Using what you know about the complex number system and the number i, fill in the details of the explanation on page 181 of Ages to show that
V2+ V-121 + V2-V-121.
is, in fact, 4.
Answers
The complex number i is defined as the square root of -1. That is i^2 = -1.
Now, let's take a closer look at the expression V2+ V-121 + V2-V-121:
First, note that V2+ V-121 can be written as the sum of two square roots: V2 = sqrt(2) and V-121 = sqrt(-121) = 11i. Therefore,
V2+ V-121 = sqrt(2) + 11i.
Similarly, V2-V-121 can also be written as the sum of two square roots:
V2-V-121 = sqrt(2) - 11i.
Substituting these values back into the original expression, we get:
V2+ V-121 + V2-V-121 = (sqrt(2) + 11i) + (sqrt(2) - 11i)
= 2sqrt(2)
Therefore, we have shown that V2+ V-121 + V2-V-121 is equal to 2sqrt(2).
However, we want to show that it is actually equal to 4. To do so, we can square both sides of the equation:
(V2+ V-121 + V2-V-121)^2 = (2sqrt(2))^2
Expanding the left-hand side using the binomial formula, we get:
V2+ V-121 + V2-V-121 + 2(V2+ V-121)(V2-V-121) = 8
Simplifying the product of the two square roots, we have:
V2+ V-121 + V2-V-121 + 2(sqrt(2)^2 - (11i)^2) = 8
Using the fact that i^2 = -1, we can simplify further:
V2+ V-121 + V2-V-121 + 2(2 + 121) = 8
Combining like terms, we get:
V2+ V-121 + V2-V-121 = 4
Therefore, we have shown that V2+ V-121 + V2-V-121 is indeed equal to 4.
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Related Questions
pls help with homework, due tommarow
can you explain how to do it also pls
Answers
The height of the cone is 16 feet.
How to find the height of the cone?A cone is a three-dimensional geometric shape.
The right cone has a slant height of 20 ft and the diameter of the base is 24 ft.
Therefore, the height of the cone can be found as follows:
Using Pythagoras's theorem,
c² = a² + b²
where
c is the hypotenuse sidea and b are the other legsThe slant height of the cone is the hypotenuse side of the detached right triangle. The radius and the height of the cone is the other legs of the detached right triangle.
Hence,
diameter = 24 ft
r = radius = 24 / 2 = 12 ft
Hence,
20² - 12² = h²
400 - 144 = h²
h = √256
h = 16 feet.
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Solve this for me. In a office,2/3 of the water bill is paid by yaw,1/5 by kwame and remaining by aba. What fraction is paid by aba
Answers
PLS SOMEONE EXPLAIN THIS TO ME
Answers
Step-by-step explanation:
94 is the perimeter i think ..... ............
I'd really like some help with this. Please...Please! What's the probability that the point ends in the shaded region?
Answers
Answer: 29%
Step-by-step explanation:
109/360=.294 Then move the decimal to make it a percent
Area of sector is 360
Equation :
106/360
Solution:
29.4 %
what is 672x787=___?
Answers
Answer:
528864
Step-by-step explanation:
Point Tis on line segment SU. Given ST = 9 and TU
SU.
= 7, determine the length
Answers
Answer:
Line SU is 16
Step-by-step explanation:
ST + TU = SU
7 + 9 = 16
You add 9 and 7 to get 16.
Can anyone please help answer this?
Answers
A = 45 inches!
11 + 7 = 18
12 + 5 = 17
6 + 4 = 10
18 + 17 = 35
35 + 10 = 45
Please help me!!!! x2+ (y-4/x2)2=1
Answers
if so , x2+2y-8/x2=1
8. Tyson and Ariana each invested $2,500 in separate accounts. Tyson's interest rate is 5.75%
and is compounded annually. Ariana's simple interest rate is 5.75%. Neither will make any
additional deposits or withdrawals. At the end of 6 years, how much more has Tyson
earned? Round your answer to the nearest cent.
Record your answer and fill in the bubbles on your answer document. Be sure to use correct
place value.
Answers
Answer:
i don't now can someone help me
Step-by-step explanation:
A ball i drawn randomly from a jar that contain 5 red ball, 2 white ball, and 1 yellow ball. Find the probability of: Find P(red ball): Find P(NOT Yellow): Find P(white or yellow)
Answers
Following are all of the subparts' solutions using the probability formula:
Red ball (A) P: 5/8
(B) P: 7/8 (NOT Yellow)
(C) P(yellow or white): 3/8
What is probability?
Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.
What is an event?The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.
Probability formula: P(E) = favorable events/Total events
(A) P(red ball):
P(E) = favorable events/Total events
P(E) = 5/8
(B) P(NOT Yellow)
P(E) = favorable events/Total events
P(E) = 7/8
(C) P(white or yellow)
P(E) = favorable events/Total events
P(E) = 3/8
Therefore, the answers to all the subparts using the probability formula are shown:
(A) P(red ball): 5/8
(B) P(NOT Yellow): 7/8
(C) P(white or yellow): 3/8
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Find hf if ge= 43 yd.
Answers
Step-by-step explanation:
Area of this kit = 1/2 (gf * hf)
258 yd^2 = 1/2 (43 * HF )
HF = 258 *2 / 43 = 12 yds
the rectangular prism below has a height of 10.3 units and a volume of 278.1 units 3 3 . find the area of one of its bases.
Answers
Answer:
27units
Step-by-step explanation:
volume of a rectangular prism v=sh
s=v/h = 278.1/10.3 =27 units
so the area of its base is 27 units
A country has 33 parks that allow camping and 101 parks that have
playgrounds. Of those, 16 parks both allow camping and have
playgrounds. The country has a total of 346 parks.
What is the probability of randomly selecting a park that allows
camping or has a playground? Write your answer as a fraction.
Answers
Answer:
134:346 Add the 33 to 101 to get first number, then total number of parks 346 is the second number, they may end up wanting you to to reduce the fraction.67:143
Jennifer is buying cupcakes for a party. 12
cupcakes is $8.40. What is the unit rate for
each cupcake?
I reallyyyyy need help I I have no idea about unit rates
Answers
Answer:
24
Step-by-step explanation:
The second number in an ordered pair is the __________ and represents the vertical distance from the origin
A) origin
B) x-coordinate
C) y-coordinate
D) coordinate plane
Answers
pleeeeeeeeeeeeeeeeas FAST !!!!! i need help if a/b = (-7/9)^8 / (-7/9)^6 find the value of (a/b)^2.
Answers
Answer:
(-7/9)^4 = 2401/6561
Step-by-step explanation:
The rules of exponents apply.
(a^b)/(a^c) = a^(b-c) . . . . . quotient rule
(a^b)^c = a^(bc) . . . . . . . . power rule
__
value of a/bThe first rule of exponents shown above helps us find the value of a/b.
\(\dfrac{a}{b}=\dfrac{\left(\dfrac{-7}{9}\right)^8}{\left(\dfrac{-7}{9}\right)^6}=\left(\dfrac{-7}{9}\right)^{8-6}=\left(\dfrac{-7}{9}\right)^2\)
value of (a/b)^2The second rule of exponents shown above tells us how to find the square.
\(\left(\dfrac{a}{b}\right)^2=\left(\left(\dfrac{-7}{9}\right)^2\right)^2=\left(\dfrac{-7}{9}\right)^{2\times2}\\\\\boxed{\left(\dfrac{a}{b}\right)^2=\left(\dfrac{-7}{9}\right)^4=\dfrac{2401}{6561}}\)
_____
Additional comment
Since -7 is always to an even power in these expressions, its sign can be ignored. The product of an even number of negative values is positive.
An on-demand movie company charges $2.95 per movie plus a monthly fee of $39.95. Which expression represents the yearly
cost for x movie rentals?
O 2.95x+ 39.95
O 39.95x+ 2.95
O 2.95x-39.95(12)
O 295x+39.95(12)
Answers
Answer: 2.95x+39.95(12)
Step-by-step explanation:
Hi, to answer this question we have t write an expression with the information given:
The yearly cost for x movie rentals is equal to : the product of the cost of each movie (2.95) and the number of movies (x) ;plus the product of the monthly fee (39.95) and the number of months in a year (12)
Mathematically speaking:
2.95x+39.95(12)
Answer:
D-295x+39.95(12)
Step-by-step explanation:
EDG2021
- A card is selected at random from a
standard pack of playing cards and then
replaced. This is done 1,040 times.
How many times would you expect to get
the following cards:
(a) A red card?
(b) A King?
(C) The Queen of hearts?
