Question

Enter the values for the variables that give the correct simplified expressions, x > 0.

V50x^2 = V25.2 - x^2 = 5x15
a) x = 2
b) x = 3
c) x = 5
d) x = 7

32x = V16-2- x = CV2x
a) x = 1
b) x = 2
c) x = 4
d) x = 5

18n = 19.2.n=en
a) n = 1
b) n = 2
c) n = 3
d) n = 4

72x^2 - 736-2-x^2 = gx 2
a) x = 1
b) x = 2
c) x = 4
d) x = 5

Answer 1

To find the values of the variables x and n, we can solve each equation separately using the correct mathematical principles. For equation 1, the value of x is approximately 0.707. For equation 2, the value of x is approximately (5 + √33) / (-2). And for equation 3, the value of x is √(2952/71) / 2.

Step-by-step explanation:

To find the values of the variables, we can solve each equation separately.

Equation 1:

V50x^2 = V25

Square both sides: 50x^2 = 25

Divide by 50: x^2 = 0.5

Take the square root: x = ±0.707

Since x > 0, the possible solution is x = 0.707

Equation 2:

-2 - x^2 = 5x

Add 2 to both sides: -x^2 - 5x + 2 = 0

Use the quadratic formula to solve for x: x = (-(-5) ± √((-5)^2 - 4(-1)(2))) / (2(-1))

Simplify: x = (5 ± √(25 + 8)) / (-2)

Simplify further: x = (5 ± √33) / (-2)

Since x > 0, the possible solution is x = (5 + √33) / (-2)

Equation 3:

72x^2 - 736 - 2 - x^2 = 0

Combine like terms: 71x^2 - 738 = 0

Divide by 71: x^2 - 738/71 = 0

Use the quadratic formula to solve for x: x = (-(-0) ± √((-0)^2 - 4(1)(-738/71))) / (2(1))

Simplify: x = ±√(4(738/71)) / 2

Simplify further: x = ±√(2952/71) / 2

Since x > 0, the possible solution is x = √(2952/71) / 2