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-BARSIC- [3]
3 years ago
6

How do you find the vertical asymptote of a rational expression?

Mathematics
1 answer:
ElenaW [278]3 years ago
5 0
Here is the answer to the question. Vertical asymptotes a<span>re vertical lines which correspond to the zeroes of the denominator of a </span>rational function. Therefore, in order to find the vertical asymptote of a rational expression, what you are going to do is to <span>set the denominator equal to 0 and solve for x. Hope this helps.</span>
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Ann is adding water to a swimming pool at a constant rate. The table below shows the amount of water in the pool after different
N76 [4]

Answer:

(a)  As time increases, the amount of water in the pool increases.

     11 gallons per minute

(b)  65 gallons

Step-by-step explanation:

From inspection of the table, we can see that <u>as time increases, the amount of water in the pool increases</u>.

We are told that Ann adds water at a constant rate.  Therefore, this can be modeled as a linear function.  

The rate at which the water is increasing is the <em>rate of change</em> (which is also the <em>slope </em>of a linear function).

Choose 2 ordered pairs from the table:

\textsf{let}\:(x_1,y_1)=(8, 153)

\textsf{let}\:(x_2,y_2)=(12,197)

Input these into the slope formula:

\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{197-153}{12-8}=\dfrac{44}{4}=11

Therefore, the rate at which the water in the pool is increasing is:

<u>11 gallons per minute</u>

To find the amount of water that was already in the pool when Ann started adding water, we need to create a linear equation using the found slope and one of the ordered pairs with the point-slope formula:

y-y_1=m(x-x_1)

\implies y-153=11(x-8)

\implies y-153=11x-88

\implies y=11x-88+153

\implies y=11x+65

When Ann had added no water, x = 0.  Therefore,

y=11(0)+65

y=65

So there was <u>65 gallons</u> of water in the pool before Ann starting adding water.

3 0
2 years ago
Read 2 more answers
Solve for (2/5)^8x=25/4
Levart [38]

Answer:

X=-1/4

Step-by-step explanation:

<h2>8x=㏒₂/₅⁽²⁵/⁴⁾</h2>
5 0
2 years ago
Tomas wrote the equation y = 3x +y equals 3 x plus StartFraction 3 over 4 EndFraction.. When Sandra wrote her equation, they dis
BaLLatris [955]

Answer:

-6x+2y=\frac{3}{2}

Step-by-step explanation:

The equation Thomas wrote is:

y=3x+\frac{3}{4} ...equation 1

Let us subtract 3x from both sides to get:

-3x+y=\frac{3}{4}

We now multiply through by 2 to get:

-6x+2y=\frac{3}{2} ....equation 2

We can see that equation one and two are equivalent and hence have the same solution.

Therefore Sandra's equation is -6x+2y=\frac{3}{2}

6 0
3 years ago
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Can you help me solve this
DochEvi [55]

Answer:

private document file

6 0
3 years ago
NEED HELP
Margaret [11]
Sorry I'm gonna take a guess.......... d?
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