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3 years ago

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! | 2x^2 + 5x + 3 | > 0 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:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

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

Step-by-step explanation:

Step 1: Define

Point (-4, -1)

Point (1, 4)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute [SF]: $\displaystyle m=\frac{4+1}{1+4}$
Add: $\displaystyle m=\frac{5}{5}$
Divide: $\displaystyle m=1$

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3 years ago

Need the answer of the b 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

Please solve this question.​

Please solve this question.