•  $1152\ cm^3$  

•  $1154\ cm^3$  

Check all of the statements that are true

• The domain of the piecewise function is

  $\left(-\infty,\ \infty\right)$

• The domain of the piecewise function is $\left(-\infty,\infty\right)$ except 0 and 4

• The range of the piecewise function is $\left[-2\right]\cup\left[0,\infty\right)$

• The range of the piecewise function is $\left(-2\right)\cup\left(0,\infty\right]$

Given the function  $c\left(x\right)=2\left(\frac{3}{5}\right)^{\left(-\frac{2}{3}x\right)}$  check all that apply

• c(x) can be rewritten as  $c\left(x\right)=2\left(1.4057\right)^x$  

• c(x) is growth and has a percent of increase of 40.57%

• c(x) can be rewritten as  $c\left(x\right)=2\left(0.711\right)^x$  

• c(x) is growth and has a percent of increase of 60%
  

• C(x) is decay and can has a percent of decrease of 28.9%

Given the rational function

 $m\left(x\right)=\frac{x^2-9x}{x^2-5x-36}$  check all that apply.

• m(x) simplifies to  $\frac{x}{\left(x+4\right)}$  

• m(x) simplifies to  $\frac{x}{x-4}$  

• m(x) has a hole at x=9 and a vertical asymptote at -4

• m(x) has vertical asymptote at -4

•  $as\ x\rightarrow\infty\ m\left(x\right)\rightarrow\ 1$  

 $g\left(x\right)=3\left(2\right)^{\left(4x+5\right)}$  What is the inverse of the function

•  $\frac{4\log_2x}{3\ \ }+5$  

•  $\frac{\log_2\left(\frac{x}{3}\right)}{-5}+4$  

•  $\frac{\log_2\left(\frac{x}{4}\right)}{3}+5$  

•  $\frac{\log_2\left(\frac{x}{3}\right)}{4}-5$