Determine whether the following statement is always, sometimes, or never true. Explain your reasoning.
Every complex number has both a real part and an imaginary part.
Answers
The statement "Every complex number has both a real part and an imaginary part" is always true.
Every complex number is defined as a number of the form "a + bi," where "a" represents the real part and "bi" represents the imaginary part.
The real part "a" is a real number, and the imaginary part "bi" is a multiple of the imaginary unit "i," where "i" is defined as the square root of -1.
Even if a complex number has a zero imaginary part, it is still considered to have both a real and an imaginary part.
In that case, "a" represents the real part, and the imaginary part "bi" becomes zero.
For example, the complex number 3 + 0i is a real number (3) and can be represented as having a real part of 3 and an imaginary part of 0i.
In conclusion, every complex number by definition consists of both a real and an imaginary part, making the statement "Every complex number has both a real part and an imaginary part" always true.
To learn more about the complex number;
https://brainly.com/question/18392150
#SPJ3
Related Questions
ILL GIVE BRAINLIEST PLS HELP
Each statement describes a transformation of the graph of y = x. Which statement correctly describes the graph of y = x + 9.5?
A.
It is the graph of y = x translated 9.5 units to the right.
B.
It is the graph of y = x translated 9.5 units up.
C.
It is the graph of y = x where the slope is increased by 9.5.
D.
It is the graph of y = x translated 9.5 units down.
Answers
Answer:
Im pretty sure is B but it might be C.
Step-by-step explanation:
Write the equation of the line that passes through the points (-3,-5) and (3,1).
Answers
Answer:
Slope intercept form : y=x-1
Point slope form : y+5=1(x+3)
It cost Irene $60 to fill her car’s gas tank with 15 gallons of gas. Select all the rates that are equivalent to Irene's cost of gas.
Answers
Answer:
Where are the cost?
Step-by-step explanation:
Evaluate |-6| + 3|4| + |-5| -0×6.
O 0
O 25
O 23
O 18
Answers
636/526 pls answer and you get points
Answers
Answer:
1.20912547529
Step-by-step explanation:
For this graph, mark the statements that are true.
A. The range is the set of all real numbers.
7
B. The range is the set of all real numbers greater than or equal to
zero.
C. The domain is the set of all real numbers.
D. The domain is the set of all real numbers greater than or equal to
-2.
Answers
Answer:
B and C are true
Step-by-step explanation: range is y values the graph can have from 0 up
domain in x values the graph can have so all number in either direction left and right
Answer:
Step-by-step explanation: The answer is B and C because range is y and it is greater than 0 and domain is x and is go infinitely in both directions
12 = 2x + 4x
solve and show your work. pls help.
i didn't pay attention to the class
Answers
Answer:
x=2
Step-by-step explanation:
Let's solve your equation step-by-step.
Step 1: Simplify both sides of the equation.
12=2x+4x
12=(2x+4x)(Combine Like Terms)
12=6x
12=6x
Step 2: Flip the equation.
6x=12
Step 3: Divide both sides by 6. 6x/6=12/6
x=2
Hope you found this helpful and have good day (.
Answer:
2
Step-by-step explanation:
plus the like-terms (x plus x): 2+4
so 12=6x. get 6 out of the x-term. X is the unknown number being multiplied by 6. To get it to the other side, divide the numbers. So: 12/6=x and 12/6 is 2. so x=2.
A water tank in Stewart's
home had a small, steady
leak.
Loss of 1 3/5 mL in 10 min.
a. Use a complex fraction to
represent the change in the
volume of water in 1 minute.
___ milliliters
10 minutes
b. Simplify the complex fraction to find the change in the volume of water in the tank in 1 minute.
Answers
The change in the volume of water in 1 minute is a decrease of 0.16 milliliters.
Since a water tank in Stewart's home had a small, steady leak loss of 1 3/5 mL in 10 min, to find the change in the volume of water in 1 minute, the following calculation must be performed:
The total leak must be calculated and divided by the 10 minutes duration. 3/5 = 0.6 1 + 0.6 = 1.6 1.6 / 10 = 0.16
Therefore, the change in the volume of water in 1 minute is a decrease of 0.16 milliliters.
Learn more in https://brainly.com/question/19747831
Help me pretty pleeaaasse? :) I will mark brainliest.
Answers
Answer:
<R = 30
LM = 6 sqrt(3)
Step-by-step explanation:
Since the figures are congruent
<R = < L
<S = <M
< T = <N
RS = LM
ST = MN
RT = LN
<L = 30 so <R = 30
RS = 6 sqrt(3) so LM = 6 sqrt(3)
The Candela brothers own two pizza restaurants, one on Park Street and one on Bridge Road.
