Use long division to find the value of 1875 ÷ 15 THIS IS A DIVISON PROBLEM SINCE THE OTHER ONE I WROTE A MULTIPLICATION PROBLEM

Determine any asymptotes (Horizontal, vertical or oblique). Find holes, intercepts and state it's domain.

vesna_86 [32]

Factorize the denominator:

$\dfrac{x^2-4}{x^3+x^2-4x-4}=\dfrac{x^2-4}{x^2(x+1)-4(x+1)}=\dfrac{x^2-4}{(x^2-4)(x+1)}$

If $x\neq\pm2$ , we can cancel the factors of $x^2-4$ , which makes $x=-2$ and $x=2$ removable discontinuities that appear as holes in the plot of $g(x)$ .

We're then left with

$\dfrac1{x+1}$

which is undefined when $x=-1$ , so this is the site of a vertical asymptote.

As $x$ gets arbitrarily large in magnitude, we find

$\displaystyle\lim_{x\to-\infty}g(x)=\lim_{x\to+\infty}g(x)=0$

since the degree of the denominator (3) is greater than the degree of the numerator (2). So $y=0$ is a horizontal asymptote.

Intercepts occur where $g(x)=0$ ( $x$ -intercepts) and the value of $g(x)$ when $x=0$ ( $y$ -intercept). There are no $x$ -intercepts because $\dfrac1{x+1}$ is never 0. On the other hand,

$g(0)=\dfrac{0-4}{0+0-0-4}=1$

so there is one $y$ -intercept at (0, 1).

The domain of $g(x)$ is the set of values that $x$ can take on for which $g(x)$ exists. We've already shown that $x$ can't be -2, 2, or -1, so the domain is the set

$\{x\in\mathbb R\mid x\neq-2,x\neq-1,x\neq2\}$

8 0

3 years ago

A hot air balloon rose between 1 and 1 feet each second. Which is the best

Ne4ueva [31]

Answer:

i think the best estimate is answer b

Step-by-step explanation:

5 0

2 years ago

Use the Distributive Property to write each expression as an equivalent algebraic expression. –9(–x + 5)

Anna11 [10]

Answer:

9x -45

Step-by-step explanation:

The distributive property tells you the factor outside parentheses applies to each of the terms inside parentheses:

-9(-x +5) = (-9)(-x) +(-9)(5)

= 9x -45

5 0

3 years ago

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If (x-2) is a factor of x^3+kx^2 +12x-8 then k=?

AURORKA [14]

Answer:

k = - 6

Step-by-step explanation:

Since (x - 2) is a factor then x = 2 is a root

Substitute x = 2 into the polynomial and equate to zero, that is

2³ + k(2)² + 12(2) - 8 = 0

8 + 4k + 24 - 8 = 0

4k + 24 = 0 ( subtract 24 from both sides )

4k = - 24 ( divide both sides by 4 )

k = - 6

5 0

3 years ago

Adam uses coconut milk for the dessert.

VARVARA [1.3K]

Since we are already given the formula and all the information, the only thing that we have to do is input all the values and simplify until we get an answer. In addition, we must also note that the radius is 4 (because the diameter is equal to twice the radius, meaning that if the diameter is 8, the radius is 4). Using the formula and information given, we get:

Volume = 3 * (4)² * 12

Which simplifies to:

Volume = 3 * 16 * 12
Volume = 576

Now, we need to know the units. Since this is a 3d shape, and the unit for the lengths of the sides are centimeters, this answer will be in centimeters cubed. That means our answer is 576 centimeters cubed.

4 0

3 years ago

Read 2 more answers

Use long division to find the value of 1875 ÷ 15 THIS IS A DIVISON PROBLEM SINCE THE OTHER ONE I WROTE A MULTIPLICATION PROBLEM​

Use long division to find the value of 1875 ÷ 15 THIS IS A DIVISON PROBLEM SINCE THE OTHER ONE I WROTE A MULTIPLICATION PROBLEM