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tatuchka [14]
1 year ago
11

2. Fran needs a bookcase to hold all of his math books. He decides to try to build the bookcasepictured below. He needs to buy t

hree pieces of wood to make the shelves. Each of thesethree pieces should be 3ş feet long. He needs to buy two pieces for the sides. These twopieces should be 4-— feet each. Finally, he will need to buy one piece for the top. This pieceshould be 4 feet. What is the total length of wood that Fran needs to buy?
Mathematics
1 answer:
astraxan [27]1 year ago
5 0

Let's rewrite the mixed number as a fractions:

\begin{gathered} 3\frac{2}{3}=\frac{11}{3} \\ 4\frac{1}{2}=\frac{9}{2} \end{gathered}

Therefore, the total length will be:

3\cdot(\frac{11}{3})+2(\frac{9}{2})+4=24ft

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\bf \stackrel{line~J}{y+8=-(x-2)}\implies y+8=-x+2
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y=-x-6\implies y=\stackrel{slope}{-1}x-6

now we know the slope of line J is -1.

a line perpendicular to J, will have a negative reciprocal slope, therefore,

\bf \textit{perpendicular, negative-reciprocal slope for slope}\quad -1\implies \cfrac{-1}{\underline{1}}\\\\
negative\implies  +\cfrac{1}{{{ \underline{1}}}}\qquad reciprocal\implies + \cfrac{{{ \underline{1}}}}{1}\implies 1

therefore, line K has a slope of 1, and passes through 3,4,

\bf \begin{array}{ccccccccc}
&&x_1&&y_1\\
%  (a,b)
&&(~{{ 3}} &,&{{ 4}}~)
\end{array}
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slope = {{ m}}\implies 1
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