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puteri [66]
3 years ago
10

If A = -3 + 5i, B = 4 - 2i, and C = 1 +6i, where i is the imaginary unit, then A - BC equals

Mathematics
1 answer:
Maslowich3 years ago
6 0

Answer:

3) -19 - 17i is our answer

Step-by-step explanation:

to solve A - BC we plug in the values given

A= -3 + 5i

B = 4 - 2i

C = 1 + 6i

-3 + 51i - (4 - 2i)(1 + 6i) is our expression. we can FOIL (4 - 2i)(1 + 6i) this expression out. FOIL stands for:

First

Outside

Inside

Last

i will highlight the terms i am using in the current step in bold and put the result next of those two terms next to the expression

F: (4 - 2i)(1 + 6i) = 4

O: (4 - 2i)(1 + 6i) = 24i

I: (4 - 2i)(1 + 6i) = -2i

L: (4 - 2i)(1 + 6i) = 12 < --- the reason why its 12 and not -12i or 12i is because <em>i</em> = √-1 and i² = -1

when we multiply -2i * 6i, we would have gotten a -12i², and i² = -1, so we are multiplying -12 by -1, which gives us 12 as the result

combining all these terms together and we have:

4 + 24i - 2i + 12

in the expression this is:

-3 + 5i - (4 + 24i - 2i + 12) < we need to distribute the negative sign into (4 + 24i - 2i + 12) and we now get:

-3 + 5i -4 - 24i + 2i - 12 < combine like terms (ex: i terms together)

-3 - 4 - 12 = -19

5i - 24i + 2i = -17i

the result of the expression is:

-19 - 17i

we cannot simplify this any further so this is our answer. the answer choice that matches this is 3, so 3) -19 - 17i is our answer

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777dan777 [17]
<span>Uphill distance = 1 4/5 = 9/5 = 18/10 km Downhill Distance = 2 7/10 = 27/10 km Total Uphill and Downhill = 18/10 + 27/10 = 45/10 = 4.5 km Hence total level ground = Total race km - (Uphill + Downhill) =10 - 4.5 = 5.5 km Hence the answer is 5.5 km.</span>
7 0
3 years ago
If y varies jointly with x and z and y=40 when x=10 and z=9 find z when x =55 and y=105
Eduardwww [97]

Answer:

  z = 189/44

Step-by-step explanation:

The "varies jointly" relationship can be expressed by ...

  y = kxz

We can find k from the given values.

  40 = k(10)(9)

  40/90 = k = 4/9 . . . divide by the coefficient of k

Now we want to find z for given values of x and y. That can be found from ...

  y = (4/9)xz

  9y/(4x) = z . . . . . multiply by 9/(4x)

Filling in the new numbers, we have ...

  z = 9·105/(4·55)

  z = 4 13/44 = 189/44 ≈ 4.2954...(repeating 54)

4 0
3 years ago
Sketch and shade the region in the xy-plane defined by the equation or inequalities.
Shtirlitz [24]

Answer:

attached below is the solution

Step-by-step explanation:

|x| < 7

= -7 < x < 7

| y | < 3

= -3< y < 3

attached below is the shaded region in the xy-plane

7 0
3 years ago
310-(30x7)=5xk solve for k
NeX [460]

Answer K= 20/x

Step-by-step explanation:

8 0
3 years ago
52 &lt; x + 24? how do i work this?
Lostsunrise [7]

Answer: 28

Step-by-step explanation:

52

Begin by isolating x. To do this, you can substract 24 on both sides.

-24+52

28

That's your answer. Any value of ''x'' must be greater than 28 for this inequality to be true.

6 0
3 years ago
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