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FinnZ [79.3K]
3 years ago
13

2/3 of a number decreases its 4/8 by 8, what is number?

Mathematics
2 answers:
anzhelika [568]3 years ago
5 0
The equation is 2 by 3 x -8 is equal to 4 by 8

2 X by 3 is equal to 4 + 6 all by 8

X equal to 4.2

hence the number is 4.2
kati45 [8]3 years ago
4 0

Answer:

The correct answer is that the number is 12.75.

Step-by-step explanation:

While this question is written in a convoluted manner, it is asking you to decrease 2/3x by 8. This is the expression for that.

2/3x - 8

And it is saying that it is equal to 4/8, which can be simplified to 1/2.

2/3x - 8 = 1/2

Now we can solve for the x.

2/3x - 8 = 1/2

2/3x = 17/2

x = 12.75

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2 years ago
The green triangle is a dilation of the red triangle with a scale factor of s=1/3 and the center of dilation is at the point (4,
klasskru [66]

Given:

The scale factor is s=\dfrac{1}{3} and the center of dilation is at the point (4,2).

Red is original figure and green is dilated figure.

To find:

The coordinates of point C' and point A.

Solution:

Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

(x,y)\to (k(x-a)+a,k(y-b)+b)

According to the given information, the scale factor is \dfrac{1}{3} and the center of dilation is at (4,2).

(x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)            ...(i)

Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using (i), we get

C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)

C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)

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Therefore, the coordinates of Point C' are C'(2,5).

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Using (i), we get

A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)

From the given figure it is clear that the image of point A is (8,4).

A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)

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\dfrac{1}{3}(m-4)=8-4

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m=12+4

m=16

And,

\dfrac{1}{3}(n-2)+2=4

\dfrac{1}{3}(n-2)=4-2

(n-2)=3(2)

n=6+2

n=8

Therefore, the coordinates of point A are (16,8).

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