Answers
Step-by-step explanation:
remember, i = sqrt(-1)
you know what an exponent means, right ?
it means you multiply the enclosed term that many times with itself.
when you envision this as a long chain of (1+i)/(1-i) multiplications, you can see you can group them into pairs, and then multiply these pairs - just half the times than for the single terms.
so,
((1+i)/(1-i))²⁰²⁰ = ((1+i)/(1-i))² ^ 1010
to get an idea what the result of the long chain of multiplications might be, let's start with the square and see, if we can find a pattern, that we then can use to come to a conclusion about the total result.
((1+i)/(1-i))² = (1+i)²/(1-i)²
(1+i)² = 1×1 + 1×i + 1×i + i² = 1 + 2i - 1 = 2i
(1-i)² = 1×1 - 1×i - 1×i + i² = 1 - 2i - 1 = -2i
so,
((1+i)/(1-i))² = 2i/-2i = -1
aha !
so,
((1+i)/(1-i))² ^ 1010 = (-1)¹⁰¹⁰
just to be sure you understand, we use the same trick again
(-1)¹⁰¹⁰ = (-1)² ^ 505 = 1⁵⁰⁵ = 1
as 1 to any power is always 1.
so, the right answer is A.
remember, a negative number to an even power results always in a positive number. and to an uneven/odd power in a negative number.
again, because such an exponent is only the summary of many multiplications.
Related Questions
Please what's -9/13 + -6/13
Answers
Step-by-step explanation:
-9/13 + -6/13
(-9 - 6)/ 13
= -15/13
hope it helps ya
Mark solved the equation 23x=9 by using the Division Property of Equality to get x=6. Did Mark solve the equation correctly? Explain why or why not.
Answers
Answer:
wrong
Step-by-step explanation:
The division property states that when we have an equation in the form [tex]ax=b[/tex], then [tex]x=b/a[/tex](i.e. we "divide" by [tex]a[/tex] on both sides).
So, Mark was supposed to get [tex]x=9/23[/tex], which is not equal to [tex]6[/tex].
So, Mark solved it [tex]\boxed{wrong}[/tex]
No, Mark solve the equation correctly.
because, Mark was supposed to get x = 27/2 , which is not equal to x= 6.
The division property of equality applicable.
The division property of equality is a property that tells us if we divide one side of an equation by a number, we must also divide the other side by the same number so that our equation stays the same. The formula for this property is if a = b, then a / c = b / c.
We have the following information available from the question is:
The equation is:
[tex]\frac{2}{3}x=9[/tex]
It solved by using the Division Property of Equality and get x = 6
If we solved for x: then,
x = 27/2
No, Mark solve the equation correctly.
So, Mark was supposed to get x = 27/2 , which is not equal to x= 6.
Learn more about Division property at:
https://brainly.com/question/11007967
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To mix a particular shade of purple paint, red paint and blue paint are mixed in the ratio 5:3. To make 20 gallons of this shade of purple paint, how many gallons of red and blue paint should be used?
Type the correct answers into the boxes below.
red paint:
gallons
blue paint
gallons
Answers
8. 8(x) = 2x² + 10x; 8(-4)
Answers
Answer:
x = {5.701562119, -0.701562119}
help math!!
------------------
Answers
Answer:
your answer is 5.............
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The Correct choice is :
E. 13Solution is in attachment ~
PLEASE HELP!!!
for questions 8-10 write an equation of the line graphed.
Answers
Answer:
8.) y=4/3x+2
9.)y=-0.5x+5
10.)x=1
Which graph represents the function h(x) = |x| + 0.5?
Answers
Answer:
Step-by-step explanation:
Answer: its graph C!, I got it right
A rectangle's length is four-fifths its width. The
perimeter is ten less than 5 times its width.
What is the area of the rectangle?
Answers
Sam bought a toy for $400 and sold it at a profit of 10% of the cost price. Calculate the SELLING PRICE of the toy.
Answers
Answer:
10% = 0.1 x 400 = 40
400 - 40 = 360$
Write an equation in which the quadratic expression 4x^2-4x-48 equals 0.
Answers
Answer:
4x2 + -4x + -48 = 0
4x2 + -4x + -48 = 0Reorder the terms:
4x2 + -4x + -48 = 0Reorder the terms:-48 + -4x + 4x2 = 0
4x2 + -4x + -48 = 0Reorder the terms:-48 + -4x + 4x2 = 0Solving
4x2 + -4x + -48 = 0Reorder the terms:-48 + -4x + 4x2 = 0Solving-48 + -4x + 4x2 = 0
4x2 + -4x + -48 = 0Reorder the terms:-48 + -4x + 4x2 = 0Solving-48 + -4x + 4x2 = 0Solving for variable 'x'.
