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Scilla [17]
3 years ago
6

Circle 1 is centered at (−4, 5) and has a radius of 2 centimeters. Circle 2 is centered at (2, 1) and has a radius of 6 centimet

ers. What transformations can be applied to Circle 1 to prove that the circles are similar? Enter your answers in the boxes. The circles are similar because you can translate Circle 1 using the transformation rule ( , ) and then dilate it using a scale factor of
Mathematics
1 answer:
IgorC [24]3 years ago
3 0
Basically, you have two circles. You are asked to take circle 1 and "move it" so that it is on top of circle 2. This process of moving is called a translation and can be thought of as sliding. You do this by ensuring that the two have the same center. So, starting at (-4,5) how do you have to move to end up at (2,1)?

To do this we need to move right 6 as the x-coordinate goes from -4 to 2. We also need to move down 4 as the y-coordinate goes from 5 to 1. So we add 6 to the x-coordinate and subtract 4 from the y-coordinate. The transformation rule is (x+6, y-4).

Once you do this the circles have the same center. Next you wish to dilate circle 1 so it ends up being the same size at circle 2. That means you stretch it out in such a way that it keeps its shape. Circle 1 has a radius of 2 centimeters and circle 2 has a radius of 6 centimeters. That is 3x bigger. So we dilate by a factor of 3.

Translations and dilations (along with reflections and rotations) belong to a group known as transformations.
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If 4^2x+1 = 4, then =
Aneli [31]

Step-by-step explanation:

step 1. what is the question? probably solve for x. okay.

step 2. 4^(2x) + 1 = 4

step 3. 4^(2x) = 3 subtract 1 from each side

step 4. ln4^(2x) = ln3 take on of each side

step 5. 2xln4 = ln3 definition of logs

step 6. 2x = ln3/ln4 divide both sides by ln4

step 7. x = ln3/2ln2^2 divide both side by 2 and replace 4 with 2^2

step 8. x = ln3/4ln2.

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3 years ago
Need answer quick for an assignment please.
lianna [129]

Answer:

y= 10x+7

Step-by-step explanan

7 0
3 years ago
Mopeds (small motorcycles with an engine capacity below 50 cm3) are very popular in Europe because of their mobility, ease of op
Mashcka [7]

Answer:

a) P(X<50)=0.9827

b) P(X>47)=0.4321

c) P(-1.5<z<1.5)=0.8664

Step-by-step explanation:

We will calculate the probability based on a random sample of one moped out of the population, normally distributed with mean 46.7 and standard deviation 1.75.

a) This means we have to calculate P(x<50).

We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:

z=\dfrac{X-\mu}{\sigma}=\dfrac{50-46.7}{1.75}=\dfrac{3.7}{1.75}=2.114\\\\\\P(X

b) We have to calculatee P(x>47).

We will calculate the z-score and then calculate the probability accordign to the standard normal distribution:

z=\dfrac{X-\mu}{\sigma}=\dfrac{47-46.7}{1.75}=\dfrac{0.3}{1.75}=0.171\\\\\\P(X>47)=P(z>0.171)=0.4321

c) If the value differs 1.5 standard deviations from the mean value, we have a z-score of z=1.5

z=\dfrac{(\mu+1.5\sigma)-\mu}{\sigma}=\dfrac{1.5\sigma}{\sigma}=1.5

So the probability that maximum speed differs from the mean value by at most 1.5 standard deviations is P(-1.5<z<1.5):

P(-1.5

3 0
3 years ago
On an exam, Mafuyu scored in the 20th percentile. If there were 50 students in the class, how many students scored lower than he
Reptile [31]

Using the percentile concept, it is found that 10 students scored lower than he did.

<h3>What is the meaning of the percentile of a measure?</h3>

When a measure is in the xth percentile of a data-set, it is greater than x% of the measures and lesser than (100 - x)%.

In this problem, he scored on the 20th percentile, that is, higher than 20% of the 50 students. Then:

0.2 x 50 = 10.

10 students scored lower than he did.

More can be learned about percentiles at brainly.com/question/24495213

#SPJ1

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What is the domain and range of the equation y = -(x - 3)2 + 9
vekshin1

Answer:y=9

Step-by-step explanation:

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