May I know the answer and steps, thank you.
(3-i/1+i)³
An imaginary number is produced when we square a negative number.
The value of I is -1.
What is the Value of i?This article's introduction included a proposition. The specific measure or value of what I stands for was the subject of the statement. It is discussed in this section of the article along with an explanation of its value.
Iota is the term used to describe the imaginary portion of a complex number. The symbol "iota" or I is used to represent an imaginary number's value. An imaginary number is produced when we square a negative number.
The value of I is -1.
The concept of complex numbers is understood using this value of i.
x2 plus 1 equals zero in a quadratic equation.
x2 = -1
x = √-1
The imaginary portion is shown as -1.
I = √-1
i2 = -1
An imaginary number can be squared to get a negative value, as was previously discussed.
I = √-1
both sides being square
i2 = -1
An imaginary number plus a real number are combined to get any complex number. Iota, sometimes known as I stands for all non-real quantities.
Real numbers include 10, -20, 3, and other like values.
The integers 2i, -5, -i, etc. are examples of imaginary numbers.
Complex numbers take the form of a + ib, where I denotes the imaginary component. In addition, the number zero is complicated. Only the imaginary component of a complex number can be added to or subtracted from the imaginary part, and vice versa for the real part of the complex number.
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Use logarithmic table to evaluate 40.79÷0.003949
Answer:
1.033×10⁴
Step-by-step explanation:
You want the quotient 40.79÷0.003949 using log tables.
Log of quotientThe log of a quotient is the difference of logs:
log(a/b) = log(a) -log(b)
Log valuesIt can work well to start by writing the numbers in scientific notation:
log(40.79) = log(4.079×10¹) = 1 +log(4.079) = 1.6106
log(0.003949) = log(3.949×10⁻³) = -3 +log(3.949) = -3 +0.5965
Log of quotientThen the log of the quotient is ...
log(40.79/0.003949) = 1.6106 -(-3 +0.5965) = 4.0141
AntilogThe antilog of this number will be ...
antilog(4.0141) = 10⁴ × antilog(0.0141) ≈ 1.033×10⁴
With our 4-digit log tables, 4 significant figures is the best we can expect.
The quotient is about 1.033×10⁴.
__
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find the indicated sum
Step-by-step explanation:
option no 2 is correct
36 I hope is helpful
In Scrabble, there are a certain number of each of the vowel: A-9, E-12, I-9, O-8, U-4. You decided to place only the vowel in a bag to conduct an experiment of drawing and replacing the letter back in the bag. The experiment' outcome wa a follow:
E, I, A, E, E, A, I, O, U, U, A, A, O, O, E
Which vowel' theoretical probability wa cloet to the experimental probability?
A and E are the vowels that theoretical probability was closet to the experimental probability.
The probability is 0.1685%
Probability:
Probability defines the probability of an event occurring. There are many real world situations where we need to predict the outcome of an event. We may or may not be certain about the outcome of an event. In such cases, I say that this event may or may not occur. Probability in general has excellent applications for making probability-based predictions in games and economics, and it also has widespread applications in this emerging field of artificial intelligence. The probability of an event can be calculated by simply dividing the number of favorable outcomes by the total number of possible outcomes using the probability formula. The value of the probability that an event will occur can range from 0 to 1. This is because the preferred number of outcomes can never exceed the total number of outcomes. Also, the resulting favorable number can never be negative. The formula for calculating the probability of a
event is:
probability (event) = favorable outcome/total outcome
Now,
According to the Question:
N vowels = N(A) + N(E) + N(I) + N(O) + N(U)
=9 + 12 + 9 + 8 + 4
=42
The total number of letters is:
1×5+2×10+3×1+4×4+6×3+8×1+9×2+12×1=100
This is because dragging the tile reduces the number of vowels and the total number of letters.
p =42×41×...×36100×99×...×94
= 5916335104300
≈ 0.1685%
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Is polynomial Y⁴+ 4y²+ 5 have zeroes or not?
The polynomial Y⁴+ 4y²+ 5 does not have zeroes.
What is polynomial?Polynomials are an essential component of the "language" of mathematics and algebra. They are used to express numbers as a result of mathematical operations in nearly every field of mathematics. Polynomials can also be used as "building blocks" in other kinds of mathematical expressions, such as rational expressions.
