Answer:
In mathematics, a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a symbol, called the imaginary unit, that satisfies the equation i² = −1. Because no real number satisfies this equation, i was called an imaginary number by René Descartes.
Step-by-step explanation:
Complex Integer
(or Gaussian integer), a number of the form a + bi, where a and b are integers. An example is 4 – 7i. Geometrically, complex integers are represented by the points of the complex plane that have integral coordinates.
Complex integers were introduced by K. Gauss in 1831 in his investigation of the theory of biquadratic residues. The advances made in such areas of number theory as the theory of higher-degree residues and Fermat’s theorem through the use of complex integers helped clarify the role of complex numbers in mathematics. The further development of the theory of complex integers led to the creation of the theory of algebraic integers.
The arithmetic of complex integers is similar to that of integers. The sum, difference, and product of complex integers are complex integers; in other words, the complex integers form a ring.
Answer:
An immediate consequence of the definition of arithmetical operations on complex numbers is that the sum, the difference, and the product of two or more complex numbers.
Step-by-step explanation:
Anna starts a fixed deposit with $178000, the bank offers 9.5% per year simple interest for 8 months. she has the option of restarting the investment using the interest earned as principal or cashing out at the end of the 8 months, (A) Calculate the interest due after 8 months. (B) if she restarts the investment into a new one calculate the total value of the investment at the end of the second 8 months
Using simple interest, we have that:
A) The interest due after 8 months is $11,272.33.
B) The total value of the investment will be of $189,986.24.
The amount of interest earning using simple interest, after t years, with an yearly interest rate of i and an initial investment of P is given by:
[tex]E = Pit[/tex]
In this problem:
Deposit of $178,000, hence [tex]P = 178000[/tex].Interest rate of 9.5% per year, hence [tex]i = 0.095[/tex].8 months, the time is in years, hence [tex]t = \frac{8}{12} = \frac{2}{3}[/tex]Item a:
[tex]E = Pit[/tex]
[tex]E = 178000(0.095)\frac{2}{3} = 11272.33[/tex]
The interest due after 8 months is $11,272.33.
Item b:
For the second interest, we consider [tex]P = 11272.33[/tex], hence:
[tex]E_2 = Pit[/tex]
[tex]E_2 = 11272.33(0.095)\frac{2}{3} = 713.91[/tex]
The total value will be composed by:
The initial deposit of $178,000.The first interest of $11,272.33.The second interest of $713,91.Hence, it will be:
[tex]T = 178000 + 11272.33 + 713.91 = 189986.24[/tex]
The total value of the investment will be of $189,986.24.
A similar problem is given at https://brainly.com/question/13176347
Please help i attached a link below to the graph
Write the linear inequality shown in the graph. The gray area represents the shaded region.
y ≥ –x – 4
y ≥ –x + 4
y ≤ –x – 4
y ≤ –x + 4
Answer: y ≤ -y+4
Step-by-step explanation:
The line in the graph:
Taking two points, we can calculate the slope of the line. I'll pick (0,4) and (4,0)
Rise/Run (slope): Rise (0-4) = -4, Run = (4-0) = 4. Slope is -4/4 or -1.
The y-intercept is 4 (the value of y when x is zero).
The equation for the line is y = -x + 4. The shades area includes all points on and under this line, so y ≤ -y+4.
Steve had 1400 pesos. Heloaned 500 pesos to a friend, spent 310 pesos, and received his800 pesos paycheck from work. How much money does he have now?
Answer:
1390
Step-by-step explanation:
1400- 500= 900 (loaned → deduction→ meaning subtraction)
900- 310 = 590 (spent→ deduction→ meaning subtraction)
590 + 800 = 1390 (received→ gained→ addition)
5.6 reccuring
as a fraction
Answer:17/3 or 5 and 2/3
Sorry for the spam, I really need help.
Answer:
x=8
y=18
Step-by-step explanation:
[tex](3x+13)+(7x-3)=90[/tex]
[tex]10x+10=90[/tex]
[tex]10x=90-10[/tex]
[tex]x=\frac{80}{10} =8[/tex]
[tex]3x+13=3(8)+13=24+13=37[/tex]
[tex]5y=180-37-53=90[/tex]
[tex]y=\frac{90}{5} =18[/tex]
I hope this help you
(04.01 MC) Which set of points includes all of the solutions for y = negative four fifths times x plus two?line going through 0 comma 2 and 5 comma negative 2 Group of answer choices (15, 10), (0, 2), and (−10, 10) (−10, 10), (−5, 6), (0, 2), (5, −2), (10, −6) (x, y) for all real numbers (x, negative four fifths times x plus two) for all real numbers
The solutions of a function are the true values of the function
The solutions are: (0,2), (5,-2), (-10, 10) and (-5,6)
The function is given as:
[tex]\mathbf{y = -\frac 45 x + 2}[/tex]
From the question, we understand that the line of the equation passes through points (0,2) and (5,-2)
This means that:
(0,2) and (5,-2) are solutions of the equation
Other possible solutions include (-10, 10) and (-5,6)
This is true because, when these values are substituted in the equation, the result of the equation is true
Hence, the true options are:
(0,2), (5,-2), (-10, 10) and (-5,6)
Read more about solutions of equations at:
https://brainly.com/question/545403
14 +6p = 5+3 p
what's the answer to this equation
Answer:
19 = -3p
Step-by-step explanation:
14 +6p =5 +3p
c.l.t
14 +5 = -6p + 3p
19 = -3p
Solve each inequality
-5y-2<8
Answer:
y > -2
Step-by-step explanation:
-5y-2<8
= -5y<8+2
= -5y<10
= y > 10/-5
∴ y > -2
Note: Anytime you multiply or divide both sides of the inequality, you must “flip” or change the direction of the inequality sign.
