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Nesterboy [21]
3 years ago
11

The recursive equation for t(n)=4.5n-8

Mathematics
1 answer:
dimulka [17.4K]3 years ago
6 0

Answer:

t(1) = -3.5, Recursive equation is t(n) = t(n-1) + 4.5

Step-by-step explanation:

t(n)=4.5n-8

Let find the sequence

Plug in n=1,2,3,4.....

n=1      t(1)=4.5(1) -8= -3.5

n=2      t(2)=4.5(2) -8= 1

n=3      t(3)=4.5(3) -8= 5.5

n=4      t(4)=4.5(4) -8= 10

so sequence is -3.5, 1, 5.5, 10................

Now we find the common difference

1 - (-3.5) = 4.5

5.5-1 = 4.5

10 - 5.5 = 4.5

common difference d = 4.5

Formula for recursive function is

t(n) = t(n-1) + d

We got d= 4.5

t(n) = t(n-1) + 4.5 , also t(1) = -3.5

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Answer:

A. d ≤ –7 or d > 8.

Step-by-step explanation:

Given  : 2d + 3 ≤ –11 or 3d – 9 > 15.

To find : What are the solutions of the compound inequality .

Solution : We have given 2d + 3 ≤ –11 or 3d – 9 > 15.

For  2d + 3 ≤ –11

On subtracting both sides by 3

2d  ≤ –11 - 3 .

2d  ≤ –14.

On dividing both sides by 2 .

d  ≤ –7.

For  3d – 9 > 15.

On adding both sides by 9.

3d > 15 + 9 .

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d > 8 .

So, A. d ≤ –7 or d > 8.

Therefore,  A. d ≤ –7 or d > 8.

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Step-by-step explanation:
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Step-by-step explanation:

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Hope that helps!

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Law of radicals
andrey2020 [161]

Answer:

1)  \sqrt{x^7}=x^{\frac{7}{2}

2)  \sqrt[3]{y^5}=y^{\frac{5}{3}

3) \sqrt[5]{a^{12}}=a^{\frac{12}{5} }

4) \sqrt[4]{z^{9}}=z^\frac{9}{4}

Step-by-step explanation:

1) \sqrt{x^7}

We know that \sqrt{x}=x^{\frac{1}{2}

So, \sqrt{x^7}=x^{\frac{7}{2}

2) \sqrt[3]{y^5}

We know that \sqrt[3]{x}=x^{\frac{1}{3}

So, \sqrt[3]{y^5}=y^{\frac{5}{3}

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We know that \sqrt[5]{x}=x^{\frac{1}{5}

So, \sqrt[5]{a^{12}}=a^{\frac{12}{5} }

4) \sqrt[4]{z^{9}}

We know that \sqrt[4]{x}=x^{\frac{1}{4}

So, \sqrt[4]{z^{9}}=z^\frac{9}{4}

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