Answer:
x = 4 and y = 8
Step-by-step explanation:
This is a special right triangle with angle measures 90-60-30 degrees
The side lengths are like the following :
The side length that sees 90 degrees is represented with a
The side length that sees 60 degrees is represented with a
The side length that sees 30 degrees is represented with 2a
now, the angle measure that sees 60 degrees is given as 4 so we understand that a is = 4 that's how we find the value of x and y
All the given equations have 2 real solutions except for equation 4 which has only one real root.
<h3>What is a quadratic equation?</h3>A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given quadratic equation
where, a = 12, b = -9 and c = 4
x =
x =
x = 1.063 or -0.313
Second Equation
where, a = 1, b = 10, c = -2
substitute the values into the equation
x =
x = 0.195 or -10.195
Third Equation
where, a = 5, b = -1, c = - 5
x =
x = 0.905 or -0.55
Fourth Equation
where, a = 1, b = -8, c = 16
x =
x =
x = 4
Learn more about quadratic equations;