Arrange the steps to solve the equation √x+3 - √2x-1= -2

√(x + 3) - √(2x - 1) = -2

The first step is to get one radical on either side of the equation:

√(x + 3) = √(2x - 1) - 2

Now raise both sides to the power of 2 :

(√(x + 3))² = (√(2x - 1) - 2)²

x + 3 = (2x - 1) - 4 √(2x - 1) + 4

Simplify to obtain the final radical term on one side of the equation :

x + 3 = 2x - 1 - 4 √(2x - 1) + 4

x + 3 = 2x + 3 - 4 √(2x - 1)

4 √(2x - 1) = x

Raise both sides to the power of 2 again :

(4 √(2x - 1))² = x²

Simplify to get a quadratic equation :

16 (2x - 1) = x²

x² - 32x + 16 = 0

Factoring this is tricky, so just use the quadratic formula to find the values of x :

x = (32 ± √((-32)² - 4•16)) / 2

x = (32 ± √960) / 2

x = (32 ± √(2⁶•3•5)) / 2

x = (32 ± 2³ √15) / 2

x = 16 ± 4 √15

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.