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3 years ago

What is 0.11 as a fraction in simplest form

Mathematics

1 answer:

bazaltina [42]3 years ago

3 0

11 hundredths , or 11/100

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What is the inverse operation of subtract 18? A. subtract 18 B. multiply by 18 C. add 18 D. divide by 18

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Answer is A. Subtract 18

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3 years ago

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Study the geometric sequence {-4, -84, -1764, -37044, ...}.

Nonamiya [84]

Answer:

$\bold{a_n=(-4)21^{n-1}}$

Step-by-step explanation:

$a_1=-4\,,\ a_2=-84\,,\ a_3=-1764\,,\ a_4=-37044\quad\implies\ \ r=21$

{-84:(-4)=21 and -1764:(-84)=21 and -37044:(-1764)=21}

geometric sequence formula: $a_n=a_1r^{n-1}$

$a_1=-4\quad and \ \ r=21$

$a_n=(-4)21^{n-1}$

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3 years ago

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The temperature is -3.5 degrees Fahrenheit at 7:00 am. During the next 4 hours, the temperature decreases by -15.5 degrees. What

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-19 degrees Fahrenheit

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4 years ago

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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3 years ago