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mixas84 [53]
2 years ago
5

10. In right triangle FGH shown below,

Mathematics
1 answer:
Vikki [24]2 years ago
5 0

Applying the leg rule, and solving algebraically, the lengths are determined as:

JG = 9

HJ = 12

<h3>What is the Leg Rule?</h3>

The Leg rule states that when an altitude bisects the right angle of a right triangle and intersects the hypotenuse, then, hypotenuse/leg = leg/part.

Find length of JG using algebraic solutions and the leg rule:

Let JG = x

Hypotenuse = x + 16

Leg = 15

Part = x

Therefore:

(x + 16)/15 = 15/x (leg rule)

Cross multiply

x(x + 16) = (15)(15)

x² + 16x = 225

x² + 16x - 225 = 0

Factorize

(x + 25)(x − 9) = 0

x = -25 or x = 9

The length of JG (x) cannot be negative, therefore, the length of JG = 9.

Find length of JG using algebraic solutions:

Let HJ = y

Based on the altitude theorem, we would have:

y = √(16 × JG)

Substitute

y = √(16 × 9)

y = √(144)
y = 12

Therefore, the length of HJ is: 12.

Learn more about the leg rule on:

brainly.com/question/25016594

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TEA [102]

Answer:

14 inch

Step-by-step explanation:

A = πr^2

153.94 = π * r^2

153.94/π = 49.001 = r^2

√49.001 = r = 7

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7 * 2 = 14 inch diameter

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3 years ago
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Answer:

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Step-by-step explanation:

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4 0
3 years ago
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Harman [31]

Equivalent equations are equations that have the same value

The equation in logarithmic form is t = \frac{\log(9)}{2}

<h3>How to rewrite the equation</h3>

The expression is given as:

10^{2t} = 9

Take the logarithm of both sides

\log(10^{2t}) = \log(9)

Apply the power rule of logarithm

2t\log(10) = \log(9)

Divide both sides by log(10)

2t = \frac{\log(9)}{\log(10)}

Apply change of base rule

2t = \log_{10}(9)

Divide both sides by 2

t = \frac{\log_{10}(9)}{2}

Rewrite as:

t = \frac{\log(9)}{2}

Hence, the equation in logarithmic form is t = \frac{\log(9)}{2}

Read more about logarithms at:

brainly.com/question/25710806

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2 years ago
45-45-90...find the value of x?
andrey2020 [161]

Answer:

<h2>         x = 19</h2>

Step-by-step explanation:

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