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Lyrx [107]
3 years ago
8

Can someone help me find this answer?

Mathematics
1 answer:
AleksAgata [21]3 years ago
8 0

Answer:

(0, - 23 )

Step-by-step explanation:

Find the equation of the line in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }

with (x₁, y₁ ) = (- 72, 25) and (x₂, y₂ ) = (- 36, 1) ← 2 ordered pairs from the table

m = \frac{1-25}{-36+72} = \frac{-24}{36} = - \frac{2}{3} , thus

y = - \frac{2}{3} + c

To find c substitute any ordered pair into the equation

Using (- 54, 13 ) , then

13 = 36 + c ⇒ c = 13 - 36 = - 23 ← y- intercept

Thus coordinates of y- intercept = (0, - 23 )

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If x-9 is a factor of x^2 -5x-36 what is the other factor?<br> A-x-4<br> B-x+4<br> C-x-6<br> D-x+6
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Answer:

B

Step-by-step explanation:

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3 years ago
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You are comparing cell phones. The old model is 7/8 of an inch thick. The new model is 3/5 of an inch thick. How much thinner is
Sloan [31]

The new model is 11/40 of an inch thinner than the old model.

In order to do this, we need to subtract the new model from the old model.

7/8 - 3/5

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3 years ago
mark has 312 books in his bookcases she has 11 as many fiction books as nonfiction books how many fiction books does mark have?
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Does anyone know how to simplify this expression? I know it has to do with properties of summation and special summation rules b
dusya [7]
<h3>Answer:     -n/(n+1)</h3>

============================================================

Explanation:

Let's expand this out up to say n = 6 terms

I'll write the summation in such a way that each (1/(k+1) - 1/k) grouping will get its own row. Each row has the same value of k.

If we plug in k = 1 through k = 6, but not evaluate just yet, we will have this:

1/(1+1) - 1/1

1/(2+1) - 1/2

1/(3+1) - 1/3

1/(4+1) - 1/4

1/(5+1) - 1/5

1/(6+1) - 1/6

All I've done so far is replace k with 1 through 6. Again, each row represents a different k value. Each row has the general format 1/(k+1)-1/k.

Let's simplify everything in the first column.

So the (1+1) turns into 2, the (2+1) turns into 3, and so on.

Doing that leads to...

1/2 - 1/1

1/3 - 1/2

1/4 - 1/3

1/5 - 1/4

1/6 - 1/5

1/7 - 1/6

Then note how we have the cancellations shown in the diagram below. The color coding shows how the terms pair up to cancel out. By "cancel out", I mean specifically that the fractions add up to 0. Eg: 1/2 + (-1/2) = 0.

Nearly everything cancels out. The only things left after the dust settles is the -1/1 in the first row and the 1/7 in the bottom row. This evaluates to 1/7-1/1 = 1/7 - 7/7 = (1-7)/1 = -6/7

If you were to try this with n = 7, then you should find that again nearly everything cancels but the fractions -1/1 and 1/8. Then 1/8 - 1/1 = -7/8.

For n = 8, you should end up with 1/9 - 1/1 = -8/9.

You can probably see the pattern.

A conjecture is that the answer is -n/(n+1). The general proof of this isn't too tricky. Simply follow the same ideas as mentioned above. Expand out a few terms and see how things cancel out. You'll find that everything cancels except for the -1/1 in the first row and the 1/(n+1) just one term before the very end. Then we can say:

1/(n+1) - 1/1

1/(n+1) - (n+1)/(n+1)

(1-(n+1))/(n+1)

(1-n-1)/(n+1)

-n/(n+1)

If we tried n = 6, then we find,

-n/(n+1) = -6/(6+1) = -6/7

which was the result we found earlier when we added the first n = 6 terms of this series. Trying out n = 7 should lead to -n/(n+1) = -7/8, and so on.

3 0
3 years ago
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