Can someone help me?

Mathematics

1 answer:

ser-zykov [4K]3 years ago

3 0

Answer:

x = 45

Step-by-step explanation:

'x' is the hypotenuse or the 'c' in the Pythagorean Theorem (a² + b² = c²)

27² + 36² = c²

729 + 1296 = c²

2025 = c²

√2025 = c

45 = c

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Answer:

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Step-by-step explanation:

$\begin{array}{rcll}75\left (\dfrac{1}{5}\right )^{\dfrac{x}{5}} & = & 3& \\\\\left (\dfrac{1}{5}\right )^{\dfrac{x}{5}} & = & \dfrac{3}{75}&\text{Divided each side by 75} \\\\\left (\dfrac{1}{5}\right )^{\dfrac{x}{5}} & = & \dfrac{1}{25}&\text{Simplified} \\\\\left (\dfrac{1}{5}\right )^{\dfrac{x}{5}} & = &25^{-1}&\text{Applied exponent rule} \\\\\left (\dfrac{1}{5}\right )^{\dfrac{x}{5}} & = &\left (5^{2} \right )^{-1}&\text{Converted 25 to base 5} \\\\\end{array}$

$\begin{array}{rcll}\left (5^{-1}\right )^{\dfrac{x}{5}} & = &\left (5^{2} \right )^{-1}&\text{Applied exponent rule} \\\\5^{-\dfrac{x}{5}} & = &5^{-2}&\text{Multiplied exponents} \\\\-\dfrac{x}{5} & = &-2 & \text{Equated exponents}\\\\x & = & \mathbf{10} & \text{Multiplied each side by -2}\\\end{array}\\\text{The exact solution is $\large \boxed{\mathbf{x = 10}}$}$