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1 year ago

Write four equivalent fractions for 3/5.

Mathematics

2 answers:

Aloiza [94]1 year ago

3 0

$\frac{6}{10} \\ \\ \frac{9}{15} \\ \\ \frac{12}{20} \\ \\ \frac{15}{25}$

elena-s [515]1 year ago

3 0

You can multiply a number for both the numerator and denominator.

So 3/5 is the same as
(3/5) x 2 = 6/10
(3/5) x 3 = 9/15
(3/5) x 4 = 12/20
(3/5) x 5 = 15/25

They will all equal the same. 3/5 is the most simplified answer.

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il63 [147K]

35=x

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3 years ago

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3 years ago

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VikaD [51]

Not sure why such an old question is showing up on my feed...

Anyway, let $x=\tan^{-1}\dfrac43$ and $y=\sin^{-1}\dfrac35$ . Then we want to find the exact value of $\cos(x-y)$ .

Use the angle difference identity:

$\cos(x-y)=\cos x\cos y+\sin x\sin y$

and right away we find $\sin y=\dfrac35$ . By the Pythagorean theorem, we also find $\cos y=\dfrac45$ . (Actually, this could potentially be negative, but let's assume all angles are in the first quadrant for convenience.)

Meanwhile, if $\tan x=\dfrac43$ , then (by Pythagorean theorem) $\sec x=\dfrac53$ , so $\cos x=\dfrac35$ . And from this, $\sin x=\dfrac45$ .

So,

$\cos\left(\tan^{-1}\dfrac43-\sin^{-1}\dfrac35\right)=\dfrac35\cdot\dfrac45+\dfrac45\cdot\dfrac35=\dfrac{24}{25}$

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3 years ago

a total of $9500 is invested, part at 10% simple interest and part at 9%. if the total annual return from the two investments is

Nutka1998 [239]

a total of $9500 is invested, part at 10% simple interest and part at 9%

if the total annual return from the two investments is $914.00

Amount invested = 9500

Total amount return means total yield = $914

Let x amount is invested at 10% simple interest

Interest for first part = 10 % times x = 0.10x

Remaining part invested is 9500 -x

Interest for remaining amount = 9% (9500 -x) = 0.09(9500-x)

Total interest yield is 914. Now we frame an equation

0.10x + 0.09(9500-x) = 914

0.10x +855 - 0.09x = 914 (combine like terms)

0.01 x + 855 = 914 (subtract 855)

0.01x = 59 ( divide both sides by 0.01)

So x = 5900

$5900 is invested in 10% simple interest

9500 - 5900 = $3600 is invested in 9% simple interest

3 0

3 years ago