$x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{Vertical asymptotes:}\\\\(x+4)(x-1)=0\iff x+4=0\ \vee\ x-1=0\\\\\boxed{x=-4\ and\ x=1}\\\\\text{Horizontal asymptotes:}$

$\lim\limits_{x\to\pm\infty}\dfrac{x^2+7x+12}{-x^2-3x+4}=\lim\limits_{x\to\pm\infty}\dfrac{x^2\left(1+\dfrac{7}{x}+\dfrac{12}{x^2}\right)}{x^2\left(-1-\dfrac{3}{x}+\dfrac{4}{x^2}\right)}=\dfrac{1}{-1}=-1\\\\\boxed{y=-1}$

6 0

4 years ago

A car dealership sold 265 cars in 5 months. At what rate did the dealership sell cars in cars per month?

RideAnS [48]

Answer:

The dealership sold 53 cars per month.

Step-by-step explanation:

To solve this, simply divide 265 by 5 to find out how many cars were sold per month. If we do this, the answer is 53. The dealership sold 53 cars per month.

5 0

3 years ago

An angle less than 90 degrees

OverLord2011 [107]

Answer:

Acute Angle

Step-by-step explanation:

Obtuse Angle is greater than 90 degrees

Right Angle is exactly 90 degrees

Acute Angle is less than 90 degrees

5 0

3 years ago

Graph the equation y= 1/2 + 4

Alika [10]

I can’t really graph on this but place a dot on the four on the y axis and go up one and over two and place a dot there. just keep repeating it till u get to the end of the graph :)

8 0

3 years ago