4x2 + -4x + -48 = 0Reorder the terms:-48 + -4x + 4x2 = 0Solving-48 + -4x + 4x2 = 0Solving for variable 'x'.Factor out the Greatest Common Factor (GCF), '4'.
4x2 + -4x + -48 = 0Reorder the terms:-48 + -4x + 4x2 = 0Solving-48 + -4x + 4x2 = 0Solving for variable 'x'.Factor out the Greatest Common Factor (GCF), '4'.4(-12 + -1x + x2) = 0
4x2 + -4x + -48 = 0Reorder the terms:-48 + -4x + 4x2 = 0Solving-48 + -4x + 4x2 = 0Solving for variable 'x'.Factor out the Greatest Common Factor (GCF), '4'.4(-12 + -1x + x2) = 0Factor a trinomial.
4x2 + -4x + -48 = 0Reorder the terms:-48 + -4x + 4x2 = 0Solving-48 + -4x + 4x2 = 0Solving for variable 'x'.Factor out the Greatest Common Factor (GCF), '4'.4(-12 + -1x + x2) = 0Factor a trinomial.4((-3 + -1x)(4 + -1x)) = 0
4x2 + -4x + -48 = 0Reorder the terms:-48 + -4x + 4x2 = 0Solving-48 + -4x + 4x2 = 0Solving for variable 'x'.Factor out the Greatest Common Factor (GCF), '4'.4(-12 + -1x + x2) = 0Factor a trinomial.4((-3 + -1x)(4 + -1x)) = 0Ignore the factor 4.
Step-by-step explanation:
hope it helps:)
i just need help with number 2, i don’t understand
Answers
Step-by-step explanation:
Assuming c = x, you would substitute 2{(5)^(5)} - 6,
5^5 = 25,
2(25) = 50,
50 - 6 = 44
Answer would be 44, but only if c = x
[tex]6^{4x-9} =(\frac{1}{36} )^{x-4}[/tex]
Answers
[tex]\displaystyle \large \boldsymbol {} 6^{4x-9} =\bigg(\frac{1}{36} \bigg)^{x-4} \\\\\\ 6^{4x-9}=(6^{-2})^{x-4 }\\\\\\ 6^{4x-9}=6^{-2x+8} \\\\\\ 4x-9=-2x+8 \\\\\\ 4x+2x=9+8 \\\\\\ \boxed{x=\frac{17}{6}=2\frac{5}{6} }[/tex]
|3 - 5 + 7|.
O 15
O 5
O -15
O -5
Answers
Answer:
5
Step-by-step explanation:
The answer is 5
because 3 - 5 = -2
and -2 + 7 = 5
so the answer is 5
please just help mee
Answers
Step-by-step explanation:
The rates of:
- coffee Bean To Go = 19/4 = $4.75
per pound
- coffee 4U = $5.25 per pound
the correct answer is :
B. coffee Bean To Go is cheaper,
selling coffee at $4.75 per pound
5+4(-20)
Be sure to consider the order of operations!!
Answers
Answer:
[tex]5 + 4( - 20) \\ 5 + ( - 80) \\ 5 - 80 \\ = - 75[/tex]
I hope I helped you^_^
Answer:
5+4(-20)
Step-by-step explanation:
So you do the one's in parentheses first, which is -20, and then you do 5+4 which is 9
how do you solve 2 to the 35th power
Answers
Answer:34359738368
Step-by-step explanation: 2 to the 35th power is basically 2 x 2 35 times. You can solve it on a caculator by typing in 2 and pushing the button that allows you to enter 35 (which is the exponent, or the little number) The button will usually have an x with a little y at the top right corner
Given the line below.
Write the equation of the line, in point-slope form. Identify (x1, y1) as the point (-2, 2). Use the box provided to submit all of your calculations and final answers.
Answers
The slope of that line is -1, so m = -1.
The point you were told to use is (-2,2), so point-slope form starts as:
( y - 2 ) = -1 • ( x - (-2) )
But we'd clean up that x-(-2) to be x+2.
y - 2 = -1 ( x+2 )
Find the slope of the line.
Answers
Answer:
The slope is y = x
Step-by-step explanation:
You can find the slope by using the rise over run method with two points.Let's take (1,1) and (2,2). From the first point to the second point, (1,1) goes up one unit and to the right one unit.So the rise over run is 1/1, or 1, which means the slope is 1.
