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AleksandrR [38]
3 years ago
6

A figure is dilated by a scale factor of 3. If the origin is the center of dilation, what is the image of a vertex located at (3

, 4)?
Mathematics
1 answer:
IrinaK [193]3 years ago
7 0

Answer:

(9,12).

Step-by-step explanation:

If a figure dilated by a scale factor of k and origin is the center of dilation, then the relation between point and its image is defined as

P(x,y)=P'(kx,ky)

It is given that a figure is dilated by a scale factor of 3 and origin is the center of dilation. So,

P(x,y)=P'(3x,3y)

We need to find the image of a vertex located at (3, 4). So, substitute x=3 and y=4 in the above rule of dilation.

P(3,4)=P'(3(3),3(4))

P(3,4)=P'(9,12)

Therefore, the image of a vertex located at (3, 4) is (9,12).

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1) \text{P(at least one boy and one girl)}=\frac{3}{4}

2) \text{P(at least one boy and one girl)}=\frac{3}{8}

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Step-by-step explanation:

Given : Mr. and Mrs. Romero are expecting triplets. Suppose the chance of each child being a boy is 50% and of being a girl is 50%.

To  Find : The probability of each event.  

1) P(at least one boy and one girl)

2) P(two boys and one girl)

3) P(at least two girls)        

Solution :

Let's represent a boy with B and a girl with G

Mr. and Mrs. Romero are expecting triplets.

The possibility of having triplet is

BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG

Total outcome = 8

\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}

1) P(at least one boy and one girl)

Favorable outcome =  BBG, BGB, BGG, GBB, GBG, GGB=6

\text{P(at least one boy and one girl)}=\frac{6}{8}

\text{P(at least one boy and one girl)}=\frac{3}{4}

2) P(at least one boy and one girl)

Favorable outcome =  BBG, BGB, GBB=3

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3) P(at least two girls)

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\text{P(at least two girls)}=\frac{4}{8}

\text{P(at least two girls)}=\frac{1}{2}

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