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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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What is the value of z in the equation 3 - 7 = 14? (2 points)<br> 03<br> 4<br> 07<br> 21
Hunter-Best [27]

Answer:

07

Step-by-step explanation:

3z - 7 = 14

3•7=21

21 - 7 = 14

3 0
3 years ago
5x+5y=-30 find the x and y intercept
Masja [62]

<em>The x and y intercept of 5x + 5y = -30 are (-6, 0) and (0, -6) respectively.</em>

<h2 /><h2>Explanation:</h2>

The Standard Form of the equation of a line is given by:

Ax+By=C \\ \\ A,B,C \ Real \ Constants \ and \ A>0

So:

5x+5y=-30

is written in Standard Form. The x and y intercepts are:

x-intercept: \ (x,0) \\ \\ y-intercept: \ (0,y)

So:

FOR X-INTERCEPT:

Let's \ set: \\ y=0 \\ \\ 5x+5(0)=-30 \\ \\ Isolating \ x: \\ \\ 5x=-30 \\ \\ x=-\frac{30}{5} \\ \\ \boxed{x=-6}

FOR Y-INTERCEPT:

Let's \ set: \\ x=0 \\ \\ 5(0)+5y=-30 \\ \\ Isolating \ x: \\ \\ 5y=-30 \\ \\ y=-\frac{30}{5} \\ \\ \boxed{y=-6}

Finally,<em> the x and y intercept of 5x + 5y = -30 are (-6, 0) and (0, -6) respectively.</em>

<h2>Learn more:</h2>

Parallel lines: brainly.com/question/12169569

#LearnWithBrainly

6 0
3 years ago
Lian has $1.00. She has only nickels and dimes. Lian has twice as many dimes as nickels. How many dimes does she have?
Anna11 [10]

Answer: 8

Step-by-step explanation:

Given

Lian has \$1.00 and she has twice as many dimes as nickels

Suppose she has x nickels

So, the number of dimes is 2x

Nickel is equivalent to 5 cents and dime is equivalent to 10 cent

\therefore \ x(0.05)+2x(0.1)=1\\\Rightarrow 0.05x+0.2x=1\\\Rightarrow 0.25x=1\\\Rightarrow x=4

Therefore she has 8 dimes with her.

5 0
2 years ago
at right is graph of this situation predict how the line would change to present the average cost of gas in dicember of 2005 whe
Lina20 [59]
The average cost represents the slope of the line of the graph.
Increasing the slope of the graph increases the steepness of the line.
Therefore, increasing the average cost of gas from $1.50 to $2.20 will increases the steepness of the line. (i.e. the line becomes closer to the vertical line).
8 0
3 years ago
\\\\\\\-------!!!!!40 POINTS!!!!-----\\\\\\\\\
aleksandrvk [35]
Let's actually find the line of best fit...

m=(nΣyx-ΣyΣx)/(nΣx^2-ΣxΣx)

m=(11*836-130*55)/(11*385-3025)

m=2046/1210  

m=93/55

b=(Σy-93Σx/55)/n

b=(55Σy-93Σx)/(55n)

b=(7150-5115)/(55*11)

b=185/55, so the line of best fit is:

y=(93x+185)/55

A)  The approximate y-intercept (the value of y when x=0) is 185/55≈3.36.

Which means that those who do not practice at all will win about 3.36 times

B) y(13)=(93x+185)/55

y(13)≈25.34

So after 13 months of practice one would expect to win about 25.34 times.
3 0
3 years ago
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