Answer:
m = 1x
Step-by-step explanation:
This is the easiest slope you'll ever have to calculate - if you even need to as it's self explanatory looking at it! Slope = rise/run, thus slope = 1/1 = 1.
Please help me solve this problem ASAP
Answers
Answer:
x=1.6
Step-by-step explanation:
explanation: causeee lol
Need help with math:/!!!!
MN is 6 units. Find the lengths of NZ and XZ.
For the image see if you have enough info to find the missing lengths. If not, explain why.
Answers
Answer:
Step-by-step explanation:
[tex]\frac{3 +NZ}{3}[/tex] = [tex]\frac{5+5}{5}[/tex] ⇒ NZ = 3
XZ = 6 × 2 = 12
The length of NZ = 3 units.
The length of XZ = 12 units
Triangle Proportionality TheoremWhat is Triangle Proportionality Theorem?A line that runs perpendicular to one side of a triangle and crosses the other two sides equally splits the two sides.
Use of Triangle Proportionality Theorem to find the sides:Step 1: Consider side NY, NZ, YM, MX
By the theorem,
[tex]\frac{YN}{NZ}=\frac{YM}{MX}[/tex]
[tex]\frac{3}{NZ}=\frac{5}{5}[/tex]
[tex]NZ=3[/tex] units
Step 2: Consider sides YM, YX, NM, ZX
[tex]\frac{YM}{YX} =\frac{NM}{ZX}[/tex]
[tex]\frac{5}{10} =\frac{6}{ZX}[/tex]
[tex]ZX = 12[/tex] units.
Therefore, the values for the sides are NZ = 3 units and XZ = 12 units.
To know more about more about similar triangles, here
https://brainly.com/question/21874653
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5)
4
3
2
1
3
-2
-1
1
- 1
2
3 4
2
3
-4
-6
Find the slope of the line graphed.
My Answer:
Answers
what is the percent of games won if a team won 95 games and lost 65 games?
Answers
Answer:
The percent for games that were won is 59.375%.
Step-by-step explanation:
Mrs.Roberts drives 3/4 miles in 1/2 minute. How many miles can she drive in 1 minute?
Answers
Answer:
1 1/2 OR 1.5 in decimal form
Step-by-step explanation:
If Mrs. Roberts drives 3/4 miles in half a minute, 1/2 x what = 1? 2. Multiply both items by 2. 3/4 x 2 = 6/4, also known as 1 1/2 or 1.5 Hope this helped!!
giúp mìn vs mngggggg
Answers
Answer:
136.99
Step-by-step explanation:
Đây là một câu hỏi dễ chỉ cần sử dụng máy tính
1 table can fit 6 people, but you want to connect them with the short sides. How many tables will you need if you want to combine the tables together?
Answers
Answer:
a.The tables to combine together
solve for x
r=xy
(Show solving steps please)
Answers
Answer:
x=r/y
Step-by-step explanation:
xy together means they are multiplying.
to move y over you do the opposite which is divide by Y on both sides
r/y = xy/y
that way x is next to 1, which we don't have to write
r/y=x
Help please I really don’t understand this
Answers
Answer:
yea i agree with scorpiowo the asnwer is B
Step-by-step explanation:
help plz its for 20 points.
Answers
Answer: 1st page
multiply divide
1)27 4
2)32 6
3)42 8
4)36 8
5)45 5
6)56 4
7)28 4
8)45 5
9)56 4
10)72 6
11)64 7
12)54 6
13)48 8
14)42 8
15)63 8
16)28 7
17)48 8
18)42 9
19)49 7
20)64 5
Step-by-step explanation: used a calculator
PLEASE PLEASE HELP ILL GIVE U BRAINEST
Answers
Answer:
I only / 1 only
Step-by-step explanation:
Function rules: no same x-values and must pass vertical line test
1: all different x-values
2: has two of the same x-values
3: doesn't pass vertical line test
Hopefully this helps!
Brainliest please?
Answer:
1 only (I hope im right)
Step-by-step explanation:
Hope this helps:)
These spam comments are getting out of hand. They’re everywhere and it’s really annoying having to post another question because of those spam comments. Like who’s behind all of this? And for what reason are they doing this?
Answers
Answer:
I agree it's annoying!!!
Step-by-step explanation:
I think the people who just spam questions are just lazy and they have nothing else to do with their lives. So they try to make themselves feel better by annoying other people. I hope you are having a good day other than people spamming questions!
people need help and others want to give help. some want both. so why do people want to step it and waste there time?!
so upsetting.