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mixas84 [53]
4 years ago
15

What % of 320 is 16?

Mathematics
1 answer:
Vinil7 [7]4 years ago
6 0

Answer:

5%

Step-by-step explanation:

(x)(320)=16

0.05

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∆abc is isosceles, ab = bc, and ch is an altitude. how long is ac, if ch = 84 cm and m∠hbc = m∠bac +m∠bch?
Tems11 [23]
Given that <span>∆abc is isosceles and ab = bc, then m<bac = m<acb and m<hbc = 180 - m<bac - m<acb

Given that </span><span>m∠hbc = m∠bac +m∠bch, then m<hbc + m<bch = m<bac + 2m<bch

But m<hbc + m<bch = 90°, thus 90° = m<bac + 2m<bch

</span><span>Also, m∠bac + m∠ach = 90° ⇒ m<bac + 2m<bch = m<bac + m<ach ⇒ 2m<bch = m<ach

Since, Δabc is isosceles with ab = bc ⇒ m<bac = m<acb.

Also, m<acb = m<ach + m<bch ⇒ m<acb = 3m<bch = m<bac

</span><span><span>Since m<bch : m<ach = 1 : 2 ⇒ bh : ah = 1 : 2

Thus, bh:bc:ch=1:3:\sqrt{8}

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\frac{bc}{ch} = \frac{bc}{84} = \frac{3}{\sqrt{8}}  \\  \\ \Rightarrow bc= \frac{3\times84}{\sqrt{8}} =63\sqrt{2}=ab

Now, ah= \frac{2}{3} (63\sqrt{2})=42\sqrt{2}

ac= \sqrt{ch^2+ah^2}  \\  \\ = \sqrt{84^2+(42\sqrt{2})^2}  \\  \\ = \sqrt{7056+3528} = \sqrt{10584}  \\  \\ =42\sqrt{6}
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