answer in feet and inches
b) (2 yd. 2 ft.) + (7 yd. 9 in)
Answer:
12 feet 9 inches
Step-by-step explanation:
There are 3 feet in a yard, and 12 inches in a foot. Multiply those together and you get 36 inches in a yard.
2 yards × 36 inches/yard = 72 inches
2 feet × 12 inches/foot = 24 inches
72 inches + 24 inches = 96 inches
------------
7 yards × 36 inches/yard = 252 inches
252 inches + 9 inches = 261 inches
==============
Add those together:
96 inches + 261 inches = 357 inches
Then to convert to feet again, you need to divide by 12 and find the remainder. I prefer to do it with a calculator like this, but you can do it however you prefer:
357 ÷ 12 = 29.75 feet (round down)
12 × 29 = 348 inches in 12 feet
Then find the remainder:
357 - 348 = 9 inches
12 feet 9 inches
Given 2x² = -8, x is
A) -2
B) 2
C) 2i or -2i
B) 4i or -4i
NO LINKS!!!
Answer:
2x^2=-8
2x^2/2=-8/2
x^2=-4
x=2
Step-by-step explanation:
HOPE THAT THIS IS HELPFUL.
HAVE AN AWESOME DAY.
Also need this answer. Thank you so much!!!!!!!!
Answer:
5
Step-by-step explanation:
h(w)=2(1)+3
h(w)=2+3
h(w)=5
please give me brainliest think took some thinking
Janie has "buy one get one free" tickets to the comedy club. She is bringing 7 people, including herself.
If the regular price is $12.25 per person, how much change will she have left from a $100 bill?
$63.25
$57.00
$51.00
$14.25
Answer:
$51.00
Step-by-step explanation:
how do i simplify these?
. X x X x X
.Y x Y x Y x Y x Y
Hello!
X*X*X=X times X times X = X³
Y*Y*Y*Y*Y=Y times Y times Y times Y times Y= Y⁵
Hope it helps you! :)
Let me know if you have any query or need further explanation. :)
~A determined gal
[tex]MagicalNature[/tex]
What is the equation in slope-intercept form of the line that passes through the point (5, 0) and is parallel to the line represented by =2.2+1.2
y
=
2.2
x
+
1.2
.
Group of answer choices
=−2.2+11
y
=
−
2.2
x
+
11
=2.2−11
y
=
2.2
x
−
11
=−2.2−5
y
=
−
2.2
x
−
5
=2.2+5
PLEASE HELP!!
100 POINTS
5^a = 2^b = 10, what is a^-1 +b^-1
Answer:
1.
Step-by-step explanation:
5^a = 10
a log 5 = log 10
a log 5 = 1
a = 1 /log 5
a^-1 = log 5
In the same way:
b = 1 / log 2
b^-1 = log 2,
So a^1 + b^-1 = log5 + log 2 = log (2*5)
= log 10
= 1.
pls help will mark as brainlist
Step-by-step explanation:
In n -sided polygon,
sum of interior angles =(n−2)×180°
Hexagon has 6 side
n=6
sum of interior angles of a hexagon =(6−2)×180°
=720°.
______________________________________
In n -sided polygon,
sum of interior angles =(n−2)×180°
Hexagon has 10 side
n=10
sum of interior angles of a hexagon =(10−2)×180°
=1440°.
hope this helps you.
Consider the line y=6/7 x -7. Find the equation of the line that is perpendicular to this line and passes through the point (6,-6). Find the equation of the line that is parallel to this line and passes through the point (6,-6) .
Answer:
[tex]y= -\frac76x +1[/tex]; [tex]y= \frac67x -\frac{78}7[/tex]
Step-by-step explanation:
We know from theory that two perpendicular lines have the product of their slope equal to -1. Let's find the second slope:
[tex]\frac67m = -1 \rightarrow m=-\frac76[/tex]
At this point we can just use the slope-point equation to get our first line:
[tex]y-y_0 = m(x-x_0)\\y-(-6) = -\frac76(x-6) \\y+6= -\frac76x +7\\y= -\frac76x +1[/tex]
Now, we know that two parallel lines have the same slope. Time to apply the same point-slope formula, with the original m this time.
