write an equation for a function that has vertical asymptotes at x=3 & x=-10

Answer:

[tex] \frac{5}{ {x}^{2} + 7x - 30} [/tex]

Step-by-step explanation:

We can write a rational function.

We need to make sure our denominator both have zeroes at 3 and 10.

Set an equation equal to zero to find the function

[tex]0 - x = 3[/tex]

[tex]0 - x = - 10[/tex]

[tex]0 - ( - 3) = = 3[/tex]

[tex]0 - 10 = 10[/tex]

So we would represent that's as

[tex]x - 3[/tex]

and

[tex]x + 10[/tex]

Multiply the two binomial together.

[tex](x - 3)(x + 10) = {x}^{2} + 7x - 30[/tex]

Let our numbetator be any interger.

Use any equation as long as the quadratic is the denominator and the interger is the numerator.

[tex] \frac{5}{ {x}^{2} + 7x - 30 } [/tex]

a 42 inch diameter tablecloth that hangs off the edge 8 inches. what is the area of the tablecloth use 3.14 for pi​

if x-1/3=k and k=3 what is the value of x

if the opposite angle of rhombus are (2x)°and (3x-40°) then what is the value of x?

Options :
A. 100°
B.80°
C.160°
D.40°​

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I need help with the Pythagorean Theroem, Anyone trying to help?

Shark tank A contains 9.2 gallon Tof water. Sarah will begin filling tank A at a rate of 2.4 gallons per minute. Shark tank contains 109.2 gallons of water. Bella will begin draining tank B at a rate of 1.6 gallon per minute. After how many minutes will both tanks contain the same amount of water?​

Which section or sections represent what is not in set HH?

HALP ME PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS

Help with this question! It’s for math

Which equation best represents the relationship between 3 and y in the graph?
у
91
8
7
6
5
3
-2
1
-7-5-5
-2-1
1
3
4 5
6
-2
2

-3|-6+7|=
Can someone help me with that pls?

Which statements are TRUE about the graphs?

A parabola with a vertex at (0,0) has a directrix that crosses the negative part of the y-axis.
Which could be the equation of the parabola?
A. x² = –4y
B. x² = 4y
c.y² = 4x
D.y² = –4x

Which of the following expressions is represented by the number line below?
A. -6 - 5
B. 6 + (-4)
C. -6 + 4
D. 6 - (-4)

use the pre image to find the coordinates. PLEASE HELP DUE BY 10:15

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Question Progress
Homework Pro
Work out the value of 10 squared – 4 cubed
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Please I need it for my test

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PLS I NED HELP PLS PLS PLS
ODE TO AN OTTER
I ought to be an otter, ‘cause when all is said and done
I could play along the riverbank, or stretch out in the sun.
I’d swim beneath the water, or backstroke up on top.
I’d dive in like a graceful swan, or do a belly flop.
My days would be so peaceful as a furry, swimming mammal
As opposed to bearing burdens like a one-humped desert camel.
I wouldn’t want to herd sheep like a working collie dog
Or end up an amphibian—a turtle, toad, or frog.
But oh, to be an otter! It would be a stroke of luck
Just to spend all day a-swimmin’, or a-rollin’ in the muck.
But oh, as fate would have it, I’m required to spend my time
Doing schoolwork. What a pity. It seems like such a crime.
The month of May has ended, and all across the nation
The schools have shut their doors, and all of the kids are on vacation.
Yet here it’s still the school year, and it can’t end too soon,
But the days are standing still, stretching till the end of June.
Ah, the otter, who, when sunshine makes the heat rise at the shore,
Stays within its coolsome burrow, eating clams and snails and more.
It swims along the river, catching crayfish, frogs, and trout.
I’d be an awesome otter—of that I have no doubt. Right now I watch the summer tapping at each window pane
And count the days till school is out, and I can swim again.
I’ll walk in glorious mud that squeezes coolness through my toes
And skip along the river, free from tests and schoolwork woes.
Till then, I’ll be an otter, but only in my head,
And start the summer early there, along the riverbed.
‘Cause if I was an otter and could romp and roll and roam,
I wouldn’t have to think of what to write for my class poem.



My days would be so peaceful as a furry, swimming mammal / As
opposed to bearing burdens like a one-humped desert camel.

What does the word burdens mean in the sentence above?

A. doubts
B. feelings
C. objects
D. rivers



Yet here it’s still the school year, and it can’t end too soon, / But the
days are standing still, stretching till the end of June.

What does the author mean by the phrase the days are standing still?

F. The days seem to pass by slowly.
G. The days are full of difficult work.
H. The speaker’s school day is longer than at most schools.
I. There are more school days left than the speaker thought.





I’ll walk in glorious mud that squeezes coolness through my toes / And
skip along the river, free from tests and schoolwork woes.

How would the effect of these lines be different if the author had used the word
walk instead of skip?

A. The speaker would seem less carefree.
B. The speaker would seem more friendly.
C. The speaker would seem to miss school.
D. The speaker would seem less serious.



What effect does the author’s use of language such as ‘cause, a-swimmin’, and
awesome create in the poem?

F. It makes the speaker sound casual.
G. It makes the speaker sound persuasive.
H. It makes the speaker seem caring toward all animals.
I. It makes the speaker seem knowledgeable about otters.



The end of the poem is ironic because the speaker.

A. decides to write a poem about an otter.
B. turns into an otter and swims away from school.
C. changes her mind and doesn’t want to be an otter.
D. has finished the poem that seemed too hard to write.

Help please I’m not sure what do do with these kind of problems

A full set of adult teeth has 160% as many teeth as a full set of baby teeth. How many teeth are there in a full set of adult teeth if there are 20 teeth in a full set of baby teeth

"All real numbers" could be used to describe the x-
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Can anyone please help me to do this with steps

If you were able to pay off and get rid of all of your debt, what is that called?

15b>75.Substitute 5 for b

True or False

Mary made two 8 ounce drinks each in a separate cup. The first cup has 4 ounces f coffee and four ounces of milk. The second cup has 6 ounces of coffee and 2 ounces of milk. After she stirred the two drinks really well, she took out a third cup that was empty. She poured 2 ounces from the first cup ad 4 ounces from the second cup into the third cup. How many ounces of coffee are in the third cup

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B)-3 and 2

C) -3≤ y ≤ 3

D)-2≤ y ≤ 3​

Consider this data set: {49, 50, 45, 23, 35, 66, 34, 74, 54, 50}
The mean is:
The median is:
The mode is:
The range is:

Suppose the value 60 is added to the data set.

The mean increases by:
The median increases by:
The mode is:
The range is:

(PLS Copy and Paste this whole thing in your answer and write the answers)

5.
The height of a cylinder is 6 Inches. The radius of the base is 8 inches.
Which expression can be used to approximate the volume of the cylinder?
A
2 x 8 x 3.14 6
B
4x3.146
с 82 3.146
D 42 x 3.146

Describe the expression. 2 * 5+7(3 + 13) Which of the following describes 7 in the expression above? 디 A. factor B. sum C. quotient D. product​