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Step-by-step explanation:

A =2

Step-by-step explanation:

B

x + 2 = 3x - x^2

Simplifying

x + 2 = 3x + -1x2

Reorder the terms:

2 + x = 3x + -1x2

Solving

2 + x = 3x + -1x2

Solving for variable 'x'.

Combine like terms: x + -3x = -2x

2 + -2x + x2 = 3x + -1x2 + -3x + x2

Reorder the terms:

2 + -2x + x2 = 3x + -3x + -1x2 + x2

Combine like terms: 3x + -3x = 0

2 + -2x + x2 = 0 + -1x2 + x2

2 + -2x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0

2 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.

2 + -2x + -2 + x2 = 0 + -2

Reorder the terms:

2 + -2 + -2x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0

0 + -2x + x2 = 0 + -2

-2x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2

-2x + x2 = -2

The x term is -2x. Take half its coefficient (-1).

Square it (1) and add it to both sides.

Add '1' to each side of the equation.

-2x + 1 + x2 = -2 + 1

Reorder the terms:

1 + -2x + x2 = -2 + 1

Combine like terms: -2 + 1 = -1

1 + -2x + x2 = -1

Factor a perfect square on the left side:

(x + -1)(x + -1) = -1

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

br

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 =   (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4   we need to find some relationship between a and b.

let's try ab = bc  

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2 

br = sqrt(3) * a

cp

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram. 

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a 

cp = sqrt(3)*a

aq

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a 

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt  3) * a which agrees with the other two.

yx = 36

step-by-step explanation:

cos f = opposite side/ hypotenuse

cos f = yw / yx

we know cos f = 4/9 and yw =16

4/9 = 16/yx

multiply each side by yx

4/9 yx = 16/ yx * yx

4/9 yx = 16

multiply each side by 9/4

9/4 * 4/9 yx = 16 *9/4

yx = 36