Hello!
Simplifying
5x2 + -7x + -3 = 8
Reorder the terms:
-3 + -7x + 5x2 = 8
Solving
-3 + -7x + 5x2 = 8
Solving for variable 'x'.
Reorder the terms:
-3 + -8 + -7x + 5x2 = 8 + -8
Combine like terms: -3 + -8 = -11
-11 + -7x + 5x2 = 8 + -8
Combine like terms: 8 + -8 = 0
-11 + -7x + 5x2 = 0
Begin completing the square. Divide all terms by
5 the coefficient of the squared term:
Divide each side by '5'.
-2.2 + -1.4x + x2 = 0
Move the constant term to the right:
Add '2.2' to each side of the equation.
-2.2 + -1.4x + 2.2 + x2 = 0 + 2.2
Reorder the terms:
-2.2 + 2.2 + -1.4x + x2 = 0 + 2.2
Combine like terms: -2.2 + 2.2 = 0.0
0.0 + -1.4x + x2 = 0 + 2.2
-1.4x + x2 = 0 + 2.2
Combine like terms: 0 + 2.2 = 2.2
-1.4x + x2 = 2.2
The x term is -1.4x. Take half its coefficient (-0.7).
Square it (0.49) and add it to both sides.
Add '0.49' to each side of the equation.
-1.4x + 0.49 + x2 = 2.2 + 0.49
Reorder the terms:
0.49 + -1.4x + x2 = 2.2 + 0.49
Combine like terms: 2.2 + 0.49 = 2.69
0.49 + -1.4x + x2 = 2.69
Factor a perfect square on the left side:
(x + -0.7)(x + -0.7) = 2.69
Calculate the square root of the right side: 1.640121947
Break this problem into two subproblems by setting
(x + -0.7) equal to 1.640121947 and -1.640121947.
Subproblem 1
x + -0.7 = 1.640121947
Simplifying
x + -0.7 = 1.640121947
Reorder the terms:
-0.7 + x = 1.640121947
Solving
-0.7 + x = 1.640121947
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = 1.640121947 + 0.7
Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = 1.640121947 + 0.7
x = 1.640121947 + 0.7
Combine like terms: 1.640121947 + 0.7 = 2.340121947
x = 2.340121947
Simplifying
x = 2.340121947
Subproblem 2
x + -0.7 = -1.640121947
Simplifying
x + -0.7 = -1.640121947
Reorder the terms:
-0.7 + x = -1.640121947
Solving
-0.7 + x = -1.640121947
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '0.7' to each side of the equation.
-0.7 + 0.7 + x = -1.640121947 + 0.7
Combine like terms: -0.7 + 0.7 = 0.0
0.0 + x = -1.640121947 + 0.7
x = -1.640121947 + 0.7
Combine like terms: -1.640121947 + 0.7 = -0.940121947
x = -0.940121947
Simplifying
x = -0.940121947
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.340121947, -0.940121947}
4 cos² x - 3 = 0
4 cos² x = 3
cos² x = 3/4
cos x = ±(√3)/2
Fixing the squared cosine doesn't discriminate among quadrants. There's one in every quadrant
cos x = ± cos(π/6)
Let's do plus first. In general, cos x = cos a has solutions x = ±a + 2πk integer k
cos x = cos(π/6)
x = ±π/6 + 2πk
Minus next.
cos x = -cos(π/6)
cos x = cos(π - π/6)
cos x = cos(5π/6)
x = ±5π/6 + 2πk
We'll write all our solutions as
x = { -5π/6, -π/6, π/6, 5π/6 } + 2πk integer k
Answer:
D
Step-by-step explanation:
360h+6,400 >8,020, with a solution is h> 4.
Answer:
Step-by-step explanation:
sales earning commission=130,000-21000=109,000
sales commission=5800-900=4900
rate of commission=4900/109,000 ×100=490/109 %
≈4.495
≈4.50%
