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2 years ago

What is (12-2i) (5+3i) multiplied?

Mathematics

1 answer:

Ilya [14]2 years ago

5 0

= 12*5 + 12*3i - 5*2i - 6i^2 (remember that i^2 = -1) so:-

= 60 +26i - 6*(-1)

= 60 + 26i + 6

= 66 + 26i

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Each bucket holds 325 gallons of water. If it takes 6 buckets to fill a tank, how much water does the tank hold?

Gemiola [76]

Answer:

1950

Step-by-step explanation:

if we do 325 gallons of water times 6 buckets of water we get 1,950 gallons of water in a fraction 325/1950

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2 years ago

Carmen Reads 2 books eachmonthaspartofher Book Club. If Carmen has read 4books so far,how many months has he been with her bookc

Xelga [282]

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2 years ago

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For a regular 30-sided polygon, what is the degree of rotation? enter your answer in the box. °

Crank

For a 30 sided regular polygon, We can divide the polygon (30 sides) into 30 inscribed triangles with central vertex angles of = $\frac{360}{30} =12^{o}$ .

This central vertex angle of <u>12 degrees</u> is the degree of rotation for a 30 sided polygon.

In other words, the 30 sided polygon has <u>12 degree</u> rotational symmetry about the center.

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3 years ago

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Find the value of b in the rhombus below

jeka94

The value of b = 26.

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3 years ago

Let a1, a2, a3, ... be a sequence of positive integers in arithmetic progression with common difference

Bezzdna [24]

Since $a_1,a_2,a_3,\cdots$ are in arithmetic progression,

$a_2 = a_1 + 2$

$a_3 = a_2 + 2 = a_1 + 2\cdot2$

$a_4 = a_3+2 = a_1+3\cdot2$

$\cdots \implies a_n = a_1 + 2(n-1)$

and since $b_1,b_2,b_3,\cdots$ are in geometric progression,

$b_2 = 2b_1$

$b_3=2b_2 = 2^2 b_1$

$b_4=2b_3=2^3b_1$

$\cdots\implies b_n=2^{n-1}b_1$

Recall that

$\displaystyle \sum_{k=1}^n 1 = \underbrace{1+1+1+\cdots+1}_{n\,\rm times} = n$

$\displaystyle \sum_{k=1}^n k = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2$

It follows that

$a_1 + a_2 + \cdots + a_n = \displaystyle \sum_{k=1}^n (a_1 + 2(k-1)) \\\\ ~~~~~~~~ = a_1 \sum_{k=1}^n 1 + 2 \sum_{k=1}^n (k-1) \\\\ ~~~~~~~~ = a_1 n + n(n-1)$