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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

answer: the answer is 35%

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.