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choli [55]
3 years ago
7

If triangle ABC is defined by the coordinated A(3,6), B(7,6), C(7,3) is dilated by a scale factor of 3, with resulting vertex A'

at (9,18). What is the the center of dilation?
Mathematics
1 answer:
Anastaziya [24]3 years ago
5 0

Answer:

Center of dilation → (0, 0)

Step-by-step explanation:

Vertices of a triangle ABC are A(3, 6), B(7, 6) and C(7, 3).

If this triangle is dilated by a scale factor of 'k' about the origin,

Rule for the dilation is,

(x, y) → (kx, ky)

If vertex A is dilated by a scale factor of 3 about the origin,

A(3, 6) → A'(3×3, 3×6)

           → A'(9, 18)

Therefore, center of dilation is origin (0, 0).

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Solve the equation 2(x-10)= 24 , what is the value of x
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Answer:

x=22

Step-by-step explanation:

2(x-10)=24

Distribute the parenthesis

2x-20=24

Add 20 to both sides

2x=44

Divide both sides by 2

\frac{2x}{2} =\frac{44}{2}

x=22

Hope this helps

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75+20 1X -40+13 X +76 + 3X -20 = 720 solve for x
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4 0
3 years ago
"A laboratory tested 73 chicken eggs and found that the mean amount of cholesterol was 230 milligrams with LaTeX: \sigmaσ = 17.4
Scrat [10]

Answer:

The 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is between 226.01 and 233.99 milligrams.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96*\frac{17.4}{\sqrt{73}} = 3.99

The lower end of the interval is the sample mean subtracted by M. So it is 230 - 3.99 = 226.01

The upper end of the interval is the sample mean added to M. So it is 230 + 3.99 = 233.99.

The 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is between 226.01 and 233.99 milligrams.

4 0
3 years ago
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