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3 years ago

Given: △RST ~ △VWX

Mathematics

1 answer:

tatiyna3 years ago

4 0

Answer:

Given

Step-by-step explanation:

Given that: △RST ~ △VWX, TU is the altitude of △RST, and XY is the altitude of △VWX.

Comparing △RST and △VWX;

TU ~ XY (given altitudes of the triangles)

<TUS = <XYW (all right angles are congruent)

<UTS ≅ <YXW (angle property of similar triangles)

Thus;

ΔTUS ≅ ΔXYW (congruent property of similar triangles)

<UTS + <TUS + < UST = <YXW + <XTW + <XWY = $180^{0}$ (sum of angles in a triangle)

Therefore by Angle-Angle-Side (AAS), △RST ~ △VWX

So that:

$\frac{TU}{XY}$ = $\frac{US}{YW}$ (corresponding side length proportion)

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3 years ago

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3 years ago

Read 2 more answers

Which of the following functions represent exponential decay?

Zina [86]

Option C: $f(x)=3^{5}\left(\frac{1}{3}\right)^{x}$ is the function that represent exponential decay.

Explanation:

The exponential decay can be represented by

$f(x)=a \cdot b^{x}$ where $a>0$ and $0$

Option A: $f(x)=3(1.7)^{x-2}$

From the function, we can see that $a=3$ and $b=1.7$

Thus, $a>0$ and $b>1$

Thus, the function $f(x)=3(1.7)^{x-2}$ does not represent exponential decay.

Hence, Option A is not the correct answer.

Option B: $f(x)=3(1.7)^{-2 x}$

From the function, we can see that $a=3$ and $b=1.7$

Thus, $a>0$ and $b>1$

Thus, the function $f(x)=3(1.7)^{-2 x}$ does not represent exponential decay.

Hence, Option B is not the correct answer.

Option C: $f(x)=3^{5}\left(\frac{1}{3}\right)^{x}$

From the function, we can see that $a=3^5=243$ and $b=\frac{1}{3} =0.3333$

Thus, $a>0$ and $0$

Thus, the function $f(x)=3^{5}\left(\frac{1}{3}\right)^{x}$ represent exponential decay.

Hence, Option C is the correct answer.

Option D: $f(x)=3^{5}(2)^{-x}$

From the function, we can see that $a=3^5=243$ and $b=2$

Thus, $a>0$ and $b>1$

Thus, the function $f(x)=3^{5}(2)^{-x}$ does not represent exponential decay.

Hence, Option D is not the correct answer.

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4 years ago

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3 years ago

on this american flag the width of the blue rectangle is 2/5 the width of the red and white stripes. What fraction of the area o

Gnesinka [82]

The area of the blue rectangle is 8/11 of the flag

The area of a shape is the amount of space it occupies

The width is given as:

$Width = \frac 25$

<h3>Blue region </h3>

The blue region of the American flag has a dimension of 8 by 11 stars.

So, we have:

$8 : 11 = x : \frac 25$

Where x represents the length of the blue region.

Express the ratio as fractions

$\frac{8 }{ 11} = x \div \frac 25$

Multiply both sides by 2/5

$\frac{8 }{ 11} \times \frac 52= x$

$\frac{20}{ 11} = x$

Rewrite as:

$x =\frac{20}{ 11}$

The area is then calculated as:

$Area =\frac{20}{ 11} \times \frac 25$

$Area =\frac{40}{ 55}$

Simplify

$Area =\frac{8}{ 11}$

Hence, the area of the blue rectangle is 8/11 of the flag