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tensa zangetsu [6.8K]
3 years ago
11

How do you use equivalent fractions to compare the fractions in each pair

Mathematics
1 answer:
Alenkasestr [34]3 years ago
8 0
Firstly you need to to reduce to a common denominator by multiplYing the whole fraction. This way you have to multiply 4/5 by 2 (both numerator and denominator). so 4/5 = 8/10. And now you have 8/10 and 9/10. You compare only numerators. This way you have 8/10 <9/10. Same goes for 2/3 and 5/8. Only here you need to multiply both fractions. The common denominator here is 24. So you have to multiply 2/3 by 8 and 5/8 by 3. You now have to compare 16/24 and 15/24. 16/24>15/24.
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Step-by-step explanation:

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Step-by-step explanation:

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Zina [86]

Question:

If cos(θ) =-8/17 and sin(θ) is negative, then sin(θ) = ___  and tan(θ) =___.

Answer:

Sin\theta = \frac{-15}{17}

Tan\theta = \frac{15}{8}

Step-by-step explanation:

Given

cos(θ) =-8/17

Required

sin(θ) = __

tan(θ) =__

The first step is to determine the length of the third side

Given that

cos(\theta) = \frac{Adj}{Hyp}

Where Adj and Hyp represent Adjacent and Hypotenuse

cos(\theta) = \frac{-8}{17}

By comparison

Adj = -8\ and\ Hyp = 17

Using Pythagoras

Hyp^2 = Adj^2 + Opp^2

By Substitution

17^2 = (-8)^2 + Opp^2

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Take square roots of both sides

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15 = Opp

Opp = 15

The question says that sin(θ) is negative; This implies that θ is in the third quadrant and as such

Opp = -15

From trigonometry

Sin\theta = \frac{Opp}{Hyp}

Sin\theta = \frac{-15}{17}

Also from trigonometry

Tan\theta = Sin\theta / Cos\theta

Tan\theta = \frac{-15}{17} / \frac{-8}{17}

Tan\theta = \frac{-15}{17} * \frac{-17}{8}

Tan\theta = \frac{-15 * -17}{17  * 8}

Tan\theta = \frac{15 * 17}{17  * 8}

Tan\theta = \frac{15}{8}

5 0
3 years ago
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