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satela [25.4K]
3 years ago
13

What is the slope of the linear function represented in the table? -7

Mathematics
1 answer:
Minchanka [31]3 years ago
6 0

Answer:

The function is linear; therefore, the slope of the line joining any two points is the same. We take any two points from the table and compute the slope or rise/ run between them— let is take points (-4, -2) and (-2, -10).

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<img src="https://tex.z-dn.net/?f=Simplify%3A%20%5Cfrac%7B%205%C3%97%2825%29%5E%7Bn%2B1%7D%20-%2025%20%C3%97%20%285%29%5E%7B2n%7
Katen [24]

\green{\large\underline{\sf{Solution-}}}

<u>Given expression is </u>

\rm :\longmapsto\:\dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }

can be rewritten as

\rm \:  =  \: \dfrac{5 \times  { {(5}^{2} )}^{n + 1}  -  {5}^{2}  \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {( {5}^{2} )}^{n + 1} }

We know,

\purple{\rm :\longmapsto\:\boxed{\tt{  {( {x}^{m} )}^{n}  \: = \:   {x}^{mn}}}} \\

And

\purple{\rm :\longmapsto\:\boxed{\tt{ \:  \:   {x}^{m} \times  {x}^{n} =  {x}^{m + n} \: }}} \\

So, using this identity, we

\rm \:  =  \: \dfrac{5 \times  {5}^{2n + 2}  - {5}^{2n + 2} }{{5}^{2n + 3 + 1}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 4}  -  {5}^{2n + 2} }

can be further rewritten as

\rm \:  =  \: \dfrac{{5}^{2n + 2 + 1}  - {5}^{2n + 2} }{{5}^{2n + 2 + 2}  -  {5}^{2n + 2} }

\rm \:  =  \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2}  - 1)}

\rm \:  =  \: \dfrac{4}{25 - 1}

\rm \:  =  \: \dfrac{4}{24}

\rm \:  =  \: \dfrac{1}{6}

<u>Hence, </u>

\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times  {25}^{n + 1}  - 25 \times  {5}^{2n} }{5 \times  {5}^{2n + 3}  -  {25}^{n + 1} }  =  \frac{1}{6} }}

4 0
2 years ago
How many repeating digits does the number 0.1515 have<br>​
timama [110]

Answer:

I suppose it has 4 digits.

Step-by-step explanation:

The fractional equivalent of the repeating decimal would be 15/99.

5 0
2 years ago
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Cube 1 has a volume of 64 cubic inches and Cube 2 has a volume of 512 cubic inches. If the ratio of the surface area of Cube 1 a
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Answer:

4 and 8

Step-by-step explanation:

You don't need the surface area to find the edge length of a cube. Length of edge = ∛volume

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Length of each edge = ∛64 = 4 in.

Area of each face = 4² = 16 in².

Surface area = 6×16 = 96 in².

Cube 2:

Length of each edge = ∛512 = 8 in

Area of each face = 8² = 64 in²

Surface area = 6×64 = 384 in²

So the surface area is in the ratio 1:4

4 0
3 years ago
-121 ___ -21 what symble makes this true
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Answer: -100

Step-by-step explanation:

-121  - -100 = -21

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2 years ago
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The answer is $33.75
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