Ask question

Ask question

All categories

3 years ago

9

Given ΔDEF : ΔRST, find the scale factor.

2 answers:

LekaFEV [45]3 years ago

8 0

Answer: The value of x is 12 units and the scale factor is $\dfrac{4}{3}.$

Step-by-step explanation: Given that the triangle DEF is similar to the triangle RST.

We are to find the value of x and the scale factor of the dilation.

We know that the corresponding sides of the similar triangles are proportional.

So, we must have

$\dfrac{DE}{RS}=\dfrac{EF}{ST}\\\\\\\Rightarrow \dfrac{3}{x}=\dfrac{4}{16}\\\\\\\Rightarrow \dfrac{3}{x}=\dfrac{1}{4}\\\\\Rightarrow x=3\times4\\\\\Rightarrow x=12.$

The scale factor is given by

$S=\dfrac{\textup{length of a side of the dilated triangle}}{\textup{length of the corresponding side of the original triangle}}\\\\\\\Rightarrow S=\dfrac{RS}{DE}\\\\\\\Rightarrow S=\dfrac{4}{3}.$

Thus, the value of x is 12 units and the scale factor is $\dfrac{4}{3}.$

Grace [21]3 years ago

5 0

The scale factor of DEF : RST is 3/4.

X = 12

You might be interested in

⅔ divided by ⅙ i need help

Aleonysh [2.5K]

2/3 / 1/6

When dividing by a fraction, flip the second fraction over and change divide to multiply:

2/3 x 6/1 = (2 x6) / (3 x 1) = 12/3 = 4

The answer is 4

7 0

3 years ago

Which quadratic function is best represented by this graph?

11Alexandr11 [23.1K]

? Pick one graph

Step-by-step explanation:

There's no graph visible

f(x) is the same as y

Hope this helps!

4 0

2 years ago

When you multiply a positive integer by a positive integer is the result positive or negative?

Usimov [2.4K]

<span>When you multiply a positive integer by a positive integer then the result must be a Positive Integer.

Hope this helps!
</span>

5 0

3 years ago

Using the given points and line, determine the slope of the line. (-3,0) and (2,7)

o-na [289]

Answer:

slope = $\frac{7}{5}$

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (2, 7)

m = $\frac{7-0}{2+3}$ = $\frac{7}{5}$

3 0

3 years ago

Read 2 more answers

Show that the cosine law simplifies to the Pythagorean theorem when the contained angle between the two known sides is 90°.

mixas84 [53]

Answer:

See Below.

Step-by-step explanation:

We want to show that the Law of Cosines simplifies to the Pythagorean Theorem when the contained angle between the two known sides is 90°.

The Law of Cosines is given by:

$c^2=a^2+b^2-2ab\cos(C)$

Where <em>a </em>and <em>b</em> are the two known sides, and C is the angle between them.

If C is 90° then we will have:

$c^2=a^2+b^2-2ab\cos(90 ^\circ)$

Recall that the cos(90°)=0. Hence:

$c^2=a^2+b^2-2ab(0)$

Simplify:

$c^2=a^2+b^2$

So, we acquire the Pythagorean Theorem as desired.

7 0

3 years ago