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butalik [34]
3 years ago
13

What is the transformation of A(4,6) when dilated with a scale factor of 2, using the point (2,1) as the center of dilation?

Mathematics
1 answer:
LUCKY_DIMON [66]3 years ago
4 0

Answer:

Option B

Step-by-step explanation:

Given that the point A(4,6) is dilated with a scale factor of 2

about the point O(2,1) as centre of dilation

This implies that the new point A' will lie on the lineOA with distance equal to double of OA.

Or A will be the mid point of OA' and AA' will have same slope as OA

Considering the above two conditions we find that

Option A cannot be right.

Option B:  Midpoint of OA' = (4,6) matches with given

Slope of AA'=\frac{11-6}{6-4} =\frac{5}{2}\\\\\frac{6-1}{4-2}= \frac{5}{2}\

= slope of OA

Thus option B satisfies both

So answer is B

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A moving company charges $40 plus $0.25 per mile to rent a van. Another company charges $25 plus $0.35 per mile to rent the same
Bond [772]
<h3>Answer:</h3>

c. 150 miles

<h3>Step-by-step explanation:</h3>

You want to find the number of miles (m) that make the charges equal.

... 40 +0.25m = 25 + 0.35m

... 15 = 0.10 m . . . . . . add -25-0.25m

... 150 = m . . . . . . . . . divide by the coefficient of m

For 150 miles, the rental cost will be the same for both companies.

4 0
3 years ago
How to find the volume of a room
yuradex [85]

multiply the height x the length x the width to find the volume of a room (or another 3d object)

5 0
2 years ago
Please Help!! I will give brainliest to the quick and correct answer
klio [65]

Answer:

The correct option is the graph on the bottom right whose screen grab is attached (please find)

Step-by-step explanation:

The information given are;

The required model height for the designed clothes should be less than or equal to 5 feet 10 inches

The equation for the variance in height is of the straight line form;

y = m·x + c

Where x is the height  in inches

Given that the maximum height allowable is 70 inches, when x = 0 we have;

y = m·0 + c = 70

Therefore, c = 70

Also when the variance = 0 the maximum height should be 70 which gives the x and y-intercepts as 70 and 70 respectively such that m = 1

The equation becomes;

y ≤ x + 70

Also when x > 70, we have y ≤ \mid-x + 70\mid   with a slope of -1

To graph an inequality, we shade the area of interest which in this case of ≤ is on the lower side of the solid line and the graph that can be used to determine the possible variance levels that would result in an acceptable height is the bottom right inequality  graph.

6 0
3 years ago
The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2885 and standard deviation
aliina [53]

Answer:

a.  X~N(2,885, 651)

b.  0.086291

c.  0.00058

d.  3213.10 calories

Step-by-step explanation:

a. -A normal distribution is expressed in the form X~N(mean, standard deviation).

-Let X a random variable denoting  the number of calories consumed.

-X is a is a normally distributed random variable with mean 2885 and standard deviation 651.

-This distribution is expressed as X~N(2,885, 651)

b. The probability that less than 2000 calories are consumed is calculated using the formula:

P(X

#substitute the given values in the formula to solve for P:

P(X

Hence, the probability of consuming less than 2000 calories is 0.08691

c. The proportion of customers consuming more than 5000 calories is calculated as:

P(X>x)=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(Z>\frac{5000-2885}{651})\\\\=P(z>3.2488)\\\\=1-0.99942\\\\=0.00058

Hence, the proportion of customers consuming over  5000 calories is 0.00058

d. The least amount of calories to get the award is calculated as:

1% is equivalent to a z value of 0.50399.

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0.01=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(z>\frac{\bar X-2885}{651})\\\\\1\%=0.50399 \\\\\frac{\bar X-2885}{651}=0.50399 \\\\\bar X=0.50399\times 651+2885\\\\=3213.09

Hence, the least amount of calories consumed to qualify for the award is 3213.10 calories.

8 0
3 years ago
Which of the aaa-values satisfy the following inequality?
mina [271]

Answer:

a = 3

Step-by-step explanation:

When you add the given value for a with 7, the resulting answer must be less than 11.

In this case, if: a = 3

Plug in 3 for a in the equation:

7 + a < 11

7 + 3 < 11

10 < 11 (True).

A) a = 3 is your answer.

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7 0
2 years ago
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