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inn [45]
3 years ago
12

Simplify the following expression:

Mathematics
1 answer:
sveta [45]3 years ago
5 0

9514 1404 393

Answer:

  D.  28 +10i

Step-by-step explanation:

As with any "collect terms" problem, you first identify the like terms, then add their coefficients. You can start with either the real or the imaginary terms to obtain a result that will point you to the correct answer choice. Of course, the distributive property works in the usual way.

  (3i+ 4) -i + 4(6 +2i) = 3i +4 -i +24 +8i . . . . eliminate parentheses

  = (4 +24) +(3 -1 +8)i . . . . . . . group like terms

  = 28 +10i

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diamong [38]

Answer:

The second option.

Step-by-step explanation:

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6 0
3 years ago
Write the following as a complex number in the form a + bi square root -245
Pepsi [2]

Answer:

Step-by-step explanation:

√(-245)=√(49×5×i^2)=7√5 i=0+7√5 i

5 0
3 years ago
Read 2 more answers
Select the correct answer.
romanna [79]

Employees salary [$}: 30,000, 30,000, 35,000, 35,000, 40,000, 40,000.

CEO Salary: $70,000.

The correct answer is this: BOTH JAN AND MARCY ARE CORRECT.

Jan says the employee average salary is $35,000. This is correct as shown below:

Average employee salary = 30,000 + 30,000 + 35,000 +35,000 + 40,000 + 40,000 / 6 = 210 / 6 =  $35,000.

Marcy says the average salary of all company members is $40,000. This is also true as shown below.

Average salary of all company members = 30,000 + 30,000 +35,000 + 35,000 + 40,000 + 40,000 + 70,000 / 7 = 280 / 7 = $40,000.

5 0
3 years ago
An aircraft on a reconnaissance mission takes off from its home base and flies 550 miles at a bearing of S 46° E to a location i
Alexandra [31]
<h3>Answer: D) 1692 miles</h3>

============================================

Explanation:

A diagram is very handy for this type of problem. Refer to the diagram below (attached image). Here are the steps used to form the diagram

  1. Plot point A and make that the home base. Plot point D directly south of point A. I'm skipping B and C because those will be used to form the triangle later.
  2. Imagine you are standing at point A and looking south at point D. Turn 46 degrees toward the east direction (this is what the notation "bearing of S 46° E" means). Then move 550 miles from A to land on point B. This is the location where the plane makes its first turn.
  3. Plot the points E and F, which are north and south of point B.
  4. Imagine we are at point B and looking directly south at point F. Turn 55 degrees toward the west, which is due to the "S 55° W" and then move 483 miles to arrive at point C. This is the plane's location where it turns around to go back to home base.

The diagram below shows all of this visually summarized. We have the segments

  • AB = 550 miles
  • BC = 483 miles
  • AC = x miles

And we have these angles

  • Angle DAB = 46 degrees and Angle ABE = 46 degrees (blue)
  • Angle ABC = 79 degrees (red)
  • Angle ACB = 55 degrees and Angle FBC = 55 degrees (green)

Angle ABC comes from the fact that the blue and green angles add with the red angle to get 180. So we basically need to solve 46+y+55 = 180 which leads to y = 79.

------------------------------

Once the diagram is set up, we'll use the law of cosines to find x.

Focus on triangle ABC. Ignore points D,E,F. Ignore any extra lines as well.

The interior angles of triangle ABC are

  • A = 46 degrees
  • B = 79 degrees
  • C = 55 degrees

The sides opposite the angles are

  • a = 483 (opposite angle A)
  • b = x (opposite angle B)
  • c = 550 (opposite angle C)

Now we can apply the law of cosines

b^2 = a^2 + c^2 - 2*a*c*cos(B)

x^2 = 483^2 + 550^2 - 2*483*550*cos(79)

x^2 = 434412.180756441

x = sqrt(434412.180756441)

x = 659.099522649229

x = 659

Side AC, or CA, is roughly 659 miles long.

------------

To find the total distance the plane travels, we add up the three sides of the triangle (ie we find the perimeter)

Distance Traveled = AB + BC + CA

Distance Traveled = 550 + 483 + 659

Distance Traveled = 1692 miles

3 0
2 years ago
A shopkeeper sold a watch for Rs 810 at 10% loss. How much did he pay to buy the watch ? <br>​
Svetlanka [38]

Answer:

Rupees 891

Step-by-step explanation:

If you multiply 810 times 0.1 which is the decimal of 10%, you get 81 which you can add to 810 to get 891 which is the price the shopkeeper payed to buy the watch.

Hope this helps!!! PLZ MARK BRAINLIEST!!!

7 0
2 years ago
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