3) IN THE ORDERED PAIR: (7,3) TELL ME WHAT IT MEANS.

Mathematics

2 answers:

anygoal [31]2 years ago

6 0

The ordered pair (7,3) means there is an “x” value of 7, and a “y” value of 3 at said coordinate.

fiasKO [112]2 years ago

3 0

I hope you are having a good day today :)

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Vaselesa [24]

It can work well here to simplify inside parentheses first.

$\displaystyle\left(\frac{4x^{-2}y^{2}}{12x^{-4}y^{-1}}\right)^{3}=\left(\frac{4}{12}x^{(-2-(-4))}y^{(2-(-1))}\right)^{3}\\\\=\left(\frac{x^{2}y^{3}}{3}\right)^{3}=\frac{x^{(2\cdot 3)}y^{(3\cdot 3)}}{3^{3}}\\\\=\frac{x^{6}y^{9}}{27}$

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3 years ago

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3 years ago

Find the sum of the first 20 terms of the arithmetic sequence 4, -4, -12, -20

Vsevolod [243]

Answer:

The sum of the first 20 terms is -1440.

Step-by-step explanation:

We want to find the sum of the first 20 terms of the arithmetic sequence:

4, -4, -12, -20...

The sum of an arithmetic sequence is given by:

$\displaystyle S=\frac{k}{2}(a+x_k)$

Where k is the number of terms, a is the initial term, and x_k is the last term.

Since we want to find the sum of the first 20 terms, k = 20.

Our initial term a is 4.

Our last term is also the 20th term as we want the sum of the first 20 terms.

To find the 20th term, we can write an explicit formula for our sequence. The explicit formula for an arithmetic sequence is given by:

$x_n=a+d(n-1)$

Where a is the initial term, d is the common difference, and n is the nth term.

Our initial term is 4. From the sequence, we can see that our common difference is -8 since each subsequent term is eight less than the previous term. Therefore:

$x_n=4-8(n-1)$