Mathematics, 23.04.2020 04:15 tylerjoshonti

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Which choices show the ratio of the area of the smaller rectangle to the area of the larger rectangle? Select three options.

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Answers

The options b) ,c) and e) are correctThe three choices shows the ratio of the area of the smaller rectangle to the area of the larger rectangle are b) $(\frac{4}{16})^2$ , c) $\frac{12}{192}$ and e) $(\frac{3}{12})^2$

Step-by-step explanation:

Given that a large rectangle has a length of 16 and width of 12.

A smaller rectangle has length of 4 and width of 3

To show the ratio of the area of the smaller rectangle to the area of the larger rectangle:

we know that "If two figures are similar, the the ratio of its areas is equal to the scale factor squared"

From the given scale factor is $\frac{1}{4}$

Let z be the scale factor

Let x be the area of the smaller rectangle

Let y be the area of the large rectangle

$z^2=\frac{x}{y}$

Since scale factor is $\frac{1}{4}$ hence $z=\frac{1}{4}$

we have $z^2=(\frac{1}{4})^2$

$=\frac{1}{16}$

∴ $z^2=\frac{1}{16}$

Now show that the ratio of the area of the smaller rectangle to the area of the larger rectangle with each options.

a) $\frac{4}{16}$

$\frac{4}{16}=\frac{1}{4}$

Compare with $\frac{1}{16}$ we get,

$\frac{1}{4}\neq \frac{1}{16}$

Hence it is not possible.

b) $(\frac{4}{16})^2$

$(\frac{4}{16})^2=\frac{16}{256}$

$=\frac{1}{16}$

Compare with $\frac{1}{16}$ we get,

$\frac{1}{16}=\frac{1}{16}$

This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.

c) $\frac{12}{192}$

$=\frac{1}{16}$

Compare with $\frac{1}{16}$ we get,

$\frac{1}{16}=\frac{1}{16}$

This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.

d) $(\frac{4}{12})^2$

$=\frac{16}{144}$

$=\frac{1}{9}$

Compare with $\frac{1}{16}$ we get,

$\frac{1}{9}\neq \frac{1}{16}$

Hence it is not possible.

e) $(\frac{3}{12})^2$

$=\frac{9}{144}$

$=\frac{1}{16}$

Compare with $\frac{1}{16}$ we get,

$\frac{1}{16}=\frac{1}{16}$

This implies that the ratio of the area of the smaller rectangle to the area of the larger rectangle.∴ options b) ,c) and e) are correctThe three choices shows the ratio of the area of the smaller rectangle to the area of the larger rectangle are b) $(\frac{4}{16})^2$ , c) $\frac{12}{192}$ and e) $(\frac{3}{12})^2$

Answer from: Quest

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this

#10 can anyone solve this for will give !

Answer from: Quest

idk

step-by-step explanation:

i don't know

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