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Verdich [7]
3 years ago
6

Please solve this question.​

Mathematics
1 answer:
Anon25 [30]3 years ago
8 0

\left(\dfrac{1}{1+2i}+\dfrac{3}{1-i}\right)\left(\dfrac{3-2i}{1+3i}\right)=\\\\\left(\dfrac{1-2i}{(1+2i)(1-2i)}+\dfrac{3(1+i)}{(1-i)(1+i)}\right)\left(\dfrac{(3-2i)(1-3i)}{(1+3i)(1-3i)}\right)=\\\\\left(\dfrac{1-2i}{1+4}+\dfrac{3+3i}{1+1}\right)\left(\dfrac{3-9i-2i-6}{1+9}\right)=\\\\\left(\dfrac{1-2i}{5}+\dfrac{3+3i}{2}\right)\left(\dfrac{-3-11i}{10}\right)=\\\\\left(\dfrac{2(1-2i)}{10}+\dfrac{5(3+3i)}{10}\right)\left(\dfrac{-3-11i}{10}\right)=

\dfrac{2-4i+15+15i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{17+11i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{-51-187i-33i+121}{100}=\\\\\dfrac{70-220i}{100}=\\\\\dfrac{70}{100}-\dfrac{220i}{100}=\\\\\boxed{\dfrac{7}{10}-\dfrac{11}{5}i}

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Help please!<br><br> | 2x^2 + 5x + 3 | &gt; 0<br> solve the inequality
vovikov84 [41]

Factorize the quadratic.

2x^2 + 5x + 3 = (2x + 3) (x + 1)

We have |ab| = |a||b|, so

|2x^2 + 5x + 3| = |2x + 3| |x + 1| > 0

Now, both |2x+3|\ge0 and |x+1|\ge0 (since the absolute value of any number cannot be negative), so we just need to worry about when the left side is exactly zero. This happens for

(2x + 3) (x + 1) = 0 \implies 2x+3 = 0\text{ or }x+1 = 0 \\\\ \implies x = -\dfrac32 \text{ or } x = -1

So the solution to the inequality is the set

\left\{x \in \Bbb R \mid x\neq-\dfrac32 \text{ and } x\neq-1\right\}

3 0
2 years ago
Is 2(√5+√7) a rational or irrational number?
kozerog [31]
It’s an irrational number

Hope this helps!
3 0
2 years ago
Find the slope of the line.
Georgia [21]

Answer:

\displaystyle m=1

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

<u>Algebra I</u>

  • Slope Formula: \displaystyle m=\frac{y_2-y_1}{x_2-x_1}

Step-by-step explanation:

<u>Step 1: Define</u>

Point (-4, -1)

Point (1, 4)

<u>Step 2: Find slope </u><em><u>m</u></em>

Simply plug in the 2 coordinates into the slope formula to find slope <em>m</em>

  1. Substitute [SF]:                    \displaystyle m=\frac{4+1}{1+4}
  2. Add:                                     \displaystyle m=\frac{5}{5}
  3. Divide:                                 \displaystyle m=1
4 0
3 years ago
Need the answer of the b <br>brainliest for the best answer​
Westkost [7]

answer

7.24

explanation

40% of 6000 = 2400

6000-2400=3600

labour's cost = 2400

material cost = 3600

15% of 2400 = 360

2400 + 360 = 2760

20% of 3600 = 720

3600 - 720 = 2880

2760 + 2880 = 5560

6000 : 5560 = 92.76

gap = 100.00 - 92.76

= 7.24

3 0
2 years ago
Find the solution of this system of equations. Separate the x- and y-values with a comma.
kotegsom [21]
The answer is Y=11, X=-1
Here's my work:

x=-12+y

-6(-12+y)+2y=28

6*12= 72

72 -6y +2y=28 (now we combine like-terms)

72-4y=28 (now divide by -4)

-18+y=-7 (add 18 to both sides)

y=11

next part we find x:

x=-12+(11)
x=-1
3 0
3 years ago
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