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ludmilkaskok [199]
3 years ago
11

Solve the equation 4x^2-4x-1=0

Mathematics
1 answer:
Dmitrij [34]3 years ago
7 0

Answer:

  x = (1 ±√2)/2

Step-by-step explanation:

We can "complete the square" to solve this.

  4x^2 -4x = 1 . . . . add 1

  x^2 -x = 1/4 . . . . .divide by 4 to make x^2 coefficient = 1

  x^2 -x +1/4 = 2/4 . . . . add the square of half the x-coefficient: (-1/2)^2 = 1/4

  (x -1/2)^2 = 2/4  . . . . write as a square

  x -1/2 = ±(√2)/2 . . . . . take the square root

  x = (1 ±√2)/2 ≈ {-0.2071, 1.2071}

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Increasing the sample size while keeping the same confidence level has what effect on the margin of error? A. Increases the marg
DiKsa [7]

Answer:

C. Decreases the margin of error and hence increases the precision

Step-by-step explanation:

If we select a sample by Simple Random Sampling in a population of “infinite” size (a population so large that we do not know its size exactly), then the margin of error is given by

\bf E=\frac{ZS}{\sqrt{n}}

where  

<em>Z = The Z-score corresponding to the confidence level </em>

<em>S = The estimated standard deviation of the population </em>

<em>n = the size of the sample. </em>

As we can see, since n is in the denominator of the fraction and the numerator is kept constant, the larger the sample size the smaller the margin of error, so the correct choice is:

C. Decreases the margin of error and hence increases the precision

4 0
2 years ago
|a+x|/2 − |a−x|/2 , if a=−2; x=−6<br><br> PLZ HELP!!!
Alchen [17]

Answer:

2

Step-by-step explanation:

|a+x|/2 − |a−x|/2 , if a=−2; x=−6

Evaluate this expression

Simply plug in the numbers

| -2 + -6 | /2   -   |-2 - -6|/2

|-8| /2  -   |4|/2

4 - 2

2

8 0
3 years ago
Read 2 more answers
#10 using right angle below find the tangent of angle A.
just olya [345]

Answer: the first option is the correct answer.

Step-by-step explanation:

Triangle ABC is a right angle triangle.

From the given right angle triangle,

AB represents the hypotenuse of the right angle triangle.

With m∠A as the reference angle,

AC represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine the tangent of angle A, we would apply the Tangent trigonometric ratio. It is expressed as

Tan θ, = opposite side/adjacent side. Therefore,

Tan A = 5/5√3 = 1/√3

Rationalizing the surd, it becomes

1/√3 × √3/√3

Tan A = √3/3

6 0
3 years ago
Need Help ASAP!!!
Drupady [299]

Answer:

B) {(-2, -3), (-3, -2), (2, 3), (3, 2)}

Step-by-step explanation:

A function cannot have replicated x-coordinates. All the other answer choices do, so you would pick this one.

I am joyous to assist you anytime.

8 0
3 years ago
Find a and b so that f(x) = x^3 + ax^2 + b will have a critical point at (2,3).
Digiron [165]

Using the critical point concept, it is found that a = -3 and b = 7.

<h3>What are the critical points of a function?</h3>
  • The critical points of a function are the values of x for which:

f^{\prime}(x) = 0

In this problem, the function is:

f(x) = x^3 + ax^2 + b

Hence, the derivative is:

f^{\prime}(x) = 3x^2 + 2ax

Then:

f^{\prime}(x) = 0

3x^2 + 2ax = 0

x(3x + 2a) = 0

x = 0

3x + 2a = 0

3x = -2a

x = -\frac{2a}{3}

Since the critical point is at x = 2, we have that:

-\frac{2a}{3} = 2

-2a = 6

2a = -6

a = -3

Then:

f(x) = x^3 - 3x^2 + b

Critical point at (2,3) means that when x = 2, y = 3, then:

3 = 2^3 - 3(2)^2 + b

8 - 12 + b = 3

b = 7

You can learn more about the critical point concept at brainly.com/question/2256078

4 0
1 year ago
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