Answer:
≈ 18.8 cm
Step-by-step explanation:
The arc length is calculated as
arc = circumference of circle × fraction of circle
The central angle is equal to the arc subtending it, that is 60°
arc = 2πr × 
= 2π × 18 × 
= 36π ×
= 6π ≈ 18.8 cm ( to 1 dec. place )
Very simple. You just use the vectors as normal numbers, and multiply the coordinates with 2 and 4 like this:
2*u = 2* (2,4) = (4,8)
4*w = 4* (-1,3) = (-4,12)
(4,8) - (-4,12) = (8,-4)
So the vector has the coordinates (8,-4)
Answer:
Victor originally had $80
Step-by-step explanation:
Let Victor have $4x
Let Susie have $7x
Since Victor spent half his money, he now has $2x
Susie spent $60 and thus now has $(7x - 60)
The final ratio of Victor's money to Susie's money is therefore 2x : $(7x - 60). This is given 1:2. Now we just need to solve the proportion by cross-multiplying
2x : (7x - 60) = 1:2
1 × (7x - 60) = 2 × 2x
7x - 60 = 4x
3x = 60
x = 20
Therefore Victor originally had $4x = $80.
-x² + 8x - 6 = 0
x = <u>-(8) +/- √((8)² - 4(-1)(-6))</u>
2(-1)
x = <u>-8 +/- √(64 - 20)</u>
-2
x = <u>-8 +/- √(44)
</u> -2<u>
</u>x = <u>-8 +/- 2√(11)
</u> -2
x = <u>-8 + 2√(11)</u> x = <u>-8 - 2√(11)
</u> -2 -2<u>
</u>x = 4 - √(11) x = -8 + √(11)
Supplementary angles definition: They add up to 180°
There are several ways to prove a parallelogram:
1. Opposite sides theorem converse
2. Opposite angles theorem converse
3. Parallelogram diagonals theorem converse
4. Parallel congruent sides theorem
∠P + ∠Q = 180° --1
∠P + ∠S = 180° --2
1: ∠P = 180° - ∠Q
Sub 1 into 2:
180° - ∠Q + ∠S = 180°
180° + ∠S = 180° + ∠Q
∠S = ∠Q
Or you can try saying the opposite sides are parallel, since they are interior angles and those are straight lines
