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OlgaM077 [116]
3 years ago
8

4

Mathematics
1 answer:
taurus [48]3 years ago
6 0

Answer:

x^2 - 2x + 10, option B

Step-by-step explanation:

Complex numbers:

The most important relation that involves complex numbers is given by:

i^2 = -1

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

ax^{2} + bx + c, a\neq0.

This polynomial has roots x_{1}, x_{2} such that ax^{2} + bx + c = a(x - x_{1})*(x - x_{2}), given by the following formulas:

x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}

x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}

\bigtriangleup = b^{2} - 4ac

In this question:

The solutions are:

x_1 = 1 - 3i, x_2 = 1 + 3i

We have to find the polynomial. All option have a = 1. So

(x - (1 - 3i))(x - (1 + 3i)) = x^2 - x(1 + 3i) - x(1 - 3i) + (1 - 3i)(1 + 3i) = x^2 - x -3ix - x + 3ix + 1^2 - (3i^2) = x^2 - 2x + 1 - 9i^2 = x^2 - 2x + 1 - 9(-1) = x^2 - 2x + 10

The correct answer is given by option b.

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$10,000 at an annual rate of 7%, compounded semi-annually, for 2 years
forsale [732]

Answer:

\$13,107.96

Step-by-step explanation:

Since interest is compounded semi-annually (half a year or 6 months), in a spawn of 2 years, the interest will have been compounded 4 times. As given in the problem, each time the interest is compounded, the new balance will be 107% or 1.07 times the amount of the old balance.

Therefore, we can set up the following equation to find the new balance after 2 years:

\text{New balanace}=10,000\text{ (old balance)}\cdot 1.07\cdot 1.07\cdot 1.07\cdot 1.07,\\\text{New balanace}=10,000\cdot 1.07^4=\boxed{\$13,107.96}

8 0
2 years ago
Candace wants to find the height of a local lighthouse. Since she knows something about similar triangles, she decides to stand
Ludmilka [50]
In short, let x be the height of the Light House
2.5/36 = 1.5/X

===> X= (36 x 1.5)/2.5 = 21.6 meters
5 0
3 years ago
25% of 180 is ? Show your work
Elenna [48]
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7 0
3 years ago
Isosceles trapezoid FGHJ has base angles that measure (8x+14) and (14x-15). Find x and the measure of each base angle.
lisov135 [29]

Answer:

See below

Step-by-step explanation:

Remark

Base angles of Isosceles triangles are equal.

Equation

That means that 8x + 14 = 14x - 15

Solution

8x + 14 = 14x - 15              Add 15 to both sides

8x + 14+15 = 14x               Combine

8x + 29 = 14x                   Subtract 8x from both sides

8x - 8x + 29 = 14x - 8x    Combine

29 = 6x                            Divide by 6

x = 29/6

x = 4 5/6

Answer

x = 4 5/6 or 4.833

8x + 14 = 8 * (4 5/6)   +  14

8x + 14 = 38 2/3 + 14

8x + 14 = 52 2/3 or 52.6666

14x - 15 = 14 *(4 5/6) - 15

14x - 15 = 67 2/3   -15

14x - 15 = 52 2/3 or 52.666

7 0
3 years ago
Find the area of each figure.<br>7<br>19-​
Iteru [2.4K]

Answer:

66.5

Step-by-step explanation:

A=b•h/2

A=19•7/2 19•7=133

A=133/2 133/2= 66.5

A=66.5

5 0
3 years ago
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