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3 years ago

If 1/4x +2y= 11/4 and - 6y - x = 7, what is half of y?

Mathematics

1 answer:

ioda3 years ago

8 0

Answer:

y/2 = 4.5

Step-by-step explanation:

1/4x + 2y = 11/4

distribute by 4 to eliminate fractions

x + 8y = 11

+ -x - 6y = 7

2y = 18

y = 9

half of 9 = 4 1/2

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Simplify: [5×(25)^n+1 - 25 × (5)^2n]/[5×(5)^2n+3 - (25)^n+1]

Alekssandra [29.7K]

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

Given expression is 

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

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

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

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

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

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

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

Hence, 

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

4 0

2 years ago

5th grade math. correct answer will be marked brainliest

monitta

Answer:

She got 9 multiple choice questions right.

She got 8 true/false questions right.

Step-by-step explanation:

you have to make them have a common denominator.

so multiply 4/5 by 2/2 and you get 8/10.

She got 9/10 multiple choice answers right and 8/10 true/false answers right.

5 0

2 years ago

Read 2 more answers

What can 23/40 be simplified by?

kicyunya [14]

23/40 can't be simplified as it has no common factors

8 0

3 years ago

sally has scores of 88, 92, 80, and 96. find the score she must make on the next exam to have an average of 90

melisa1 [442]

The score range that sally would have to make a 90 average is 85-100

3 0

3 years ago

Add grouping symbols to make the equation true 10-6•2+8=40

Nitella [24]

Your answer should be:
(10-6)x(2+8)=40

4 0

3 years ago