Polynomials can be used to represent a wide range of everyday mathematical processes. A polynomial can be formed by adding the costs of items on a grocery bill. A polynomial can be used to calculate the distance travelled by a vehicle or object. Polynomials can be used to calculate the perimeter, area, and volume of geometric figures. These are just a few of the many uses for polynomials.
We know that, (a +b)² = a² + b² + 2ab
Here given that,
⇒ y⁴ + 4y² + 5 = 0
⇒ y⁴ + 4y² + 4 + 1 = 0
⇒ (y² + 2)² + 1 = 0
Because the first term is a square, the expression (y² + 2)² + 1 will never be zero for any value of y.
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Solve the formula V = πr²h for r.
Answer:
v=πr²h
divide both sides by πh
v/πh=r²
r²=v/πh
square root both sides
r=√v/√πh
I hope this helps
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answer:
Step-by-step explanation:
4/56\8
Which set of ordered pairs represents a function?
1-{(−5,−4),(3,4),(7,−6),(7,1)}
2-{(8,−2),(6,8),(6,3),(−4,−2)}
3-{(7,5),(7,−9),(−2,−3),(4,−1)}
4-{(−8,−7),(0,−7),(−4,0),(4,−5)}
Answer:
The 4th set only has unique x values as it is not repeated making it a function frm the others
You buy a gallon of milk that costs $3. 50. The milk is discounted for 10% off. You also have to pay tax of 6. 25% on the discounted price. What is the final cost?
As per the given percentage of tax and discount, the final cost of the milk is $3.8186
The term percentage in math is known as a relative value indicating hundredth parts of any quantity.
Here we have given that You buy a gallon of milk that costs $3. 50.
And here we also know that the milk is discounted for 10% off.
Here we have also have to pay tax of 6. 25% on the discounted price.
First we have to calculate the discounted prices, that can be obtained by the following calculation,
=> 3.50 - [3.50 x 10/100]
=> 3.50 - [3.50 x 0.1]
=> 3.50 - 0.35
=> 3.15.
Now, we have to calculated the tax for the price of the milk,
=> 3.50 + [3.50 x 6.25/100]
=> 3.50 + [3.50 x 0.0625]
=> 3.50 + 0.2186
=> 3.8186.
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Math Subject: Symmetry.
Question is attached below.
The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves.
What is Symmetry?A definition of symmetry states that whether one form is moved, rotated, or flipped, it looks precisely like the other shape. Just fold the paper, draw one-half of the heart at the fold, then cut it out to discover that the second half precisely matches the first half when you are instructed to cut out a "heart" from a sheet of paper. The heart-shaped carving is an illustration of symmetry.
Symmetry is defined in mathematics as "a mirror image." Symmetry is the property of an image that remains unchanged after a form has been rotated or flipped. There are patterns in it. In daily life, you may have heard the word "symmetrical" frequently. One half of a thing is the mirror image of the other half, which is a balanced and proportionate likeness. Asymmetrical refers to a form that is not symmetrical. In nature, architecture, and the arts, symmetrical things are all around us.
The term "line of symmetry" refers to the fictitious axis or line that you fold a figure along to create its symmetrical halves. In essence, it splits one thing into two mirror images. The symmetry line may run vertically, horizontally, or diagonally. There might be one or many symmetry lines.
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Answer:
1. Choose Your Shape: Start with a shape that you want to create a line of symmetry for. It could be a simple shape like a square, rectangle, or triangle.
2. Draw the Shape: Draw the shape neatly on a piece of paper using a pencil.
3. Identify the Line of Symmetry: Decide where you want to place the line of symmetry. This line should divide the shape into two equal halves.
4. Draw the Line of Symmetry: Draw a straight line through the center of the shape, from one side to the other. Use a ruler to ensure the line is straight and passes through the center.
5. Create the Mirror Image: To create the mirror image on the other side of the line, imagine that the line is a mirror. Reflect each point on one side of the line to the other side while maintaining the same distance from the line. You can also use a ruler or straightedge to guide you as you draw.
6. Check for Symmetry: Carefully examine both sides of the line to make sure they are mirror images of each other. The distances and angles should match.
7. Finalize the Drawing: Once you're satisfied with the symmetry, trace over your pencil lines with a pen or darken them to make your drawing more prominent.
