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3 years ago

Which of the following statements is false?

Mathematics

1 answer:

barxatty [35]3 years ago

3 0

A is false, therefore the correct answer

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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.

5 0

3 years ago

If X = -6 and Y = 10 then find |x|-|3y|/|xy|

jek_recluse [69]

Answer:

(2)

Step-by-step explanation:

6 0

2 years ago

Solve the inequality

storchak [24]

Answer:

m ≥ –6

Step-by-step explanation:

m+5 ≥ –1

subtract 5 from both sides

m ≥ -6

3 0

2 years ago

Yesterday, Julie’s bank account balance was –$10.28. She deposited some money into her account so that her balance is now $39.89

Tcecarenko [31]

10.28+39.89=50.17

hope this helps

5 0

3 years ago

Read 2 more answers

Expression 1:

e-lub [12.9K]

1. Did it mentally think it’s 16. Make sure to yield to order of operations.
2. Because none of the operations are multiplication or division, parenthesis can be put anywhere that isn’t between exponents and it will yield 22.

7 0

3 years ago