Module E Outcome 12 Operations with Rational Expressions

Given $g\left(x\right)=\frac{2x-10}{x+4}$ and  $h\left(x\right)=\frac{x^2-16}{x-5}$  Determine which statements are true

• The product of g(x) and h(x) is  $2x-8$  

• The product of g(x) and h(x) is  $2x-4$  

• x=-4 is a vertical asymptote on the graph g(x)

• For h(x)  $as\ x\rightarrow\infty\ \ \ \ h\left(x\right)\rightarrow\infty$  

• For g(x) as  $x\rightarrow\infty\ \ g\left(x\right)\rightarrow1$  

Given $s\left(x\right)=\frac{2x^2-6x}{x^2+6x-27}$  and  $r\left(x\right)=\frac{x^2+14x+45}{x^3+5x^2}$ , determine the statements that are true. 

• The product of s(x) and r(x) is  $\frac{3}{x}$  

• The product of s(x) and r(x) is  $\frac{4}{x}$  

• The rational function s(x) has a hole at x=3 and a vertical asymptote at -9

• The rational function r(x) simplifies to  $\frac{x+9}{x^2}$  

• The horizontal asymptote of r(x) is y = 0

Given $h\left(x\right)=\frac{x^2+4}{x^2-7x+6}\$  and  $p\left(x\right)=\ \frac{8}{x-6}$  
Determine the true statements.

• The difference of h(x) and p(x) is  $\frac{x-2}{x-1}$  

• The difference of h(x) and p(x) is  $\frac{x^2+8x-4}{x^2-7x+6}$  

• The quotient of h(x) and p(x) is  $\frac{x^2+4}{8x-8}$  

• The quotient of h(x) and p(x) is  $\frac{8x^2+32}{\left(x-6\right)^2\left(x-1\right)}$  

 $n\left(x\right)=\frac{13x+21}{6x^2+5x-4}$  and  $p\left(x\right)=\frac{1}{3x+4}$  Determine the values of A,B, and C that make the statement  $n\left(x\right)\ +\ p\left(x\right)\ =\ \frac{Ax^2+Bx\ +C}{2x-1}$  True.

• A = 0   B = 15  C = 22  

• A = 1  B = 0  C= 5

• A= 0   B = 0   C = 5

• A = 0 B = 13  C = 22

A parallelogram has an area of  $A\left(x\right)=\frac{x^2+x-2}{x^3}$  . What expression represents the height of the parallelogram if the base is  $b\left(x\right)=\frac{x-1}{x^2}$  

•  $h\left(x\right)=\frac{x^2}{x-1}$  

•  $h\left(x\right)=\frac{x^2+2x}{x^2}$  

•  $h\left(x\right)=\frac{x+2}{x}$  

•  $h\left(x\right)=\frac{x}{x+2}$  

Given Rhombus ABCD. Determine all of the true answers below.

Youtube: MATTDOESMATH
Video: Properties of Rhombus

• The perimeter of ABCD IS 30

• The length of segment DB IS 8

• The length of segment CA is $8\sqrt{3}$

• The length of segment CA is $4\sqrt{3}$

• The perimeter of segment ABCD IS 32

A culture of bacteria was started started with 64 bacteria. An hour later there are 192 bacteria. Through observation the scientist has determined the bacterial growth is exponential. Determine the true statements below.

• $b\left(m\right)=64\left(1.0185\right)^m$ is the function that represents the growth of the bacteria per minute.

• $b\left(d\right)=64\left(3\right)^{24d}$ is the function that models the daily growth of the bacteria

• $b\left(h\right)=64\left(3\right)^h$ is the function that models the hourly growth of the bacteria

• $b\left(s\right)=64\left(1.00031\right)^s$ is the function that represents the growth of the bacteria each second.

Determine the Volume and Surface of the area of the given Sphere.

Youtube: MattDoesMath
Video: Volume and Surface area of a sphere

• Surface Area  $676\pi\ in^2$  

• Surface area  $2704\pi\ in^2$  

• Volume  $9202.8\ in^3$  

• Volume  $73,622.18\ in^3$  

What is the remainder of $\frac{p\left(x\right)}{g\left(x\right)}$  if  $p\left(x\right)=3x^3+5x^2-3x-4$   and  $g\left(x\right)=x-3$   

• 113

• -31

• 1.113

• 3

 $\log_u125=3$  

Convert the following Logarithmic statement to an exponential statement.

•  $u^3=125$  

•  $3^u=125$  

•  $u^{125}=3$  

•  $3^{125}=u$