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2 years ago

I need help with this question

Mathematics

2 answers:

Masja [62]2 years ago

5 0

Answer:

B (39)

Step-by-step explanation:

Using the Pythagorean theorem (a^2+b^2=c^2) and X=BC length

15^2+36^2=x

225+1296=x

√1521=x

x=39

Basile [38]2 years ago

4 0

Answer:

Step-by-step explanation:

The Pythagorean Theorem

a^2+b^2=c^2

In this case it's c^2=a^2+b^2

c^2=15^2+36^2

c^2=225+1296

c^2=1521

c= the square root of 1521

c=39

So...

the length of line segment BC is 39

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One alloy is 82% gold and, the second can be chosen between 25% gold, 50% gold, so there are two cases.

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$\Rightarrow 75 \times 14 = 82 \times x + 50 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 50 \times14-50\times x \\\\\Rightarrow 75 \times 14 = 32 \times x + 50 \times14 \\\\\Rightarrow 32 \times x =75 \times 14 - 50 \times14 \\\\$

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and $y = 14-x= 14-10.9375=3.0625$ grams.

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Case 2: 82% gold + 25% gold

Let x grams of 82% gold and y grams of 25% gold added to make x+y=14 grams of 75% gold, so

75% of 14 = 82% of x + 25% of y

$\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times y \\\\\Rightarrow 75/100 \times 14 = 82/100 \times x + 25/100 \times (14-x) \\\\ \Rightarrow 75 \times 14 = 82 \times x + 25 \times (14-x) \\\\\Rightarrow 75 \times 14 = 82 \times x + 25 \times14-25\times x \\\\\Rightarrow 75 \times 14 = 57 \times x + 25 \times14 \\\\\Rightarrow 57 \times x =75 \times 14 - 25 \times14 \\\\$