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3 years ago

15 POINTS A 4-inch length is represented as 1/8 on a scale drawing. What is the scale used on the drawing?

Mathematics

1 answer:

-BARSIC- [3]3 years ago

8 0

9514 1404 393

Answer:

(b) 1 foot = 3/8 inch

Step-by-step explanation:

The given ratio is ...

actual : scale = 4" : 1/8"

You know that 1 foot = 12 in = 3×4 in, so you can multiply the above ratio by 3 to see what it is for 1 foot.

actual : scale = 3×4" : 3×1/8"

= 12" : 3/8"

= 1 foot : 3/8 in

______

Alternate approach

Essentially, we're saying that the ratios between actual measures and those on a scaled drawing or model form a proportion.

scale / actual = (1/8")/(4 in) = ??/(12 in)

Multiplying by 12 in, we get ...

?? = (12 in)(1/8")/(4 in) = 3×1/8"

?? = 3/8"

More detail

Notice that this only works when the units in the ratio (12 in)/(4 in) cancel to give a pure number 12/4 = 3.

If we had put 1 foot in the proportion, then we would end up with ?? being expressed in feet, not inches:

(1/8")/(4") = ??/(1 ft)

?? = (1 ft)(1/8")/(4") = (1 ft)(1/32) = 1/32 ft

Then, to find the answer to the question, we would have to find out how many inches is 1/32 ft.

1/32 ft = (1/32)(12 in) = 12/32 in = 3/8 in

End comment

For best results, the units in corresponding parts of a proportion should be the same.

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notka56 [123]

Answer:

AC = { 4, 5, 6, 7 }

Step-by-step explanation:

If you see, the diagonal AC forms two triangles, Δ ABC, and Δ ADC. In Δ ABC, AC = 3 units and BC = 6 units, while AC is yet to be known. Respectively in Δ ADC, AD = 4 units and CD = 4 units, while AC is again yet to be known.

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3 years ago

Given a triangle with vertices P(-9,7), Q(-3,7), and R(-3,1), and S is the midpoint of PQ and T is the midpoint of QR, what is t

Natalija [7]

Check the picture below.

so we know S is the midpoint of PQ, and T is the midpoint of QR, thus

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&P&(~ -9 &,& 7~) 
% (c,d)
&Q&(~ -3 &,& 7~)
\end{array}\quad
% coordinates of midpoint 
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
S=\left( \cfrac{-3-9}{2}~,~\cfrac{7+7}{2} \right)\implies S=(-6,7)\\\\
-------------------------------$

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&Q&(~ -3 &,& 7~) 
% (c,d)
&R&(~ -3 &,& 1~)
\end{array}
\\\\\\
T=\left(\cfrac{-3-3}{2}~,~\cfrac{1+7}{2} \right)\implies T=(-3,4)$

so, what's the distance from S to T?

$\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&S&(~ -6 &,& 7~) 
% (c,d)
&T&(~ -3 &,& 4~)
\end{array}\\\\\\ 
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
ST=\sqrt{[-3-(-6)]^2+[4-7]^2}\implies ST=\sqrt{(-3+6)^2+(4-7)^2}
\\\\\\
ST=\sqrt{3^2+(-3)^2}\implies ST=\sqrt{18}\implies ST=\sqrt{9\cdot 2}
\\\\\\
ST=\sqrt{3^2\cdot 2}\implies ST=3\sqrt{2}$

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