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2 years ago

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A system of linear equations is graphed on the grid. Ty 10. +7 S. -FO 4 0 ve g What is the approximate solution to the system of

linear equations? O a b (-1,-3) (-2,-3) (-3,-1) С Od (-3,-2)

1 answer:

leonid [27]2 years ago

6 0

Answer:

dcsa

Step-by-step explanation:

f

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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

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

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3 years ago

a family of 4 went to a lacrosse game and spent a total of $74. they each had a hot dog, popcorn, and a soda. a hot dog cost $3,

Taya2010 [7]

Answer:

12$

Step-by-step explanation:

74 - 4(1.50+3+2) = 48

48 / 4 = 12

4 0

3 years ago

Clare made $160 babysitting last summer. She put the money in a savings account that pays 3% interest per year. If Clare doesn't

N76 [4]

Answer:

I believe its $5492.99

Step-by-step explanation:

First I divided $160 by 3%.

Than I multiplied my answer by 1.03.

4 0

3 years ago

Read 2 more answers

The two lines y= 6x+15 and y= mx+4 intersect at x= -2. What is the y-coordinate of their intersection point

taurus [48]

Answer:

The y-coordinate of their intersection point is 3

That is y=3

Step-by-step explanation:

Given two lines are y=6x+15 and y=mx+4

Given that the two lines intersect at x=-2

To find the y coordinate of their intersection point :

Equating the two lines

6x+15=mx+4

6x+15-mx-4=0

6x-mx+11=0

(6-m)x+11=0

At x=-2 (6-m)x+11=0

(6-m)(-2)+11=0

(6-m)(-2)=-11

$6-m=\frac{11}{2}$

$-m=\frac{11}{2}-6$

$-m=\frac{11-12}{2}$

$-m=\frac{-1}{2}$

$m=\frac{1}{2}$

Substitute the value $m=\frac{1}{2}$ in y=mx+4 we get

$y=\frac{1}{2}x+4$

At x=-2 $y=\frac{1}{2}(-2)+4$

$=-1+4$

$=3$

Therefore y=3

Therefore the y-coordinate of their intersection point is 3

7 0

3 years ago

3/4(x + 3) = 9<br><br><br> How do I solve this

Sonbull [250]

Answer:

x = 10

Step-by-step explanation:

so first distribute the 3/4 to everything on the inside

3/4x + 1 1/2 = 9

now subtract 1 1/2 on both sides

3/4x = 7 1/2

Now divide both sides by 3/4

x = 7 1/2 divided by 3/4

x = 15/2 divided by 3/4

x = 15/2 times 4/3

x = 5/1 times 2/1

x = 10

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2 years ago