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3 years ago

How can we get rid of i in the denominator?

Mathematics

1 answer:

Sloan [31]3 years ago

8 0

Answer:

When you have an imaginary number in the denominator multiply the numerator and the denominator by the conjugate of the denominator.

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Which is the value of this expression when a = 5 and k = negative 2? (3^2 a^-3)(3 a^-4)^-2

lozanna [386]

Answer:

$5^5=3125$

Step-by-step explanation:

$Given\ (3^2a^{-3})(3a^{-4})^{-2}\\\\=3^2a^{-3}\cdot(3)^{-2}(a^{-4})^{-2}\\\\=3^2\times3^{-2}\times a^{-3}\times a^8\ \ \ \ \ \ (x^{-m})^{-n}=x^{mn}\\\\=3^{2-2}\times a^{-3+8}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^m\times x^n=x^{m+n}\\\\=3^0\times a^5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^0=1\\\\=1\times a^5\\\\=a^5\\\\put\ value\ a=5\\\\=5^5\\\\=3125$

6 0

3 years ago

What is the likelihood that a fair coin will land heads or tails?

Marina CMI [18]

Answer:

I believe it is 0.5

Step-by-step explanation:

If you flip a normal coin (called a “fair” coin in probability parlance), you normally have no way to predict whether it will come up heads or tails. Both outcomes are equally likely. There is one bit of uncertainty; the probability of a head, written p(h), is 0.5 and the probability of a tail (p(t)) is 0.5. The sum of the probabilities of all the possible outcomes adds up to 1.0, the number of bits of uncertainty we had about the outcome before the flip. Since exactly one of the four outcomes has to happen, the sum of the probabilities for the four possibilities has to be 1.0. To relate this to information theory, this is like saying there is one bit of uncertainty about which of the four outcomes will happen before each pair of coin flips. And since each combination is equally likely, the probability of each outcome is 1/4 = 0.25. Assuming the coin is fair (has the same probability of heads and tails), the chance of guessing correctly is 50%, so you'd expect half the guesses to be correct and half to be wrong. So, if we ask the subject to guess heads or tails for each of 100 coin flips, we'd expect about 50 of the guesses to be correct. Suppose a new subject walks into the lab and manages to guess heads or tails correctly for 60 out of 100 tosses. Evidence of precognition, or perhaps the subject's possessing a telekinetic power which causes the coin to land with the guessed face up? Well,…no. In all likelihood, we've observed nothing more than good luck. The probability of 60 correct guesses out of 100 is about 2.8%, which means that if we do a large number of experiments flipping 100 coins, about every 35 experiments we can expect a score of 60 or better, purely due to chance.

6 0

3 years ago

Read 2 more answers

I NEED HELP PLS THIS IS DUE IN 3 HOURS

Mariulka [41]

Answer:

Part 1) $x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})$

Part 2) $x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})$

Step-by-step explanation:

we know that

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

Part 1)

in this problem we have

$x^{2} -2x-2=0$

$a=1\\b=-2\\c=-2$

substitute in the formula

$x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-2)}} {2(1)}\\\\x=\frac{2(+/-)\sqrt{12}} {2}\\\\x=\frac{2(+/-)2\sqrt{3}} {2}\\\\x_1=\frac{2(+)2\sqrt{3}} {2}=1+\sqrt{3}\\\\x_2=\frac{2(-)2\sqrt{3}} {2}=1-\sqrt{3}$

therefore

$x^{2} -2x-2=(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))$

$x^{2} -2x-2=(x-1-\sqrt{3})(x-1+\sqrt{3})$

Part 2)

in this problem we have

$x^{2} -6x+4=0$

$a=1\\b=-6\\c=4$

substitute in the formula

$x=\frac{-(-6)(+/-)\sqrt{-6^{2}-4(1)(4)}} {2(1)}$

$x=\frac{6(+/-)\sqrt{20}} {2}$

$x=\frac{6(+/-)2\sqrt{5}} {2}$

$x_1=\frac{6(+)2\sqrt{5}}{2}=3+\sqrt{5}$

$x_2=\frac{6(-)2\sqrt{5}}{2}=3-\sqrt{5}$

therefore

$x^{2} -6x+4=(x-(3+\sqrt{5}))(x-(3-\sqrt{5}))$

$x^{2} -6x+4=(x-3-\sqrt{5})(x-3+\sqrt{5})$

5 0

3 years ago

The length of a rectangle is three less than twice the width. If the perimeter is 156cm, find it’s dimensions.

Monica [59]

Answer:

length = 47, width = 25

Step-by-step explanation:

L = 2W - 3

2L + 2W = 156

2( 2w -3) + 2W = 156

4w - 6 + 2W = 156

6W = 150

W = 25

L = 2(25) - 3

L = 47

8 0

3 years ago

3^6 over 3^? = 3^4<br><br> What is the missing value?

netineya [11]

For the question mark, we can insert a variable considering it is an unknown number.

$\frac{3^6}{3^x} = 3^4 \\ \\ 3^{6-x} = 3^4 \ / \ use \ qotient \ rule \\ \\ 6 - x = 4 \ / \ cancel \ out \ 3 \\ \\ -x = 4 - 6 \ / \ subtract \ 6 \ from \ each \ side \\ \\ -x = -2 \ / \ simplify \\ \\ x = 2 \ / \ multiply \ each \ side \ by \ -1 \\ \\ Answer: \fbox {x = 2}$

5 0

3 years ago