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Leni [432]
3 years ago
11

Solve by completing the square. x^2 + 4x – 1= 0

Mathematics
1 answer:
NNADVOKAT [17]3 years ago
8 0

Answer:

x = -2 ± sqrt(5)

Step-by-step explanation:

x^2 + 4x – 1= 0

Add 1 to each side

x^2 + 4x – 1+1= 0+1

x^2 +4x = 1

Take the coefficient of x

4

Divide by 2

4/2 =2

Square it

2^2=4

Add it to each side

x^2 +4x+4=1+4

(x+2)^2 = 5

Take the square root of each side

sqrt((x+2)^2 )=± sqrt(5)

x+2 = ± sqrt(5)

Subtract 2 from each side

x+2-2 = -2 ± sqrt(5)

x = -2 ± sqrt(5)

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Find the inverse of each function.
Temka [501]

Answer:

dunno

Step-by-step explanation:

4 0
2 years ago
Please help with imaginary numbers worksheet!
mihalych1998 [28]

Problem 5

<h3>Answer:   6i</h3>

------------------

Explanation:

We have these four identities

  • i^0 = 1
  • i^1 = i
  • i^2 = -1
  • i^3 = -i

Notice how computing i^4 leads us back to 1. So i^4 = i^0. The pattern repeats every 4 terms. So we divide the exponent by 4 and look at the remainder. We ignore the quotient entirely. We can see that 28/4 = 7 remainder 0. Meaning that i^28 = i^0 = 1.

We can think of it like this if you wanted

i^28 = (i^4)^7 = 1^7 = 1

Then the sqrt(-36) becomes 6i

So overall, we end up with the final answer of 6i

=============================================

Problem 6

<h3>Answer:  -3i</h3>

------------------

Explanation:

We'll use the ideas mentioned in problem 5

46/4 = 11 remainder 2

i^46 = i^2 = -1

sqrt(-9) = 3i

The two outside negative signs cancel out, but there's still a negative from -1 we found earlier. So we end up with -3i

In other words, here is one way you could write out the steps

-i^{46}*-\sqrt{-9}\\\\-i^{2}*-3i\\\\i^{2}*3i\\\\-1*3i\\\\-3i\\\\

=============================================

Problem 7

<h3>Answer:   -1</h3>

------------------

Work Shown:

i^10 = i^2 because 10/4 = 2 remainder 2

i^19 = i^3 because 19/4 = 4 remainder 3

i^7 = i^3 because 7/4 = 1 remainder 3

Again, all we care about are the remainders.

i^{10}+i^{19} - i^{7}\\\\i^{2}+i^{3} - i^{3}\\\\i^{2}\\\\-1

=============================================

Problem 8

<h3>Answer:    -1 + i</h3>

------------------

Work Shown:

i^22*i^6 = i^(22+6) = i^28

Earlier in problem 5, we found that i^28 = i^0 = 1

So,

i^1 - \left(i^{22}*i^{6}\right)\\\\i^1 - i^{28}\\\\i^1 - i^{0}\\\\i - 1\\\\-1+i

8 0
2 years ago
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Write 7/11 as a decimal ( round to three decimal places as needed
Degger [83]
0.636
Add a 0 then a decimal .you will see the number 70 goes with 6 *11=66
then the remainder will be 4 , add a 0 and you will see the number goes with 3*11= 33 then the remainder will be 7 again add a 0  and multiply 6. You will get your answer.
3 0
3 years ago
Solve the equation. 25-3x=40 what does x equal?
9966 [12]

Answer:

x=-5

Step-by-step explanation:

25 - 3x = 40

-3x + 25 =40

-3x +25--25=40-25

-3x=15

-3x÷-3=25÷-3

x=-5

6 0
2 years ago
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2
Rainbow [258]

Answer:

tha anser us B

Step-by-step explanation:

it is very easy you just read the question carefully

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