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

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

6 0

3 years ago

HELPme

aalyn [17]

Answer:

1. Rectangle

2. 376.8 cm

3. 379.94 square feet

4. –4 and 4

Step-by-step explanation:

A square is always a rectangle.

If a wheel has a radius of 15 cm, it would travel approximately 376.8 cm per 4 revolutions.

If the diameter of a circular garden is 22 feet, the approximate area of the garden is 379.94 square feet.

The solutions to the equation y2 – 1 = 15 is –4 and 4.

3 0

3 years ago

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Factor x^8-26x^4+25=0

Black_prince [1.1K]

The answer is (x^4-1)(x^4-25)

5 0

3 years ago

Which equation demonstrates the additive identity property?

Bezzdna [24]

Answer:

Step-by-step explanation:

We first need to simplify the expression removing parentheses

Simplify 41o(7 + 4): Distribute the 41o to each term in (7+4)

41o * 7 = (41 * 7)o = 287o 41o * 4 = (41 * 4)o = 164o

Our Total expanded term is 287o + 164o

Simplify 41o(7 + 41): Distribute the 41o to each term in (7+41)

41o * 7 = (41 * 7)o = 287o 41o * 41 = (41 * 41)o = 1681o

Our Total expanded term is 287o + 1681o

Our updated term to work with is (7 + 4) + (7 - 41) = 14©(7 + 4) + 0 = 7 + 287o + 164o(1) = 7 + 287o + 1681o + ( - 7 - 41) = 0

We first need to simplify the expression removing parentheses

Simplify 164o(1): Distribute the 164o to each term in (1)

164o * 1 = (164 * 1)o = 164o Our Total expanded term is 164o

Our updated term to work with is (7 + 4) + (7 - 41) = 14©(7 + 4) + 0 = 7 + 287o + 164o = 7 + 287o + 1681o + ( - 7 - 41) = 0

Step 1: Group variables: We need to group our variables (7 and 14©(7. To do that, we subtract 14©(7 from both sides (7 - 14©(7 = 14©(7 - 14©(7

0o 0 = 0 0 o =

5 0

3 years ago

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