The computer output below summarizes the distribution of weekly revenues at each
restaurantâ€"26 weeks for Park Street and 40 weeks for Bridge Avenue.
Answers
The mean, median and mode are measures of central tendency, that is they tend to indicate the location middle of the data
Required values;
(a) The performance for the week for Park Street
Revenue is Q₂ < $7,500 < Q₃The sales for the week is better than 72.91% of all salesThe performance for the week for Bridge Road
Revenue; Q₂ < $7,100 < Q₃The sale for the week is better than 59.87% of all sales(b) The mean is $3611
The median is $3,600
The standard deviation is $3250
The Interquartile range is $6075
Reason:
The table of values that maybe used to find a solution to the question is given as follows;
[tex]\begin{array}{|l|l|l|}\mathbf{Variable} &\mathbf{Park}&\mathbf{Bridge}\\N&36&40\\Mean&6611&5989\\SE \ Mean&597&299\\StDev&3580&1794\\Minimum&800&1800\\Q_1&3600&5225\\Median&6600&6000\\Q_3&9675&7625\\Maximum&14100&8600\end{array}\right][/tex]
(a) Park Street revenue = $7,500
Bridge Road's revenue = $7,100
The two stores sold close to but below the 75th percentile
Bridge Road revenue;
The z-score is given as follows;
[tex]Z = \dfrac{x - \mu }{\sigma }[/tex]
[tex]Z = \dfrac{7100 - 5,989 }{1794 } \approx 0.6193[/tex]From the Z-Table, we have;
The percentile= 0.7291
Therefore, the sale for the week for Park Street is better than 72.91% of all the salesPark Street revenue;
The z-score is given as follows;
[tex]Z = \dfrac{7500 - 6611}{3580} \approx 0.25[/tex]From the Z-Table, we have;
The percentile = 0.5987
Therefore, the sale for the week is better than 59.87 % of all the sales(b) Given that the operating cost is $3,000, frim which we have;
The subtracted value is subtracted from the mean and median to find the new value
Profit = The revenue - Cost
New mean = 6611 - 3000 = 3611
The new mean = $3,611The new median = 6600 - 3000 = 3600
The new median = $3,600The standard deviation and the interquartile range remain the same, therefore, we have;
The standard deviation = $3,580The interquartile range = 9675 - 3600 = 6075
The interquartile range = 6075Learn more here:
https://brainly.com/question/21133077
https://brainly.com/question/23305909
the mean of eight numners is 41 the mean of two of the numbers is 29 work out the mean of the other six numbers
Answers
Answer: 270/6 =45
Step-by-step explanation:
There are 3 different sets of numbers involved here.
A set of six, a set of two and the set of all eight.
Each set has its own mean.
Question 15
5 pts
Nicole babysits on the weekends. She charges a
flat fee of $10 and then $5 per hour. If she made
$40 on Friday night, how many hours did she
babysit?
Choose the equation to represent this situation.
O
o 10h + 40 = 5
10h + 5 = 40
o 5 + 10 = 40h
o 5h + 10 = 40
-
Answers
Some help PLZ make sure it’s right will mark brainiest:)
Answers
Answer:
y= 7/9x -17/9
Step-by-step explanation:
(5,2) (-4,-5)
slope intercept of a line is
y = mx +b
m = y2-y1/ x2-x1
= -5-2/ -4-5 = -7/-9
=7/9
if the line is passing through (5,2)
2= 7/9(5)+ b
2=35/9 +b
b = 2-35/9
b= -17/9
y= 7/9x -17/9
is 1/3 more than the number 3?
Answers
Answer:
1/3 is less than 3
Step-by-step explanation:
1/3 = 0.3333 which is less than 3
Hugh drove on the highway at a constant rate. He traveled 204 miles in 3 hours. How far did hugh travel in 1 hour? At what rate was he traveling?
Answers
Find an equation of the line with slope 3 that
contains the point (7.11).
y = mx + b
Answers
Solve for c. 2a + 3b = c
Please help as soon as possible. Thanks! =D
Answers
Answer:
a = c - 3b/2
Step-by-step explanation:
2a + 3b - 3b = c - 3b
2a = c - 3b
2a/2 = c/2 - 3b/2
therefore your answer is a = c - 3b/2
In 2012 Joe had $ 104
in his bank account. BY
2017 he had $889 in his
account. Determine
the annual rate of
change.
Answers
Answer:
$157Step-by-step explanation:
The amount of change is:
889 - 104 = 785The time difference in years:
2017 - 2012 = 5The annual rate of change is the ratio of the difference in amount to the time difference:
785/5 = 157A large rectangle is made up of nine identical rectangles whose longer side equals 10. What is the area of the large rectangle?
