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3 years ago

Given the expression (8 + 6i) − (−2 + 7i), perform the indicated operation and write the answer in the form a + bi

Mathematics

1 answer:

Oliga [24]3 years ago

6 0

We can distribute the negative to get 8 + 6i + 2 - 7i, and we can simplify that to get 10 - i.
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Suppose you are going to form a committee of students and faculty. You have 10 total students and 11 total faculty to pick from.

zlopas [31]

Answer:

0.189

Step-by-step explanation:

We are using combination to solve for this.

C(n,r) = nCr = n!/r! (n - r)!

We have 10 total students and 11 total faculty = 21 people

Step 1

Selecting 3 students out of 10 total students

= 10× 9× 8×7×6×5×4×3×2×1/ 3×2×1 × 7×6×5×4×3×2×1/

= 120

Step 2

Select 6 faculty out of 11 faculty

11C6 = 11!/6!(11 - 6)!

= 11!/6! × 5!

= 11×10× 9× 8×7×6×5×4×3×2×1/6×5×4×3×2×1 × 5×4×3×2×1/

= 462

Step 3

Selecting 9 people out of 21 people to form a committee

21C9 = 21!/9!(21 - 9)!

= 21!/9! × 12!

= 293,930

Step 4

The fourth and final step of having a committee of 9 people =

(120 × 462)/293,930

= 55440/293,930

= 0.1886163372

Rounded to 3 decimal places = 0.189

Therefore, the probability that you select 3 students and 6 faculty = 0.189

3 0

3 years ago

21 more than a number

Kobotan [32]

Answer:

N+21

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Which long division problem can be used to prove the formula for factoring the difference of two perfect cubes?

Lostsunrise [7]

Answer:

The correct options, rearranged, are:

Options:

$A)(a^2+ab+b^2)/(a-b)\\\\B)(a^2-ab+b^2)/(a+b)\\\\C)(a^3+0a^2+0ab^2-b^3)/(a+b))\\\\ D)(a^3+0a^2+0ab^2-b^3)/(a-b)$

And the asnwer is the last option (D).

Explanation:

You need to find which long division can be used to prove the formula for factoring the difference of two perfect cubes.

The difference of two perfect cubes may be represented by:

$a^3-b^3$

And it is, as a very well known special case:

$a^3-b^3=(a-b)(a^2+ab+b^2)$

Then, to prove, it you must divide the left side, $a^3-b^3$ , by the first factor of the right side, $a-b$

Note that, to preserve the places of each term, you can write:

$(a^3-b^3)=(a^3+0a^2+0ab^2-b^3)$

Then, you have:

$(a^3+0a^2+0ab^2-b^3)=(a-b)(a^2+ab+b^2)$

By the division property of equality, you can divide both sides by the same factor, which in this case will be the binomial, and you get:

$(a^3+0a^2+0ab^2-b^3)/(a-b)=(a^2+ab+b^2)$

That is the last option (D).

3 0

3 years ago

Read 2 more answers

The function y=sin^3 x/cos^3 x is (an even, an odd, neither an even nor an odd function) function, and the function y=1/sec^3 x

Andrew [12]

Answer:

Step-by-step explanation:

sustiute 1 and -1 to x y=tan^3(x) you get postive and negative values , odd function

y=1/sec^3 x is even and same goes on

6 0

4 years ago

-5y = -5

Vsevolod [243]

-5y = -5 = 1

7x + 6y = 7

=-1.167

your answer is B) no

4 0

4 years ago