8. Erase Construction Lines: Gently erase any construction lines or guidelines you drew in the earlier steps.
A weight is suspended from a spring is set into oscillating
motion by compressing it into a point 3 cm above its resting
position and releasing it. It will displace 3 cm past its resting
point. From the time it is released it will bounce at a rate of 3
cycles per second.
a. Draw a graphical representation and give the equation
involving the situation.
b. What is the displacement of the spring after 2.5
seconds?
a. The graphical representation of the oscillation of the weight suspended from a spring is a sine wave, with the displacement of the weight on the y-axis and time on the x-axis. The equation involving the situation would be y = Asin(2pift + phi) where A is the amplitude of the oscillation (3 cm in this case), f is the frequency of oscillation (3 cycles per second in this case), t is the time elapsed since the weight was released, and phi is the phase offset (0 in this case).
b. To find the displacement of the spring after 2.5 seconds, we can substitute 2.5 seconds for t in the equation: y = Asin(2pift + phi) = 3sin(2pi32.5 + 0) = 3sin(15pi) = 3*0 = 0 cm. So the displacement of the spring after 2.5 seconds is 0 cm.
What is an oscillation period?By definition, period of oscillation of an oscillator is the time interval that the oscillating object needs to pass through its equilibrium position with velocity in the same direction.
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Rachel is arranging 12 cans of food in a row on a shelf. She has 8 cans of beets, 3 cans of corn, and 1 can of beans. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?
Given:
Total number of food cans = 12
Cans of Beets = 8
Cans of corn = 3
Can of beans = 1
To find:
How many distinct orders can the cans be arranged if two cans of the same food are considered identical.
Solution:
To find the distinct ways arrangement, we have a formula:
[tex]\text{Number of distinct ways}=\dfrac{n!}{r_1!r_2!...r_k!}[/tex] ...(i)
Where, n is the number of objects and [tex]r_1,r_2,...,r_k[/tex] are repeated objects.
Total number of food cans is 12. So, [tex]n=12[/tex].
She has 8 cans of beets. So, [tex]r_1=8[/tex]
She has 3 cans of corns. So, [tex]r_2=3[/tex]
She has 1 can of beans. So, [tex]r_3=1[/tex]
Substituting these values in (i), we get
[tex]\text{Number of distinct ways}=\dfrac{12!}{8!3!1!}[/tex]
[tex]\text{Number of distinct ways}=\dfrac{12\times 11\times 10\times 9\times 8!}{8!\times 3\times 2\times 1\times 1}[/tex]
[tex]\text{Number of distinct ways}=\dfrac{11880}{6}[/tex]
[tex]\text{Number of distinct ways}=1980[/tex]
Therefore, the number of distinct orders to arrange the cans is 1980.
PLSS helpppppppppppppp like plssss
Answer:
f=21-16, 5
Step-by-step explanation:
Just subtract 16 from both sides to get 5 as the solution
Answer:
ADDITION
16+f=x
Step 1: Add -16 to both sides.
f+16+−16=x+−16
f=x−16
Answer:
f=x−16
Step-by-step explanation:
SUBTRACTION
16−f=x
Step 1: Add -16 to both sides.
−f+16+−16=x+−16
−f=x−16
Step 2: Divide both sides by -1.
−f /−1 = x−16 /−1
f=−x+16
Answer:
f=−x+16
Can you solve this problem for me please
The required scale factor that Amir will use to go from Polygon F to G is 1/9.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
here,
Area of polygon F = 36 square units
Area of polygon G = 4 square units
Now,
The scale factor to go from polygon F to polygon G is given as,
SF = Area of polygon G / Area of polygon F
SF= 4/36
SF = 1/9
Thus, the required scale factor that Amir will use to go from F to G is 1/9.
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What type of graph is an inverse relationship?
On a graph, an inverse relationship always has a negative slope.
What is an inverse relationship?In statistics, if higher values of one variable tend to be related to lower values of the other, there is a negative association or inverse relationship between the two variables.
A negative link between two variables typically denotes a negative correlation, or what is similar in some cases, a negative slope on the associated graph.
Anticorrelation or inverse correlation are other terms for a negative correlation between two variables.
When two variables change in an inverse relationship, they do so in opposite directions: one increases while the other drops, and vice versa.
