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svp [43]
3 years ago
14

Determine the slope of the line that passes through the points:

Mathematics
1 answer:
miskamm [114]3 years ago
4 0

Answer:

The slope of the line is 4.

Step-by-step explanation:

Recall that slope = rise over run:  rise / run.

From the table we see that if x changes from 0 to 4, a run of 4, y changes from -1 to 15, a rise of 16, the slope of this line must be

m = rise / run = 16/4 = 4

The slope of the line is 4.

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After a storm damage is the community center sent Kiya and her friends hold fundraising events to help pay for repairs after the
andrew-mc [135]

Answer: the total amount of money that they wanted to raise is $2400

Step-by-step explanation:

Let x represent the total amount of money that Keelan and her friends want to raise.

After the first event they raise $240 which is 10% of the total amount they want to raise. The amount of money that raised after the first event is expressed as

10/100 × x = 0.1 × x = 0.1x

Therefore,

0.1x = 240

Dividing both sides of the equation by 0.1, it becomes

x = 240/0.1

x = $2400

7 0
3 years ago
A new bagel store opened. The first day 15 customers entered the store. The number of customers that enter the store triples eac
Lelu [443]

Answer: it triples by 3 so 15,45, 135

Step-by-step explanation: this is by 3 because it goes on by 15,45,135

3 0
3 years ago
Solve xy − 2 = k for x.
MA_775_DIABLO [31]
Isolate x
So xy - 2 = k
Then
xy = k + 2

x = (k+2)/y
6 0
2 years ago
Binomial Expansion/Pascal's triangle. Please help with all of number 5.
Mandarinka [93]
\begin{matrix}1\\1&1\\1&2&1\\1&3&3&1\\1&4&6&4&1\end{bmatrix}

The rows add up to 1,2,4,8,16, respectively. (Notice they're all powers of 2)

The sum of the numbers in row n is 2^{n-1}.

The last problem can be solved with the binomial theorem, but I'll assume you don't take that for granted. You can prove this claim by induction. When n=1,

(1+x)^1=1+x=\dbinom10+\dbinom11x

so the base case holds. Assume the claim holds for n=k, so that

(1+x)^k=\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k

Use this to show that it holds for n=k+1.

(1+x)^{k+1}=(1+x)(1+x)^k
(1+x)^{k+1}=(1+x)\left(\dbinom k0+\dbinom k1x+\cdots+\dbinom k{k-1}x^{k-1}+\dbinom kkx^k\right)
(1+x)^{k+1}=1+\left(\dbinom k0+\dbinom k1\right)x+\left(\dbinom k1+\dbinom k2\right)x^2+\cdots+\left(\dbinom k{k-2}+\dbinom k{k-1}\right)x^{k-1}+\left(\dbinom k{k-1}+\dbinom kk\right)x^k+x^{k+1}

Notice that

\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!}{\ell!(k-\ell)!}+\dfrac{k!}{(\ell+1)!(k-\ell-1)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)}{(\ell+1)!(k-\ell)!}+\dfrac{k!(k-\ell)}{(\ell+1)!(k-\ell)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(\ell+1)+k!(k-\ell)}{(\ell+1)!(k-\ell)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{k!(k+1)}{(\ell+1)!(k-\ell)!}
\dbinom k\ell+\dbinom k{\ell+1}=\dfrac{(k+1)!}{(\ell+1)!((k+1)-(\ell+1))!}
\dbinom k\ell+\dbinom k{\ell+1}=\dbinom{k+1}{\ell+1}

So you can write the expansion for n=k+1 as

(1+x)^{k+1}=1+\dbinom{k+1}1x+\dbinom{k+1}2x^2+\cdots+\dbinom{k+1}{k-1}x^{k-1}+\dbinom{k+1}kx^k+x^{k+1}

and since \dbinom{k+1}0=\dbinom{k+1}{k+1}=1, you have

(1+x)^{k+1}=\dbinom{k+1}0+\dbinom{k+1}1x+\cdots+\dbinom{k+1}kx^k+\dbinom{k+1}{k+1}x^{k+1}

and so the claim holds for n=k+1, thus proving the claim overall that

(1+x)^n=\dbinom n0+\dbinom n1x+\cdots+\dbinom n{n-1}x^{n-1}+\dbinom nnx^n

Setting x=1 gives

(1+1)^n=\dbinom n0+\dbinom n1+\cdots+\dbinom n{n-1}+\dbinom nn=2^n

which agrees with the result obtained for part (c).
4 0
3 years ago
There are 84 boys in a senior class of 146 students. find the ratio of boys to girls. (note: if you know the total number of stu
vladimir1956 [14]
84 to 62. You have to subtract 146-84 to get the number of girls from the class.
4 0
3 years ago
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