Answer:
i) 28 - 30i
ii) 36 + 28i
Step-by-step explanation:
i) x = 6 + i ⇒2x = 2(6 + i) = 12 + 2i
z = 4 - 8i ⇒ 4z = 4(4 - 8i) = 16 - 32i
2x + 4z = (12 + 2i) + (16 - 32i) = 28 - 30i
ii) w = -1 + 5i and z = 4 - 8i
w × z = (-1 + 5i)(4 - 8i) = -4 + 8i + 20i - 40
⇒collect like terms
w × z = -4 + 28i - 40
∵ 
∴w × z = -4 + 28i - 40(-1) = -4 + 28i + 40 = 36 + 28i
Answer:
x = 88.2
Step-by-step explanation:
The angle at the top of the triangle = 90° - 10° = 80°
and the left side of the triangle is x ( opposite sides of a rectangle )
Using the tangent ratio in the right triangle
tan80° = 
= 
Multiply both sides by x
x × tan80° = 500 ( divide both sides by tan80° )
x = 
≈ 88.2
Answer: She has $15
Step-by-step explanation:
20*0.75=15
Answer:
80%; 30%
Step-by-step explanation:
There is 5 blue marbles, 2 black marbles, and 3 red marbles. In other words, there is a total of 10 marbles.
There are only 2 black marbles and 8 marbles that are not black. Therefore, the probability of <em>not</em> drawing a black marble is 8/10 or 4/5 or 80%.
There are only 3 red marbles out of the 10 total marbles. Therefore, the probability of drawing a red marble is 3/10 or 30%.
