The product of two numbers is 450. the first number is half the second number. which equation can be used to find x, the greater number?

Given:
product of 2 numbers is 450.
first number is half the second number.

Let us make our own equation based on the given data.

Let x and y be the two numbers.

y * x = 450

y is the 1st number. It is said that it is half the second number, x.

y = 1/2 * x = x/2

Let us substitute y of the 1st equation by its value in the second equation.

x/2 * x = 450

x² / 2 = 450
x² = 450 * 2
x² = 900
√x² = √900
x = 30

The value of x, the 2nd number, is 30. 

y = x/2 = 30/2 = 15

The value of y, the 1st number, is 15.

To check:

y * x = 450
15 * 30 = 450

450 = 450

The product of two numbers is 450. The first number is half the second number. Which equation can be used to find x, the greater number?

The first number is half the second number, then:
The second number is the greater number: x
Let be:
The first number: y

The product of two numbers is 450:
xy=450

The first number is half the second number:
y=x/2

The equation of the product can be used to find x:
Replacing y by x/2 in the equation of the product:
x(x/2)=450
Solving for x:
x^2/2=450
2(x^2/2)=2(450)
x^2=900
sqrt(x^2)=sqrt(900)
x=30

y=x/2=30/2→y=15

C. expression because any expression or equation may contain more than one variable

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

ac ≅ ab (given)< cax ≅ < bax   (given)ax ≅ ax (common side)

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

ac ≅ ab (given)< cay ≅ < bay (since < cax ≅ < bax is given and xy is the extension of line ax)ay ≅ ay (common side)

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)