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3 years ago

14

Graph the line that represents the equation

1 answer:

Anastaziya [24]3 years ago

3 0

Answer:

<h3>In the attachment.</h3>

Step-by-step explanation:

We need only two points.

Choose any two values of x. Put them to the equation and calculate the value of y:

$y=-\dfrac{2}{3}x+1\\\\\text{for}\ x=0\\\\y=-\dfrac{2}{3}\cdot0+1=0+1=1\to A(0;\ 1)\\\\\text{for}\ x=3\\\\y=-\dfrac{2}{3}\cdot3+1=-2+1=-1\to B(3;\ -1)$

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A playground is being designed where children can interact with their friends in certain combinations. If there is 1 child, ther

mariarad [96]

<h2>Answer:</h2>

<em><u>Recursive equation for the pattern followed is given by,</u></em>

$a_{n}=a_{n-1}+(n-1)^{2}$

<h2>Step-by-step explanation:</h2>

In the question,

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We need to find out the pattern for the recursive equation for the given conditions.

So,

We see that,

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Therefore, on checking, we observe that,

$a_{n}=a_{n-1}+(n-1)^{2}$

On checking the equation at the given values of 'n' of, 1, 2, 3 and 4.

<u>At, </u>

<u>n = 1</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{1}=a_{1-1}+(1-1)^{2}\\a_{1}=0+0=0\\a_{1}=0$

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<u>At, </u>

<u>n = 2</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{2}=a_{2-1}+(2-1)^{2}\\a_{2}=a_{1}+1\\a_{2}=1$

Which is also true.

<u>At, </u>

<u>n = 3</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{3}=a_{3-1}+(3-1)^{2}\\a_{3}=a_{2}+4\\a_{3}=5$

Which is true.

<u>At, </u>

<u>n = 4</u>

$a_{n}=a_{n-1}+(n-1)^{2}\\a_{4}=a_{4-1}+(4-1)^{2}\\a_{4}=a_{3}+9\\a_{4}=14$

This is also true at the given value of 'n'.

<em><u>Therefore, the recursive equation for the pattern followed is given by,</u></em>

$a_{n}=a_{n-1}+(n-1)^{2}$

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Answer:

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Step-by-step explanation:

(X is another 2)

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Answer:

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Step-by-step explanation:

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