Answer:
3.0.8
4.8
5.11.51
Step-by-step explanation:
1)
x^2 - 49 = 0
factor
(x+7)(x-7) = 0
x+7 = 0; x = -7
x -7 = 0; x = 7
2)x^2 - 18x + 81 = 0
factor
(x- 9)(x - 9) = 0
x - 9=0; x = 9
3)
x^2 + 3x = 40
x^2+3x - 40 = 0
factor
(x + 8)(x - 5) = 0
x+8 = 0; x = -8
x -5 = 0; x = 5
4)
3x^2 - 75 = 0
3(x^2 - 25) = 0
3(x+5)(x-5) = 0
x + 5 = 0; x = -5
x - 5 = 0; x = 5
5)
2x^2 - 15 = 7x
2x^2 - 7x - 15 = 0
(2x + 3)(x - 5) = 0
2x+3 = 0; x = -3/2
x - 5= 0; x = 5
6)
4x^2 + 16x - 48 = 0
4(x^2 + 4x - 12) = 0
4(x + 6)(x - 2) = 0
x + 6 = 0; x = -6
x - 2 = 0 ; x = 2
Sin ( t ) = √ ( 1 - (-9/11)²) = √ ( 1 - 81/121 )= √ 40/121
sin ( t ) = - 2 √10 / 11
cos ( 2 t ) = cos² t - sin² t = 81/121 - 40 / 121 = 41 /121
sin ( 2 t ) = 2 sin t cos t = 2 · ( - 2 √10/11 ) · ( - 9 /11 ) = 36√10 / 121
cos ( t/2 ) = √( 1 + cos t ) / 2 = 1 /√11
sin ( t/2 ) = √( 1 - cos t ) / 2 = √( 10/11 )
Answer:
x = 8
Step-by-step explanation:
Diagonals of a kite cross at right angles. That gives us a relation that can be solved for x.
<h3>Setup</h3>
The measure shown is equal to the angle measure of 90°.
14x -22 = 90
<h3>Solution</h3>
We can solve this 2-step linear equation in the usual way.
14x = 112 . . . . . . step 1, add the opposite of the constant to get x alone
x = 112/14 = 8 . . . step 2, divide by the coefficient of x
The value of x is 8.