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8090 [49]
3 years ago
8

What is the standard form of (1+2√-3)/(1+√-3)

Mathematics
2 answers:
miv72 [106K]3 years ago
7 0
1.75+0.43301270i
hope this helped and let me know if i was right plz

ExtremeBDS [4]3 years ago
3 0

Answer:

\frac{7}{4} +\frac{3}{4} i

Step-by-step explanation:

(1+2\sqrt{-3} )/(1+\sqrt{-3})

To remove the negative sign from square root use 'i'

square root (-1) is 'i'

\frac{1+2\sqrt{3}i}{1+\sqrt{3}i}

Multiply top and bottom by conjugate of (1+\sqrt{3}i)

Conjugate of (1+\sqrt{3}i) is (1-\sqrt{3}i)

Multiply it at the top and bottom

\frac{1+2\sqrt{3}i}{1+\sqrt{3}i} \cdot \frac{1-\sqrt{3}i}{1-\sqrt{3}i}

Multiply numerator and denominator using FOIL method

\frac{1-\sqrt{3}i+2\sqrt{3}i-3i^2}{1+3}

the value of i^2 is -1

\frac{1+\sqrt{3}i-6(-1)}{4}

\frac{1+\sqrt{3}i+6}{4}

\frac{7+\sqrt{3}i}{4}

\frac{7}{4} +\frac{3}{4} i

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What is the solution to the inequality below. x(absolute value) <5
jok3333 [9.3K]

Answer:

-5 < x < 5

Step-by-step explanation:

|x| < 5

This can be split into two cases: x < 5 and -x < 5 because |x| could be either x or -x depending on whether x is positive, negative, or 0. Solving the second one we get x > -5 so the answer is -5 < x < 5.

8 0
3 years ago
Jenna ordered 28 shirts for her soccer team 75% of those shirts size large how many large shirts did you know order
Ymorist [56]
28 x 75% = 21
Jenna ordered 21 large shirts.
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A waether forecast predicts a 30% chance of rain for each of the next 3 days. Describe a way to stimulate the chance that it wil
DerKrebs [107]
Using a binomial distribution considering there's a 30% chance it will rain on any of the three days: 

<span>The probability of it raining on 0 days is (1)(0.7)(0.7)(0.7) = 34.3%. </span>
<span>The probability of it raining on 1 day is (3)(0.3)(0.7)(0.7) = 44.1%. </span>
<span>The probability of it raining on 2 days is (3)(0.3)(0.3)(0.7) = 18.9%. </span>
<span>The probability of it raining on 3 days is (1)(0.3)(0.3)(0.3) = 2.7%. </span>

<span>There's a 65.7% chance that it will rain at least once over the three-day period.</span>
5 0
3 years ago
In Exercises 45–48, let f(x) = (x - 2)2 + 1. Match the<br> function with its graph
MA_775_DIABLO [31]

Answer:

45) The function corresponds to graph A

46) The function corresponds to graph C

47) The function corresponds to graph B

48) The function corresponds to graph D

Step-by-step explanation:

We know that the function f(x) is:

f(x)=(x-2)^{2}+1

45)

The function g(x) is given by:

g(x)=f(x-1)

using f(x) we can find f(x-1)

g(x)=((x-1)-2)^{2}+1=(x-3)^{2}+1

If we take the derivative and equal to zero we will find the minimum value of the parabolla (x,y) and then find the correct graph.

g(x)'=2(x-3)

2(x-3)=0

x=3

Puting it on g(x) we will get y value.

y=g(3)=(3-3)^{2}+1

y=g(3)=1

<u>Then, the minimum point of this function is (3,1) and it corresponds to (A)</u>

46)

Let's use the same method here.

g(x)=f(x+2)

g(x)=((x+2)-2)^{2}+1

g(x)=(x)^{2}+1

Let's find the first derivative and equal to zero to find x and y minimum value.

g'(x)=2x

0=2x

x=0

Evaluatinf g(x) at this value of x we have:

g(0)=(x)^{2}+1

g(0)=1

<u>Then, the minimum point of this function is (0,1) and it corresponds to (C)</u>

47)

Let's use the same method here.

g(x)=f(x)+2

g(x)=(x-2)^{2}+1+2

g(x)=(x-2)^{2}+3

Let's find the first derivative and equal to zero to find x and y minimum value.

g'(x)=2(x-2)

0=2(x-2)

x=2

Evaluatinf g(x) at this value of x we have:

g(2)=(2-2)^{2}+3

g(2)=3

<u>Then, the minimum point of this function is (2,3) and it corresponds to (B)</u>

48)

Let's use the same method here.

g(x)=f(x)-3

g(x)=(x-2)^{2}+1-3

g(x)=(x-2)^{2}-2

Let's find the first derivative and equal to zero to find x and y minimum value.

g'(x)=2(x-2)

0=2(x-2)

x=2

Evaluatinf g(x) at this value of x we have:

g(2)=(2-2)^{2}-2

g(2)=-2

<u>Then, the minimum point of this function is (2,-2) and it corresponds to (D)</u>

<u />

I hope it helps you!

<u />

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earnstyle [38]

All of them are 3.14

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