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sleet_krkn [62]
3 years ago
14

A tree casts a 20-foot shadow. Brian is 6 feet tall and casts a 4-foot shadow. How tall is the tree

Mathematics
2 answers:
harkovskaia [24]3 years ago
8 0
Hello! So Brian is 6 feet tall and casts a 4 foot shadow and the tree’s shadow is 20 feet. To find the height of the tree, we can write and solve a proportion. Set it up like this:

6/4 = x/20

This is because we are looking for the height of the tree, and having it set up like this will help us get to the right answer. Let’s cross multiply. 6 * 20 is 120. 4 * x is 4x. That simplified to 120 = 4x. Now, divide each side by 4 to isolate the x. 4x/4 cancels our. 120/4 is 30. Let’s cross multiply to check out answers. 6 * 20 is 120. 30 * 4 is 120. 120 = 120. There. x = 30. The tree is 30 feet tall.
Gemiola [76]3 years ago
5 0
The tree is 22 feet because the shadow is 2 feet smaller
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<img src="https://tex.z-dn.net/?f=%285%5E%7B3%7D%29%5E%7B-3%7D" id="TexFormula1" title="(5^{3})^{-3}" alt="(5^{3})^{-3}" align="
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<h3>\frac{1}{1953125} ✅</h3>

\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}

( { {5}^{3} })^{ - 3}  \\   \\ which\:means \:that \: {5}^{3}\:  is \:multiplied \:thrice\: with\: itself\\ \\ =  {5}^{3 \times  - 3}  \\ \\   =  {5}^{ - 9}  \\  \\=  \frac{1}{ {5}^{9} }  \\  \\  =  \frac{1}{5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5}  \\   \\ =  \frac{1}{1953125}

<u>Note</u>:-

( { {a}^{m} })^{n}  =  {a}^{m \times n}

{a}^{ - m}  =  \frac{1}{ {a}^{m} }

\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}

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