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2 years ago

Someone please answer this for me ASAP

Mathematics

1 answer:

Agata [3.3K]2 years ago

6 0

Answer:

m=-1/2

Step-by-step explanation:

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If a/b < c/d with b > 0, d > 0, prove that a+c / b+d lies between the two fractions a/b and c/d .

Tems11 [23]

Divide through everything by b :

$\dfrac{a+c}{b+d} = \dfrac{\dfrac ab + \dfrac cb}{1 + \dfrac db}$

Since a/b < c/d, it follows that

$\dfrac{a+c}{b+d} < \dfrac{\dfrac cd+\dfrac cb}{1 + \dfrac db}$

Multiply through everything on the right side by b/d to get

$\dfrac{a+c}{b+d} < \dfrac{\dfrac{bc}{d^2}+\dfrac cd}{\dfrac bd+1} = \dfrac{\dfrac cd\left(\dfrac bd+1\right)}{\dfrac bd+1} = \dfrac cd$

and so (a + c)/(b + d) < c/d.

For the other side, you can do something similar and divide through everything by d :

$\dfrac{a+c}{b+d} = \dfrac{\dfrac ad + \dfrac cd}{\dfrac bd + 1}$

and a/b < c/d tells us that

$\dfrac{a+c}{b+d} > \dfrac{\dfrac ad + \dfrac ab}{\dfrac bd + 1}$

Then

$\dfrac{a+c}{b+d} > \dfrac{\dfrac ab + \dfrac{ad}{b^2}}{1 + \dfrac db} = \dfrac{\dfrac ab\left(1+\dfrac db\right)}{1 + \dfrac db} = \dfrac ab$

and so (a + c)/(b + d) > a/b.

Then together we get the desired inequality.

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2 years ago

What is the closest perfect square greater than 54

Anna35 [415]

Answer:

Step-by-step explanation:

Perfect squares are integers multiplied by themselves.

2 times 2 = 4
3 times 3 = 9
4 times 4 = 15

The closest perfect squares to 54 are 49 (7^2) and 64 (8^2).

49 is less than 54, so that's ruled out.

Therefore, the closest perfect square to 54 that is greater than it is 64.

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3 years ago

3 -1 ___ 1/4 a.= b.< c.>

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The answer to this is question is C

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2 years ago

What is 3/8 divided by 4/5

creativ13 [48]

15/32 hope this helps

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2 years ago

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I just need the answer please! ! !

OLEGan [10]

The first one x>7 nsdnejsjdhwkakns stupid 20 characters

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2 years ago