ΔAOB is a right angled triangle. Therefore the Pythagorean Theorem applies in this situation.
θ is the angle from a standard position of the line OA
The length of the y component is √(1-0)2 +(-3-(-3))2] =√(12+ 02) = 1 A(-3,1) to B(-3,0) which is opposite
Then the length of the x-component is √[(-3-0)2 +(0-0)2] = √(9+0)= 3 B(-3,0) to O(0,0) which is adjacent
The length of vector OA is √[(-3-0)2 + (1-0)2] = √(9+1) = √(10) A(-3,1) to O(0,0) which is the hypotenuse of the triangle
θ = 180 - α
sinθ = sin(180-α) = opposite/hypotenuse = 1/√10
cosθ = adjacent/hypotenuse = -3/√10
tanθ = opposite/adjacent = 1/-3 = -1/3
α= arcsin(1/√10) ≈ 18
θ =180 -18 ≈162
Solution:
Rewrite 3 ≥ y - 2 for easier calculation:
y - 2 ≤ 3
Move the term:
y ≤ 3 + 2
y ≤ 5
When graphing the solution, filled dot (black arrow) is used for ≤ and ≥ while empty dot (white arrow) is used for < >
Answer:
4
Step-by-step explanation:
The distance from B to C is the same as the distance from A to D. Points B and C will both have the same x-value, as do points A and D. Points B and C will have the same difference in y-values (2 -(-2) = 4) that points A and D have.
The distance from B to C is 4 units.
Answer:
Step-by-step explanation:
Total marble = 4+6+7 = 17
Number of green = 7
Prob(1st green) = 7/17
Now their are 6 green left and 16 marble
Prob(2nd green) = 6/16 = 3/8
Now their are 5 green left and 15 marble
Prob(3rd green) = 5/15 = 1/3
Prob(1st and 2nd and 3rd green) will be = 7/17 × 3/8 × 1/3
= 7/(17×8)
= 7/136
