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3 years ago

What is the scale factor of the dilation?

Mathematics

2 answers:

LenaWriter [7]3 years ago

5 0

Answer:

1/3

Step-by-step explanation:

To find the scale factor write a ratio from the side length of the small triangle to a corresponding side length of the large triangle.

C'B' has the distance 3 units and CB has the distance 9 units.

The ratio then is 3/9 = 1/3. So the scale factor is 1/3 because it is shrinking the larger triangle to the smaller as shown by the ' marks on the letters.

vovikov84 [41]3 years ago

3 0

Answer: C. $\dfrac{1}{3}$

Step-by-step explanation:

The coordinates of vertices of any figure(pre-image) (x,y) after dilation with scale factor 'k' will become : (kx,ky)→ Image.

such that $k=\dfrac{\text{coordinate of x in image}}{\text{coordinate of x in pre-image}}$

From the given figure, the coordinates of point C (in pre-image)=(-6,-6)

And the coordinates of image = (-2,-2)

$\\\\\Rightarrow\ k=\dfrac{-2}{-6}=\dfrac{1}{3}$

Hence, the scale factor of the dilation = $\dfrac{1}{3}$

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marysya [2.9K]

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3 years ago

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Which of the following is not equal to sin⁡(-230°)?

xenn [34]

From trigonometry we know that:

if $sin(\theta)=sin(\alpha)$

then, $\theta=n\pi+(-1)^n\alpha$ (where $n$ is an integer)

This can be rewritten in degrees as:

$\theta=n(180^{\circ})+(-1)^n\alpha$ .............(Equation 1)

Now, in our case, $\alpha=-230^{\circ}$

Therefore, (Equation 1) can be written as:

$\theta=n(180^{\circ})+(-1)^n(-230^{\circ})$ ..........(Equation 2)

Now, to find the correct options all that we have to do is replace n by relevant integers and find the values of $\theta$ that match.

For n=2, (Equation 2) gives us: $\theta=2\times 180^{\circ}+(-1)^2(-230^{\circ})=360^{\circ}-230^{\circ}=130^{\circ}$ .

Thus, $sin(230^{\circ})=sin(130^{\circ})$

Now, we know that: $-sin(-50^{\circ})=sin(50^{\circ})$

Let n=-1, then:

$\theta=(-1)\times 180^{\circ}+(-1)^{-1}(-230^{\circ})=-180^{\circ}+230^{\circ}=50^{\circ}$

Thus, $sin(-230^{\circ})=-sin(-50^{\circ})$

Likewise, $sin(-230^{\circ})=sin(50^{\circ})$

Only the last option $sin(-50^{\circ})$ will never match $sin(-230^{\circ})$ because no integral value of $n$ will ever give $\theta=-50^{\circ}$

Thus the last option is the correct option.

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3 years ago

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shtirl [24]

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Step-by-step explanation:

To factorize completely, we may adopt the difference of 2 squares approach. The theory states that difference of two square is the product of the difference of the number and the sum of the numbers.

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Hence 36y² - 1

= 6²y² - 1²

= (6y)² - 1²

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4 years ago

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Mama L [17]

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