Is 3x + 2y = 6 a function??

<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

Can someone please answer this for brainlist pls.

o-na [289]

Answer:

If your answer is linear, I would suggests: 1,2,4 maybe there's another one but I'm confident about those though. Hopefully I helped you with my options.

Step-by-step explanation:

8 0

2 years ago

If a cat catches 120 mice in 30 days,how many mice does it catch in 5 days?

Elanso [62]

Answer:

ITS 24

Step-by-step explanation:

divide it 120÷4=24

7 0

2 years ago

Read 2 more answers

A teacher puts five packages of craft paper into a cabinet each package has 80 sheets of paper what is the total number of sheet

aliina [53]

Answer:

C

Step-by-step explanation:

If we have 5 packages and each contains 80, we are basically doing 80+80+80+80+80 (5 TIMES) which is referred to as 80×5=400

7 0

2 years ago

Read 2 more answers

PLEASE HELP ME ASAPP !!

Andreas93 [3]

Answer:

1. you start with $ 3 and save $1 each month

2. your total savings is 3 times the number of month multiplied by itself

3. you save $3 the first month and then each month the amount triples

Step-by-step explanation:

1.

as y axis represents savings while x axis represents months

the statement "you start with $ 3 and save $1 each month"

is best described by the graph of straight line having slope of 1 and intercept of 3.

2. your total savings is 3 times the number of month multiplied by itself

= 3(x)(x)

= 3x^2

3. as y axis represents savings while x axis represents months

the statement "you save $3 the first month and then each month the amount triples" is best described by the exponential graph starting to rise from point (1,3) which means $3 save at 1 month.

!

4 0

3 years ago