What does | 3+i | equal

Answers

Answer 1

Answer: The straight lines are asking to find the modulus or the size of the complex number.
For a complex number z = x + iy, [z] = √(x^2 +y^2)
Where x = Real Number, y = Imaginary number.
For 3 +i, x = 3, y = 1 (Note y is what number that is attached to i)

[3 + i] = √(3^2 +1^2) = √10 = 3.162

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∡1 and ∡2 are vertical angles. If m∡1 = 64°, find m∡2

Answers

Answer:

m∡2 = 64°

Step-by-step explanation:

By definition of vertical angles, the angles opposite of each other are equal each other.

∴ IF ∡1 and ∡2 are vertical angles, AND m∡1 = 64°, THEN m∡2 = 64°. (CPCTC - Definition of Vertical Angles).

Final answer:

Vertical angles are equal. Therefore, if ∡1 is 64°, then ∡2 is also 64°.

Explanation:

In mathematics, vertical angles are a pair of non-adjacent angles formed when two lines intersect. By definition, vertical angles are equal in measure.

Therefore, when angle 1 (∡1 ) and angle 2 ( ∡2 ) are vertical angles, if the measure of angle 1 ( m∡1 ) equals 64° as per the question, then the measure of angle 2 (m∡2) will also equal 64°.

So, m∡2 = 64°.

Learn more about Vertical Angles here:

https://brainly.ph/question/287711

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If 12 cows produce 70 gallons of milk, how many gallons of milk would 42 cows produce?A. 20
B. 245
C. 512
D. 840

Answers

This is a proportions question
12 42
------ = -------
70 ?

Cross multiply

70x42=2940
12x?=2940
294/12=245

42 cows can produce 245 gallons of milk.
So the answer is B.

Hope I helped!

Answer: 245 gallons

Step-by-step explanation: Set up a ratio, cows/gallons = 12/70 = 42/x, then cross multiply to get 12x = 70*42. Divide to get 245 gallons.

Answer question number 5

Answers

Answer:

36 is answer

Step-by-step explanation:

A cube has 6 sides.

216÷6=36

so therefore one side is 36 cubic inches

$\tt Step-by-step~explanation:$

$\tt Step~1:$

Let's solve for one side first. The equation to solve for one side with only the volume provided is V ^ 1/3.

$\tt 216^{(1)/(3)} \n216^{(1)/(3)} =6$

One side of the cube is 6, so that means all sides of the cube is equal to 6.

$\tt Step~2:$

To find the area of one side of the cube, we take one side and multiply it by itself, since the formula for solving for the area is length • width.

$\tt 6*6=36$

$\large\boxed{\tt Our~final~answer:Area~of~one~side=36~in.^2}$

To check our answer, we can multiply 36 by 6 and see if it equals to 216.

$\tt 36*6=216=correct$

a teacher and 10 students are to be seated along a bench in the bleachers at a basketball game. In how many ways can this be done if the teacher must be seated in the middle and a difficult student must sit to the teachers immediate left?

Answers

Wow !

OK. The line-up on the bench has two "zones" ...

-- One zone, consisting of exactly two people, the teacher and the difficult student.
   Their identities don't change, and their arrangement doesn't change.

-- The other zone, consisting of the other 9 students.
   They can line up in any possible way.

How many ways can you line up 9 students ?

The first one can be any one of 9.   For each of these . . .
The second one can be any one of the remaining 8. For each of these . . .
The third one can be any one of the remaining 7. For each of these . . .
The fourth one can be any one of the remaining 6. For each of these . . .
The fifth one can be any one of the remaining 5. For each of these . . .
The sixth one can be any one of the remaining 4. For each of these . . .
The seventh one can be any one of the remaining 3. For each of these . . .
The eighth one can be either of the remaining 2. For each of these . . .
The ninth one must be the only one remaining student.

   The total number of possible line-ups is

   (9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = 9! = 362,880 .

But wait ! We're not done yet !

For each possible line-up, the teacher and the difficult student can sit

-- On the left end,
-- Between the 1st and 2nd students in the lineup,
-- Between the 2nd and 3rd students in the lineup,
-- Between the 3rd and 4th students in the lineup,
-- Between the 4th and 5th students in the lineup,
-- Between the 5th and 6th students in the lineup,
-- Between the 6th and 7th students in the lineup,
-- Between the 7th and 8th students in the lineup,
-- Between the 8th and 9th students in the lineup,
-- On the right end.

That's 10 different places to put the teacher and the difficult student,
in EACH possible line-up of the other 9 .

So the total total number of ways to do this is

   (362,880) x (10) = 3,628,800 ways.

If they sit a different way at every game, the class can see a bunch of games
without duplicating their seating arrangement !

Answer:

Step-by-step explanation:

362,880

10. need help with this question-percentages and proof

Answers

Answer:

the value increased by0.0388

Step-by-step explanation

4% - 3% equals 0.0388 becuase its the diffrence between them is 0.0388

Taylor cuts 1/5 sheet of construction paper. What fraction is equivalent to 1/5 ?1/6 3/15 15/45 15/3

Answers

3/15 is equal to 1/5.

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