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Svetradugi [14.3K]
3 years ago
12

A roofing company is going to install a new roof on a house. The roof is 40 feet off of the ground, while the pallet of shingles

on the ground is 60 feet away from the base of the house. How long of a conveyor belt would be needed to get the shingles to the top of the house?
Mathematics
1 answer:
yKpoI14uk [10]3 years ago
5 0
|
|     <height=40 feet(a)
|
|______<base=60 feet(b)
c^2=a^2+b^2
c^2=40^2+60^2
c^2=5200 feet^2
c=(5200)^(1/2)
c=72.11102551 feet

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\huge\text{Hey there!}

\huge\textbf{Equation:}

\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}

\huge\textbf{Solve:}

\mathbf{1 \dfrac{1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}

\mathbf{\rightarrow \dfrac{1\times5+1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}

\mathbf{\rightarrow \dfrac{5 + 1}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}

\mathbf{\rightarrow \dfrac{6}{5} \times \dfrac{x}{3} = \dfrac{9}{10}}

\huge\textbf{Simplify it:}

\mathbf{\rightarrow \dfrac{2}{5}x = \dfrac{9}{10}}

\huge\textbf{Multiply \boxed{\bf \dfrac{5}{2}} to both sides:}

\mathbf{\rightarrow \dfrac{5}{2}\times \dfrac{2}{5}x = \dfrac{5}{2}\times \dfrac{9}{10}}

\huge\textbf{Simplify it:}

\mathbf{\rightarrow x = \dfrac{5}{2}\times \dfrac{9}{10}}

\mathbf{\rightarrow x = \dfrac{5\times9}{2\times10}}

\mathbf{\rightarrow x = \dfrac{45}{20}}

\mathbf{\rightarrow x = \dfrac{45\div5}{20\div5}}

\mathbf{\rightarrow x = \dfrac{9}{4}}

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\huge\textbf{Therefore, your answer should be:}

\huge\boxed{\mathsf{x = }\frak{2 \dfrac{1}{4}}}\huge\checkmark

\huge\text{Good luck on your assignment \& enjoy your day!}

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y: half of x (1, 2, 3, or 4)

z: an even number (0, 2, 4, 6, or 8).

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Choose one of the digits and look at your options (if any).

when x=2, then y = 1, which means z has to be 11 (NOT VALID)

when x=4, then y = 2, which means z has to be 8 (428 works!)

For fun, let's see if any other numbers work:

when x=6, then y = 3, which means z has to be 5 (NOT VALID)

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