[tex]y-(-6) = \frac67(x-6)\\y+6 = \frac67x -\frac{36}7\\y= \frac67x -\frac{36}7 -{\frac{42}7[/tex]
[tex]y= \frac67x -\frac{78}7[/tex]
Solve 22 x 104 = ________. (1 point) A. 2,200,000 B. 220,000 C. 22,000 D. 2,200
[tex]22 \times {10}^{4} \\ = 22 \times 10 \times 10 \times 10 \times 10 \\ = 22 \times 10000 \\ = 220000[/tex]
Answer:B. 220,000
Hope it helps.
Do comment if you have any query.
help me with this pls asap
Answer: 0.29
Step-by-step explanation:
Divide x by y. See attachment.
Time(h)
Distance (mi)
12 3 4 5
14 26 38 50 62
The table shows Eli's distance from home as he
rides his bike at a steady rate after meeting a
friend. Write an equation in slope-intercept form
that represents the miles, y, that Eli goes in x hours.
y = 12x + 2
y = 2x + 2
y = 12x + 12
y = 2x + 12
Answer:
y = 12x + 2
Step-by-step explanation:
To know:
[] These equations are in y = mx + b form
() Also known as slope-intercept form
() m is the slope
() b is the y-intercept
Now, let's solve
[] Slope / m
() Slope is "change in y over change in x," let hours be our x and distance by our y
() [tex]\frac{62 - 14}{5 - 1}=\frac{48}{4}=12[/tex]
[] Y-intercept / b
() We will plug in a set of points into our current equation, then solve for b
() y = mx + b -> y = 12x + b -> 14 = 12(1) + b -> 14 = 12 + b -> 2 = b
Last, we will find our answer
Our b is 2, and our m is 12. This leaves us with option 1, y = 12x + 2
Have a nice day! - table I made is attached
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
5/6 divided by 2 =?
Need answer soon!!
Answer:
0.416666667
Step-by-step explanation:
(winks and runs off)
Answer:
5/12
Step-by-step explanation:
5/6÷2
5/6÷2/1
5/6•1/2
5/12
Can I get some help..please?
Answer:
-2 and 21/50
Step-by-step explanation:
PEMDAS says that paranthases go first, so we solve 2 and 1/5 minus 33/12. 2 and 1/5 simplifies to the improper fraction, 11/5. Then we find a common denominater between 11/5 and 33/12 to get 60. 11/5=132/60, and 33/12=165/60. (132/60)-(165/60)=-33/60. Then we multipl that by 4 and 2/5, which can simplify to the improper fraction, 22/5. (22/5)*(-33/60) is -726/300, and simplifies to -2 and 21/50. Hope this helps!
Fraction of alphabets in word PRAKASH made of 3 straight line is
please right answer due is tomorrow
Answer:
The answer 4/7
Step-by-step explanation:
A K A H
4 letters in the word PRAKASH are made of 3 straight lines. That's why the fraction is 4/7.
In the word, 4/7 fraction of the letters is made up of 3 straight lines.
What is a fraction?A fraction is written in the form of p/q, where q ≠ 0.
Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.
In the word PRAKASH, there are 7 letters, In which 2 A's, 1 K, and 1 H is made up of 3 straight lines so (2 + 1 + 1) = 4.
∴ The fraction of the alphabet made up of three straight lines is,
= 4/7
learn more about fractions here :
https://brainly.com/question/10354322
#SPJ2
Which of the following is(are) the solution(s) to |11x +3 = 6 ?
In ⊙V, QT ≅ RS. If UV = 4 cm, then VW = _______ cm.
Answer:
VW = 4 cm
Step-by-step explanation:
Congruent chords are equidistant from the centre , so
VW = UV = 4 cm
6 less than the quotient of 4 and a number
Answer:
4/n subtracted by 6 or the third option
Step-by-step explanation:
If 12 inches = 1 foot, and 3 feet = 1 yard, how many inches are there in 2.5 yards? step by step
Could someone please help?
Answer:
snap for secsy pics
Step-by-step explanation:
cat.lover
How much is 25% of a 4 gallon jug of milk?
the answer is 1 because .25x4=1
Answer:
1 gallon
Step-by-step explanation:
4 / 4 = 1
(because 25% is 1/4 of 100%)
:)
On the grid below, which point is located in the quadrant where the x-coordinate is a positive number and the y-coordinate is a negative number?
A coordinate plane is shown. Point A is in quadrant 1, point B is in quadrant 2, point C is in quadrant 3, and point D is in quadrant 4.
A
B
C
D
hurry!!
Answer:
The answer is A.......
Step-by-step explanation: