All categories

2 years ago

Find the ratio of X to Y in the following: x^2+y^2=(x+2y)^2

Mathematics

2 answers:

murzikaleks [220]2 years ago

7 0

Answer:

-3/4

Step-by-step explanation:

x^2+y^2=(x+2y)^2

x^2+y^2=(x+2y) (x+2y)

Foil the right side

x^2 +y^2 = x^2 + 2xy + 2xy + 4y^2

Combine like terms

x^2 +y^2 = x^2 +4xy + 4y^2

Subtract x^2 +y^2 from each side

x^2 +y^2 - x^2 - y^2 = x^2 +4xy + 4y^2- x^2 - y^2

0 = 4xy + 3y^2

Subtract 3y^2 to each side

-3y^2 = 4xy

Divide each side by y^2

-3y^2 / y^2 = 4xy/ y^2

-3 = 4x/y

Divide each side by 4

-3/4 = x/y

The ratio is -3/4

maks197457 [2]2 years ago

6 0

Answer:

-3 : 4

Step-by-step explanation:

x^2+y^2=(x+2y)^2

x² + y² = x² + 4xy + 4y²

3y² + 4xy = 0

y(3y + 4x) = 0

3y + 4x = 0

3y = -4x

x/y = -3/4

x : y

-3 : 4

You might be interested in

Need po answer plssss

Ede4ka [16]

Answer:

owshhittttttt mic drop️

7 0

2 years ago

A post is supported by two wires (one on each side going in oppositedirections) creating an angle of 80° between the wires. The

Vladimir [108]

Using the Sine rule,

$\frac{\sin A}{A}=\frac{\sin B}{B}=\frac{\sin C}{C}$ $\begin{gathered} \text{Let A = 14m,} \\ Substituting the variables into the formula,Where the length of the wires are, AP = xm and BP = ym[tex]\begin{gathered} \frac{\sin80^0}{14}=\frac{\sin40^0}{x} \\ \text{Crossmultiply,} \\ x\times\sin 80^0=14\times\sin 40^0 \\ Divide\text{ both sides by }\sin 80^0 \\ x=\frac{14\sin40^0}{\sin80^0} \\ x=9.14m \end{gathered}$

Hence, the length of wire AP (x) is 9.14m.

For wire BP (y)m,

Sum of angles in a triangle is 180 degrees,

$A^0+P^0+B^0=180^0$ $\begin{gathered} \text{Where A}^0=\text{ unknown,} \\ P^0=80^0\text{ and,} \\ B^0=40^0 \\ A^0+80^0+40^0=180^0 \\ A^0+120^0=180^0 \\ A^0=180^0-120^0 \\ A^0=60^0 \end{gathered}$

Using the side rule to find the length of wire BP,

$\begin{gathered} \frac{\sin 60^0}{y}=\frac{\sin 80^0}{14} \\ \text{Crossmultiply,} \\ y\times\sin 80^0=14\times\sin 60^0 \\ \text{Didive both sides by }\sin 80^0 \\ y=\frac{14\times\sin 60^0}{\sin 80^0} \\ y=12.31m \end{gathered}$

Hence, the length of wire BP (y) is 12.31m

Therefore, the length of the wires are (9.14m and 12.31m).