Combinations = n! / (n - r)! r!
In this case:
n = 4
r = 3
Combinations = 4! /(4-3)! 3! = 24/(1)(6) = 24/6 = 4
Answer:
4 arrangements
Answer:
x = 0
y = 5
z = -5.
Step-by-step explanation:
X-5y-z=-20
-2x-y-6z=25
-x-4y-z=-15
Add equation 1 and 3:
-9y - 2z = -35 .......... A
Multiply the first equation by 2:
2x - 10y - 2z = -40
Now add this to equation 2:
-11y -8z = -15.............B
Now multiply equation A by -4:
36y + 8x = 140.........C
Add equations B and C:
25y = 125
y = 5.
Substitute for y in equation A:
-9*5 - 2z = -35
2z = -45 + 35 = - 10
z = -5.
Now find x by substituting for y and z in the first equation:
x - 5(5) - (-5) = -20
x - 20 = -20
x = 0.
<u>Answer and explanation</u>
(1+sinθ)(1-sinθ)=cos²θ
We are to prove that the left hand side is equal to the right hand side.
(1+sinθ)(1-sinθ) = 1(1-sinθ) + sinθ(1-sinθ)
= 1 - sinθ + sinθ - sin²θ
= 1 - sin²θ
From the trigonometric identity sin²θ + cos²θ = 1,
1 - sin²θ = cos²θ
Answer:
8x - 6 = x + 9 : Given
7x - 6 = 9 :Subtraction property of equality
7x = 15 : Addition property of equality
x = 15/7 : Division property of equality
x = 2.143
Step-by-step explanation:
Match the properties with the steps to solving the following equation.
(8x - 6) = x + 9
8x - 6 = x + 9 : Given
8x - x - 6 = x + 9 - x
7x - 6 = 9 :Subtraction property of equality
7x - 6 + 6 = 9 + 6
7x = 15 : Addition property of equality
7x/ 7 = 15/7
x = 15/7 : Division property of equality
x = 2.143
