The sum of two numbers is 47, and their difference is 15. The larger number is

Mathematics

1 answer:

Paraphin [41]3 years ago

4 0

Answer:

The large number is 31, and the small number is 16

Step-by-step explanation:

Given data

let the first number be x

and the second number be y

x+y= 47------------1

and

y-x= 15-------------2

from eqn1

x= 47-y

put this in eqn 2

y-(47-y)=15

y-47+y=15

2y= 15+47

2y=62

divide both side by 2

x= 62/2

x=31

From eqn 1

x+y= 47

31+y=47

y=47-31

y=16

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<h3>Answers:</h3>

$W(-2,-1) \to \\W \ ' \ (-4,4)\\\\X(0,2) \to \\X \ ' \ (0,4)\\\\Y(3,-1) \to \\Y \ ' \ (6,-2)\\\\V(-2,-1) \to \\V \ ' \ (-4,-2)\\\\$

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Explanation:

The scale factor is 2, which means we double each coordinate of each point. The general rule is $(x,y) \to (kx,ky)$ with k = 2. So we can say the more specific dilation rule is $(x,y) \to (2x,2y)$

Something like W(-2,2) moves to W ' (-4, 4) after multiplying each coordinate by 2. Do the same for the other points as well.

The given preimage points

V = (-2, -1)
W = (-2, 2)
X = (0, 2)
Y = (3, -1)

will dilate to the corresponding image points

V ' = (-4, -2)
W ' = (-4, 4)
X ' = (0, 4)
Y ' = (6, -2)

as shown below. This causes the image to be larger compared to the preimage (since the scale factor is larger than 1). Any given point is twice as far from the origin as compared to before, which in turn means the distance between any two points is twice as much.