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What is the solution of -8/2y-8=5/y+4-7y+8/y^2-16

Mnenie [13.5K]

<h2>Answer:</h2>

The solution of the given equation is:

y=6

<h2>Step-by-step explanation:</h2>

The expression is given by:

$\dfrac{-8}{2y-8}=\dfrac{5}{y+4}-\dfrac{7y+8}{y^2-16}$

Now on solving for the given equation

$\dfrac{-8}{2(y-4)}=\dfrac{5}{y+4}-\dfrac{7y+8}{(y-4)(y+4)}$

since,

$a^2-b^2=(a-b)(a+b)\\\\so,\\\\y^2-16=y^2-4^2\\\\i.e.\\\\y^2-16=(y-4)(y+4)$

Hence, we get:

$\dfrac{-4}{y-4}=\dfrac{5\times (y-4)-(7y+8)}{(y+4)(y-4)}\\\\i.e.\\\\\dfrac{-4}{y-4}=\dfrac{5y-20-7y-8}{(y-4)(y+4)}$

$-4\times (y-4)(y+4)=(-2y-28)(y-4)\\\\i.e.\\\\(y-4)(-4\times (y+4))=(-2y-28)(y-4)\\\\i.e.\\\\(y-4)(-4y+16)=(-2y-28)(y-4)\\\\i.e.$

$(y-4)(-4y+16)-(-2y-28)(y-4)=0\\\\i.e.\\\\(y-4)(-4y-16+2y+28)=0\\\\i.e.\\\\(y-4)(-2y+12)=0\\\\i.e.$

$y-4=0\ or\ -2y+12=0\\\\i.e.\\\\y=4\ or\ 2y=12\\\\i.e.\\\\y=4\ or\ y=6$

but y≠ 4

since, the denominator of the term in the left side of the given equality and the second term in the right side of the given equality will be zero and hence, the expression will be not defined.

Hence, the value of y is: 6

7 0

4 years ago

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88, 92, 76, 42, 88, 90, 100, 110, 115, 5, 88, 92, 95

salantis [7]

Answer:

Mean = 83.15

Median = 90

Mode = 88

Range = 110

Outlier = 5

Step-by-step explanation:

Mean - (88+92+76+42+88+90+100+110+115+5+88+92+95)/2 = 83.15

Median - 5, 42, 76, 88, 88, 88, <u>90</u>, 92, 92, 95, 100, 110, 115 = 90

Mode - <u>88</u>, 92, 76, 42, <u>88</u>, 90, 100, 110, 115, 5, <u>88</u>, 92, 95 = 88

Range - 115 - 5 = 110.

Outlier - 88, 92, 76, 42, 88, 90, 100, 110, 115, <u>5</u>, 88, 92, 95 = 5

hope it helps :)

please mark brainliest!!! (took a lot effort!)

8 0

4 years ago

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When a point moves right on a coordinate plane,<br> what happens to its x-value?

lord [1]

Answer:

The coordinate plane is like a cross right? Just remember if you go right the x value is going into the positive direction, if you go up the y value is also going into the positive direction. And positive direction means the value will increase.

So (3,0), would be further left than (10,0). Or (0,5) would be higher than (0,2) on the graph.

4 0

3 years ago

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Help please just look at the picture it has the question and answer choices

ratelena [41]

C is ur answer............

6 0

3 years ago

The table shows the times of the top six swimmers in the women’s 100 meter butterfly at the 2012 Olympic Games. A 2-column table

DENIUS [597]

Answer:

The difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds.

Step-by-step explanation:

The first positioned swimmer took 55.98 seconds and the second positioned swimmer took 56.87 seconds to complete the race.

So, the difference is (56.87 - 55.98) = 0.89 seconds.

The second positioned swimmer took 56.87 seconds and the third positioned swimmer took 56.94 seconds to complete the race.

So, the difference is (56.94 - 56.87) = 0.07 seconds.

The third positioned swimmer took 56.94 seconds and the fourth positioned swimmer took 57.17 seconds to complete the race.

So, the difference is (57.17 - 56.94) = 0.23 seconds.

The fourth positioned swimmer took 57.17 seconds and the fifth positioned swimmer took 57.27 seconds to complete the race.

So, the difference is (57.27 - 57.17) = 0.10 seconds.

The fifth positioned swimmer took 57.27 seconds and the sixth positioned swimmer took 57.35 seconds to complete the race.

So, the difference is (57.27 - 57.35) = 0.08 seconds.

Therefore, the difference in finishing time between the 2nd and 3rd places is the shortest and it is 0.07 seconds. (Answer)

5 0

3 years ago

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