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maw [93]
3 years ago
5

In the image, two circles are centered at A The circle containing was dilated to produce the circle containing B’.What is the sc

ale factor of the
dilation?

Mathematics
1 answer:
denpristay [2]3 years ago
8 0

Answer:

The scale factor of the  dilation is 1/2

Step-by-step explanation:

we have that

The radius of the circle containing B is

r_1=2\ units

The radius of the circle containing B' is

r_2=1\ units

The dilation of circle containing B to circle containing B'  is a reduction

To find out the scale factor divide the radius of circle containing B'  by the radius of the circle containing B

so

\frac{r_2}{r_1}= \frac{1}{2}

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Answer:

15 years old

Step-by-step explanation:

Start by defining the variables that we are going to use throughout our working:

Let the current age of Wei Ling and Wei Xuan be L and X years old respectively.

Next, form equations using the given information.

<u>5 years </u><u>ago</u>

Wei Ling: (L -5) years old

Wei Xuan: (X -5) years old

Given that the ratio of Wei Ling's age to that of Wei Xuan's is 2: 5,

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Cross multiply:

2(X -5)= 5(L -5)

Expand:

2X -10= 5L -25

2X= 5L -25 +10

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<u>9 years time</u>

Wei Ling: (L +9) years old

Wei Xuan: (X +9) years old

Given that the ratio of Wei Ling's age to that of Wei Xuan is 3: 4,

\frac{L + 9}{X + 9}  =  \frac{3}{4}

Cross multiply:

3(X +9)= 4(L +9)

Expand:

3X +27= 4L +36

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3X= 4L +9 -----(2)

Let's solve using the elimination method.

(1) ×3:

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(2) ×2:

6X= 8L +18 -----(4)

(3) -(4):

6X -6X= 15L -45 -(8L +18)

0= 15L -45 -8L -18

0= 7L -63

7L= 63

L= 63 ÷7

L= 9

Substitute L= 9 into (1):

2X= 5(9) -15

2X= 45 -15

2X= 30

X= 30 ÷2

X= 15

Thus, Wei Xuan is 15 years old now.

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Step-by-step explanation:

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