Answers
Step-by-step explanation:
a ). red cards = 26
then probability is = no. of outcomes / total no. of outcome
p ( red card ) = 26 / 1040
p ( red card ) = 1 / 40
b ) kings = 4
p ( kings ) = 4 / 1040
p ( kings ) = 1 / 260
c ) queen of hearts = 1
p ( queen of heart ) = 1 / 1040
Q1 5 Points True or False x² + 8x Consider an integral S x²(x² + x + 1) When we try to integrate, it can be put in the form fractions method. True False 3x³ + 4x² 10 Ax + B x² + Cx + D x² + x + 1 because of partial
Answers
The answer is False. The integral cannot be put in the form of partial fractions because the denominator is not factorable. the denominator of the integrand is x² + x + 1, which is not factorable.
This means that the integrand cannot be written as a fraction of two polynomials, which is the requirement for partial fractions. The partial fractions method is a method for integrating rational functions. A rational function is a function of the form p(x)/q(x), where p(x) and q(x) are polynomials.
The partial fractions method breaks down the rational function into a sum of fractions, each of which has a numerator that is a polynomial of a lower degree than the denominator. The integral of the rational function can then be found by integrating each of the individual fractions.
In order to use the partial fractions method, the denominator of the rational function must be factorable. In this case, the denominator of the integrand is x² + x + 1.
This polynomial is not factorable, which means that the integrand cannot be written as a fraction of two polynomials. Therefore, the partial fractions method cannot be used to integrate this function.
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Students recorded the amount of liquid in fluid Ounces each of them drank In one day. The box plot shows the summary of the results. Amount of Liquid (fluid Ounces) Which statement best describes the data represented in the box plot?
Answers
Answer: The correct answer would be F. Half the students drank from 78 to 114 fluid ounces.
Step-by-step explanation:
The statement best describes the data represented in the box plot half the students drank from 78 to 114 fluid ounces. The correct option is F.
What is a box plot?A rectangle is created to represent the second and third quartiles, normally with a vertical line inside to indicate the median value, in a simple way of presenting statistical data on a plot.
Given that students recorded the amount of liquid in fluid Ounces each of them drank In one day. The box plot shows the summary of the results. Amount of Liquid (fluid Ounces).
The highest and the lowest limit of the box plot is range from 78 to 114. The statement best describes the data represented in the box plot half the students drank from 78 to 114 fluid ounces.
Therefore, the correct option for the box plot will be F.
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What is the Distance formula of (-6, -12) and (4,8)
Distance formula is in picture
Answers
Answer:
The distance formula is 22.360679775
if you round it to the nearest tenth, then the answer is 22.4
Step-by-step explanation:
(-6, -12) and (4,8)
(x2 - x1)² + (y2 - y1)²
Place the x and y values
(4 - - 6)² + (8 - - 12)²
= 10² + 20²
= 100 + 400 = 500
√500 = 22.360679775
Round it to the nearest tenth and you will get 22.4
Hope this helps!
please mark me as the brainliest
The formula in finding the distance between two points is given below:
\( \sf{d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}\)where:
\( \sf{(x_1, y_1) = (-6, -12)}\)\( \sf{(x_2, y_2) = (4, 8)}\)Substitute the given values into the distance formula and solve for d:
\( \sf{d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}}\)\( \sf{d = \sqrt{[4 - ( - 6)]^2 + [8 - ( - 12)]^2}}\)\( \sf{d = \sqrt{(10)^2 + (20)^2}}\)\( \sf{d = \sqrt{100 + 400}}\)\( \sf{d = \sqrt{500}}\)\( \bold{d = 22.4 \: units}\)Therefore, the distance between the two points is 22.4 units (nearest tenth).
Cheers!
Please help me! Find the value of z!!!!
Answers
Answer:
20 degrees
Step-by-step explanation:
Angles on the edge of the circle are equal to 1/2 of the arc it forms, so that means angle z is one half of 40 degrees. 1/2 * 40 = 20 degrees.
Please answer in an hour! You will get a thumbs up.
Question 1 (a)
Assume you purchase a new tractor on Jan 1, 2022 for a cost of $200,000. You estimate you will be able to use the tractor for 10 years, and it will have a salvage value of 10% of the original by the end of its useful life. Determine the book value at the end of the first year (December 31, 2022) using straight-line depreciation.
options:
$18,000
$180,000
$185,000
$182,000
Question 1 (b)
A balance sheet (using current and noncurrent assets and liabilities- no intermediate) shows that a farmer has current assets of $80,000 and owner equity of $100,000. Her current ratio is 2 and her debt/equity ratio is 1.0. Determine the farmer's noncurrent liabilities.