Y declines as X rises in an inverse relationship.
An inverse relationship always has a negative slope on a graph.
Therefore, on a graph, an inverse relationship always has a negative slope.
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Solve using system of elimination. -x-10y=5 -x-10y=9
Answer:
No Solution.
Step-by-step explanation:
-x-10y=5
-x-10y=9
--------------
-x-10y=5
-(-x-10y)=-9
------------------
-x-10y=5
x+10y=-9
----------------
0=-4
no solution
Mr. Thompson earns $ 11.52 per hour. Last week he worked 37 hours how much F.I.C.A tax did he have to pay at 7.65%?
Answer:
$32.61
Step-by-step explanation:
First, we multiply the amount he earns per hour by the amount of hours he worked. $11.52 * 37 = $426.24. Then, we figure out what 7.65% of $426.24 is, which we can do by multiplying 426.24 by 0.0765. This gives us $32.60736, but since there is no form of US money that is worth less than 1 cent, we round to the nearest cent and get $32.61.
Hope this helps!
A batch of bottles were packed in 25 boxes with 12 bottles in each box. If the same batch is packed using 20 bottles in each box, how many boxes would be filled?
hey ,
here is your answer,
_______________
Let the number of boxes filled, by using 20 bottles in each box, be x.
The following table is obtained.
______________________
| Number of bottles. 12. 20 |
| |
| Number of boxes 25. x. |
---------------------------------------------
More the number of bottles, lesser will be the number of boxes.
Hence, the number of bottles and the number of boxes required to pack these are inversely proportional to each other.
Therefore,
12 × 25 = 20× x
Hence, the number of boxes required to pack these bottles is 15.
Answer:
The answer is 15 Box.
No of bottles = 25 boxes × 12 bottles
= 300 bottles
So there were total 300 bottles in a box.
Now If 20 bottles are filled ina box then
no. of box required = 300/20
And answer is 15 boxes
Question 3 A student solved a quadratic equation as shown here
Answer:
Didn't move the 12 on the other side of the equal sign to make
2x^2 + 5x - 12 = 0
the other steps error city.
Step-by-step explanation:
2x^2 + 5x - 12 = 0
(2x - 3)(x + 4)= 0
2x - 3 = 0
2x = 3
x = 3/2
x + 4 = 0
x = -4
1. What is the unit of measurement for speed using the metric system?
Answer:
meter per second(m/s)
Answer:
Hey there! The metric system has a unit called meters per second for measuring speed. It's abbreviated as m/s and it's used to measure how far something travels in a certain amount of time. For example, if something goes 50 meters in 10 seconds, its speed would be 50 m/s / 10 s = 5 m/s. There are other units for measuring speed too, like kilometers per hour (km/h) and centimeters per second (cm/s). It just depends on what you're measuring and how precise you need to be.
________________________________________________________
How do things like distance and time affect the speed of an object?Well, speed is all about how far something goes in a certain amount of time. So if you increase the distance traveled or decrease the time it takes to travel that distance, the speed will increase. On the other hand, if you decrease the distance traveled or increase the time it takes to travel that distance, the speed will decrease.
Why is it important to measure and calculate speed in certain situations?There are all sorts of situations where knowing the speed of something is important. For example, if you're driving a car, it's important to know how fast you're going so you can stay safe and follow the speed limits. In sports, measuring speed can help coaches and players improve their performance. And in science, measuring the speed of light or other phenomena can help us better understand the world around us. So as you can see, speed is a pretty important concept!
Which matrix represents the system of equations shown below?
2x - 9y = 12
-5x - 7y = 15
O A.
[2 -9 12
5 -7 15
O B.
1-2 -9 127
5 -7 15
O C.
2 -9 127
-5 -7 15
O D. 13:53
1-2 -9 -121
-5 -7 -15
Answer:
c because c is c kkjwjwjjjwjwjsjssjsjjssmsswnsnsnsnnsns
The matrix that is represented by the system of equations is:
[tex]\left[\begin{array}{ccc}2&-9&12\\-5&-7&15\end{array}\right][/tex]
Option C is the correct answer.
What is a matrix?A matrix is a set of numbers arranged in rows and columns such that it forms a rectangular array.
