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2 years ago

Which of the following properly describe "slope"? Select all that apply.

Mathematics

1 answer:

blondinia [14]2 years ago

5 0

Answer:

I would assume you're referring to this test? if so the answer is

a, d and e

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How many terms of the arithmetic sequence {1,22,43,64,85,…} will give a sum of 2332? Show all steps including the formulas used

MA_775_DIABLO [31]

There's a slight problem with your question, but we'll get to that...

Consecutive terms of the sequence are separated by a fixed difference of 21 (22 = 1 + 21, 43 = 22 + 21, 64 = 43 + 21, and so on), so the n-th term of the sequence, a (n), is given recursively by

• a (1) = 1

• a (n) = a (n - 1) + 21 … … … for n > 1

We can find the explicit rule for the sequence by iterative substitution:

a (2) = a (1) + 21

a (3) = a (2) + 21 = (a (1) + 21) + 21 = a (1) + 2×21

a (4) = a (3) + 21 = (a (1) + 2×21) + 21 = a (1) + 3×21

and so on, with the general pattern

a (n) = a (1) + 21 (n - 1) = 21n - 20

Now, we're told that the sum of some number N of terms in this sequence is 2332. In other words, the N-th partial sum of the sequence is

a (1) + a (2) + a (3) + … + a (N - 1) + a (N) = 2332

or more compactly,

$\displaystyle\sum_{n=1}^N a(n) = 2332$

It's important to note that N must be some positive integer.

Replace a (n) by the explicit rule:

$\displaystyle\sum_{n=1}^N (21n-20) = 2332$

Expand the sum on the left as

$\displaystyle 21 \sum_{n=1}^N n-20\sum_{n=1}^N1 = 2332$

and recall the formulas,

$\displaystyle\sum_{k=1}^n1=\underbrace{1+1+\cdots+1}_{n\text{ times}}=n$

$\displaystyle\sum_{k=1}^nk=1+2+3+\cdots+n=\frac{n(n+1)}2$

So the sum of the first N terms of a (n) is such that

21 × N (N + 1)/2 - 20N = 2332

Solve for N :

21 (N ² + N) - 40N = 4664

21 N ² - 19 N - 4664 = 0

Now for the problem I mentioned at the start: this polynomial has no rational roots, and instead

N = (19 ± √392,137)/42 ≈ -14.45 or 15.36

so there is no positive integer N for which the first N terms of the sum add up to 2332.

4 0

3 years ago

Hello,

adelina 88 [10]

Answer:

go down there

Step-by-step explanation:

dsbfgriuuir

3 0

3 years ago

Tentukan himpinan penyelasaian dari plsv berikut. A:3x+=2x+12

Lena [83]

Answer:

x=12

Step-by-step explanation:

3x=2x+12

3x-2x=12

x=12

4 0

3 years ago

What is 5 times 9 divided 5 add 40 subtract 100

Sladkaya [172]

Answer:

-51

Step-by-step explanation:

5 0

3 years ago

A package of cookies contains 6 cookies. Each package of cookies costs $1.49. A function, f(x), is written to represent the cos

Ronch [10]

You define a function f(x) which gives the cost of buying x packages of cookies. You are asked for the domain of the function. That is, what values can x take on? x is the number of packages bought.

It makes no sense to buy a negative number of packages. It also makes no sense to buy 1/2 a package or 3/4 of a package as the store won’t sell you a fraction of a package. Try going to the store and buying half a package of oreo cookies. I doubt you’ll get very far :)

So it makes sense to buy 0, 1, 2, 3, 4, ... boxes of cookies. These are whole numbers. So the domain is the set of whole numbers. You could also write the domain like this {0, 1, 2, 3, ...} making sure to use the curly brackets as those denote a set.

4 0

4 years ago