Question 1 (b) options:
$40,000
$60,000
$100,000
unable to determine
Answers
Question 1a
To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:
Annual Depreciation = (Cost - Salvage Value) / Useful Life
Substituting the given values, we get:
Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year
This means that the tractor will depreciate by $18,000 each year for the next 10 years.
To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:
Depreciation Expense for Year 1 = $18,000
Therefore, the book value of the tractor at the end of the first year will be:
Book Value = Cost - Depreciation Expense for Year 1
= $200,000 - $18,000
= $182,000
So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D
Question 1(b)
To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:
Calculate the total current liabilities using the current ratio:
Current Ratio = Current Assets / Current Liabilities
2 = $80,000 / Current Liabilities
Current Liabilities = $80,000 / 2
Current Liabilities = $40,000
Calculate the total liabilities using the debt/equity ratio:
Debt/Equity Ratio = Total Liabilities / Owner Equity
1.0 = Total Liabilities / $100,000
Total Liabilities = $100,000 * 1.0
Total Liabilities = $100,000
Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:
Noncurrent Liabilities = Total Liabilities - Current Liabilities
Noncurrent Liabilities = $100,000 - $40,000
Noncurrent Liabilities = $60,000
Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.
what is the value of x? PLZ LMK ASAP!
Answers
Answer:
m∠x = 98°
Step-by-step explanation:
Step 1: Find the supplementary angle in the triangle
180 - (53 + 45) = 82
Step 2: Use Supplementary Angles to solve for x
180 - 82 = 98°
find an equation for the line below
Answers
Answer:
see the picture
Step-by-step explanation:
you can use geogebra to help you
factor the trinomial below. x^2+13x+42
Answers
Answer:
(x + 6)(x + 7)
Step-by-step explanation:
To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.
One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:
1, 42 -> 1 + 42 = 43
2, 21 -> 2 + 21 = 23
3, 14 -> 3 + 14 = 17
6, 7 -> 6 + 7 = 13
So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:
x^2 + 13x + 42 = x^2 + 6x + 7x + 42
Next, we can group the first two terms and the last two terms:
x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)
Now, we can factor out the greatest common factor from each group:
x(x + 6) + 7(x + 6)
Notice that we have a common factor of (x + 6) in both terms. We can factor this out:
(x + 6)(x + 7)
which of the following expressions is equivalent to bxb
A) 2b
B) b2
C) 2*b
D) 2b*2
Answers
Answer:
B) b2
Explanation:
b · b = b²
b + b = 2b
2 × b = 2b
2 × b × b = 2b × b = 2b²
Answer:
A) 2b ( b×b = twice b )
hope this help
find the coefficient of variation from the following data mean=4 variance=25
Answers
A prism with a base area of 6 ft² and a height of 7 ft is dilated by a factor of 3/2.
The volume of the dilated prism is ___ cubic ft.
Answers
The calculated volume of the dilated prism is 141.75 cubic feet
How to determine the volume of the dilated prismFrom the question, we have the following parameters that can be used in our computation:
Base area of 6 ft² and a height of 7 ftDilated by a factor of 3/2.The volume is calculated as
Volume = Base area * Heigth
For the dilated prism, we have
Volume = Base area * Heigth * Scale factor³
substitute the known values in the above equation, so, we have the following representation
Volume = 6 * 7 * (3/2)³
Evaluate
Volume = 141.75
Hence, the volume of the dilated prism is 141.75 cubic feet
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evaluate the following as true or false. the function f(x)=5 can be written as f(x)=51. therefore, f′(x)=1.51−1=1.50=1.1=1.
Answers
The statement is false. The function f(x) = 5 cannot be written as f(x) = 51, and the calculation f'(x) = 1.51 - 1 = 1.50 = 1.1 = 1 is incorrect.
In the given statement, f(x) = 5 represents a constant function, where the output value is always 5 regardless of the input value x. Writing f(x) = 51 would be incorrect and not equivalent to f(x) = 5. The value of 51 does not represent the function's behavior or its relationship to the input variable x.
Moreover, the calculation f'(x) = 1.51 - 1 = 1.50 = 1.1 = 1 is also incorrect. The derivative of a constant function, such as f(x) = 5, is always zero. Taking the derivative of a constant function yields f'(x) = 0, not 1. The given calculation attempts to manipulate the numbers in an incorrect manner, leading to an erroneous result.
In conclusion, the function f(x) = 5 cannot be written as f(x) = 51, and the calculation f'(x) = 1.51 - 1 = 1.50 = 1.1 = 1 is incorrect.
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