We have,
Here, the coefficient matrix is the matrix on the left-hand side, the variable matrix is the column matrix containing the variables x and y, and the constant matrix is the column matrix on the right-hand side containing the constants 12 and 15.
To solve the system of equations, we can use matrix operations to transform the coefficient matrix into the identity matrix, while performing the same row operations on the variable matrix and the constant matrix.
Once we have transformed the coefficient matrix into the identity matrix, the variable matrix will be transformed into the solution vector containing the values of the variables x and y that satisfy the system of equations.
Thus,
The matrix that is represented by the system of equations is:
[tex]\left[\begin{array}{ccc}2&-9&12\\-5&-7&15\end{array}\right][/tex]
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A jar of coins contains only quarters and dimes. The total amount of money in the jar is $4.40, and there are 23 coins.
A. Write a system of equations that can be used to find d, the number of dimes, and q, the number of quarters, in the jar.
B. How many quarters are in the jar?
Answer:
(1) d+q=23 (the total number of coins is 23)
(2) 10d+25q = 440 (the total value of the coins, at 10 cents for each dime and 25 cents for each quarter, is 440 cents)
there are 14 quarters and 9 dimes
Step-by-step explanation:
what is the difference of 1 and a number?
r a t e me 1 0 and thank u
Answer:
10
Step-by-step explanation:
10/10 For sure. I see that musical ly logo. Good times
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Find the measure of the indicated angle. Need help please.
I need explanation,
thank you
Answer:
107
Step-by-step explanation:
Sum of all angles is 180
12+BC+61 = 180
73+ BC = 180
73 - 73 + BC = 180 - 73
BC = 107
Please provide step by step and answer what x and y is.
Answer:
Step-by-step explanation:
x=11
y=14
Pls answer! this problem
Answer:
9k + 36 represent the perimeter of the triangle. (I think)
Step-by-step explanation:
3k + 5 + 15 + 4k + 2k + 16 = the perimeter of the triangle
reorganize:
(3k + 4k + 2k) + (5 + 15 + 16)
9k + 36
Have a nice day!
What is the slope of an absolute value function?
Its slope is m = 1 on the right side of the vertex, and m = - 1 on the left side of the vertex.
Absolute Value Function:
An absolute value function is a function that contains an algebraic expression within the absolute value sign. Remember that the absolute value of a number is its distance from 0 on the number line. To graph the absolute value function, select some values of x and find some ordered pairs.
In mathematics, the absolute value or modulus of the real number x, represented as.
|x| is the non-negative value of x, regardless of sign.
x is positive and |xI =-x}. For example, the absolute value of 3 is 3, and the absolute value of -3 is also 3. The absolute value of a number can be thought of as the distance from zero.
Generalizations of the absolute value of real numbers are made in a variety of mathematical contexts. For example, absolute value is also defined for complex numbers, quaternions, ordinal rings, fields, and vector spaces. Absolute value is closely related to the concepts of magnitude, distance, and norm in various mathematical and physical contexts.
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please answer this quick thank u so much
Answer: 3 hours and 45 minutes
Step-by-step explanation:
We can see that the first clock is at 10:30 am (the short hand is the hour, and it's pointing at 10, and the long hand is the minutes, and it's pointing at 6, which would mean 30 minutes since you multiply 6 by 5)
The second clock is at 2:15 pm using the same logic.
12:00 is when the time changes from am to pm. So, find the time difference from 10:30 am to 12:00
Subtract 30 from 60, and we get thirty, so after 30 minutes, the time will change from 10:30 to 11:00. Then we have 1 hour from 11:00 to 12:00. This means that from 10:30 to 12:00, the time spent is 1 hour and 30 minutes.
Finally, we add 2 hours and 15 minutes, since that's the second time.
Add both those times together:
1 hour and 30 minutes plus 2 hours and 15 minutes = 3 hours and 45 minutes.
Answer:
4 hours and 45 minutes
Step-by-step explanation:
the first clock shows 10:30am and the second clocks shows to be at 2:15pm
which you count by hours is 10,11,12,1,2 so you went but 4 hours and 45 minutes
Roger averages 3 hits for every
12 times he is at bat. At this rate,
how many times must he bat to
get 12 hits?
Answer:
48
Step-by-step explanation:
if 3;12
12;X
so 3x=12 X 12
so x =48