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2 years ago

Which is in an equation of the line through (0,0) and (-8,-5)?

Mathematics

1 answer:

Lina20 [59]2 years ago

4 0

Step-by-step explanation:

Since the first coordinates are both (0,0) it implies that the line passes through the origin.

The slope of the line is therefore 5/8

The equation:

y-0=5/8(x-0)

y=5/8x

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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

What is 169 +169/23? give answer

erica [24]

Answer:

14.6956521739

Step-by-step explanation:

8 0

2 years ago

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Cos (pi/2 -x) = sin x is this true or false?

Ksenya-84 [330]

The above statement is true meaning cos(π/₂-x)=sin(x)

Step-by-step explanation:

We know that sine and cosine function are mutual cofunctions.

Hence this would mean that these two functions are complimentary of each other meaning cos(π/₂-x) = sin(x)

This can be verified mathematically by assuming “x” as 30°

Hence Cos (π/₂-30°) = cos 60°= 0.5 (from trigonometric table values)

Similarly Sin 30°= 0.5 (from trigonometric table values)

This can be proved through using the formula

Cos(A-B)= Cos A.Cos B + Sin A.Sin B

Here A=90° and b=x°

Putting the values we get (it is to be remembered that cos 90°=0 and sin 90°=1)

Cos 90°.cos x+ sin 90.sin x

0+sinx= sinx

Hence it is proved that cos(π/₂-x)=sin(x)

7 0

3 years ago

Simplify the expression 3s - 3s 35 - 3s =

Kisachek [45]

Answer:

6s-35

Step-by-step explanation:

not sure

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3 years ago

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A machine at a factory produces 30 toy cars every 2 minutes. What is the unit rate for producing a toy car using this machine

Lera25 [3.4K]

THE ANSWER IS A 24% YUNIT RATE

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3 years ago

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