Answers
• The middle row has 5 rectangles with all of their short sides equaling the top row, 20
• So 5x = 20 where x is the short side of the rectangle
• x = 4
• So each rectangle’s area = 4 x 10 = 40
• There are 9 rectangles
• So 9 x 40 = 360 = area of the large rectangle
• We can check our work
• Large rectangle side 1 = 10 + 10 = 20
• Large rectangle side 2 = 4 + 10 + 4 = 18
• 18 x 20 = 360
==========================================================
Explanation:
Refer to the diagram below.
A small rectangle has its longer side equal to 10 and its shorter side is x, which is some real number on the interval 0 < x < 10.
Across the top, the two sides of length 10 add to 20. So the larger rectangle has a horizontal dimension of 20 units.
The vertical side of the larger rectangle is x+10+x = 2x+10 units
The area would be
area = length*width = 20(2x+10) = 40x+200
Each of the nine smaller rectangles has area of length*width = 10x. Since we have 9 identical copies, the smaller rectangle areas must add to 9*10x = 90x
---------------
Equate those two expressions and solve for x
90x = 40x+200
90x-40x = 200
50x = 200
x = 200/50
x = 4
So each smaller rectangle has area of 10*x = 10*4 = 40 square units. In total, the nine smaller rectangles combine to an area of 9*40 = 360 square units
Note how x = 4 leads 40x+200 to result in 360 as well.
Need Helpp!!!
Line segment CD is shown on a coordinate grid:
The line segment is reflected about the y- axis to from C’D’.
Which statement describes C’D’
C’D’ is perpendicular to CD
C’D is half the length of CD
C’D’ is greater than twice the length of CD
C’D’ and CD are equal in length
Thanks!
Answers
Answer: -1.56i^ +1.07j^
Step-by-step explanation:Vector C = -1.56i^ +1.07j^
This question requires that we use the properties of the scalar product of two vectors to find the required x and y component.
The dot product of two perpendicular vectors is equal to and the product of two vectors that are not parallel is equal to a nonzero value.
These are the properties that have been used in solving this problem alongside solving the simultaneous questions generator.
Explanation:
The full solution can be found in the attachment below.
Thank you for reading and I hope this post is helpful to you.
work out the value of 3^2 + 2^3
Answers
Answer:
17
Step-by-step explanation:
3² + 2³
= 9 + 8
= 17
Answer:
3/2 can be written as 3*1/2.
Now in 3*1/2 apply PEDMAS
3*0.5
Now multiply 3 with 0.5
The answer is 1.5…
3/2 means half of a three that is 1.5…it is fraction form of 1.5…
Step-by-step explanation:
The manager of a food court estimates that he needs 7 pretzels for every 20 people who attend a hockey game. What constant of proportionality relates the number of pretzels to people?
A. 0.35
B. 2.86
C. 35
D. 140
Answers
Answer:
a) 0.35
Step-by-step explanation:
The manager of a food court estimated that he needed 7 pretzels for every 20 people who attend that hockey game. This means that 20 people need/require to have 7 pretzels. 20 people= 7 pretzels.
Plz help! A,B,C OR D
Answers
Answer:
c
Step-by-step explanation:
Answer:
Option DStep-by-step explanation:
All steps correct apart from the last one.
The student worked out the value of b = 4.4 but when finalizing the equation he subtracted 4.4 instead of adding:
y = -2x + 4.4 ⇒ correcty = -2x - 4.4 ⇒ wrongCorrect answer choice is D
8th grade algebra pleas help
Answers
Write the slope-intercept form of the equation for each line.
Answers
Answer:
y = x + 2
Step-by-step explanation:
Slope = 1x
y-intercept = 2
y = x + 2
2(x-y)(x+y)+(x+y)^2+(x-y)^2
Answers
Hope it helps
Select ALL that could take P to Q:
Answers
Answer:
No question.
Step-by-step explanation:
Help me, please!!!
Lesson 3-8. Write an equation for the line perpendicular to the given line through the given point.
Answers
Answer:
y = -3x + 14Step-by-step explanation:
Given line:
y = 1/3x - 2/5Perpendicular lines have negative-reciprocal slopes.
We will have a line:
y = -3x + bUse the coordinates of the given point to find the value of b:
-1 = -3(5) + b-1 = - 15 + bb = 14So the line is:
y = -3x + 14Exit
What is the decimal equivalent of 4/5
Answers
Answer:
0.8
Step-by-step explanation:
to find the decimal equivalent we must get the denominator to 100
to do that we must multiply it by 20, 4/5 * 20/20 is 80/100
80/100 is also 80%, which is also 0.80 (which can be simplified to 0.8)
plz help me solving me math questions