Simplify completely.
(2 + 3i) + (-4+i)
Answer:
-2+4i
Step-by-step explanation:
Simplify by combining the real and imaginary parts of each expression.
The simplified form of the complex expression is -2 + 4i.
What are Complex Numbers?Complex numbers are numbers which are of the form [tex]a+ib[/tex],
where a and b are real numbers and i is the imaginary number called iota whose value is [tex]i^{2}[/tex] = -1.
Given expression is (2 + 3i) + (-4 + i).
Addition of complex numbers is defined as,
(a + ib) + (a' + ib') = (a + a') + i(b + b')
Using the definition of addition of complex numbers, given expression can be added as,
(2 + 3i) + (-4 + i) = (2 + -4) + i(3 + 1) = -2 + 4i
Hence the resulting value is -2 + 4i.
To learn more about Complex Numbers, click on the link given below :
https://brainly.com/question/28007020
#SPJ2
1.
The distance from the Sun to Mercury is 3.598. 10^7
miles. The distance from the Sun to Neptune is
2.798. 10^9 miles. How far is Mercury from Neptune?
Write your answer in scientific notation.
Answer:
Exponente positivo
Potencias de 10
Escribe estos números en forma ordinaria:
7'3·103; 4'724·108; 8'24·105
Notación científica. Orden de magnitud. Comparaciones
Expresa en notación científica las siguientes cantidades e indica su orden de magnitud.
235'74; 1985; 12 billones; 320 millones; 37.800.000.000; 220.000.
La desaparición de los dinosaurios ocurrió hace 65 millones de años, aproximadamente 108 años. Por ello hemos situado la D debajo de la potencia correspondiente:
El nacimiento del Universo (U) ocurrió hace 15 mil millones de años . Sitúa U en la casilla que le corresponde. Haz lo mismo con:
El califato cordobés de Abderramán (A): aproximadamente 800 años.
El control, del fuego (F): hace 600.000 años.
Aparición del hombre de Cromagnon (C): 30.000 años.
El nacimiento de la Tierra: (T): 4.5 mil millones de años.
El primer paso del hombre en la Luna (L): hace una veintena de años.
El primer paso del hombre en la Tierra (H): tres millones de años
La invención de la imprenta por Gutenberg (G): hace 550 años.
La nebulosa "Triangulum" está a 1'4·1022 metros de la Tierra. Escribe esta distancia en forma ordinaria.
Step-by-step explanation:
Find the volume of a pyramid with a square base, where the perimeter of the base is
18.5 ft and the height of the pyramid is 7.6 ft. Round your answer to the nearest
tenth of a cubic foot.
Answer:
132 cm. 3. 3. a rectangular pyramid with a height of 5.2 meters and a base 8 ... 7. an oblique cone with a height of 10.5 millimeters and a radius of 1.6 ... base is about 15,400 square feet, find the volume of air that the ... ANSWER: 32.2 ft. 3. Find the volume of each solid. Round to the nearest tenth. eSolutions ...
Step-by-step explanation:
Robert has x books. Marie has twice as many books as Robert has. Together they have 18 books. Which of the following equations can be used to find the number of books that Robert has? Choose one multiple choice answer
x+2=18
x+x+2=18
x+2x=18
2x=18
Answer:
the answer: x+2x=18
Step-by-step explanation:
HELP ME ASAP!!!!!!!!!
Hello, please do not cheat on classwork on brainly, as this is against the honor code. Please do not continue this activity.
help me please !! Geometry
Tucker goes to bed at 8:25 pm every
night. He wakes up at 6:45 am. How
long does Tucker sleep each night?
Answer:
10 hours and 20 minutes.
Step-by-step explanation:
We can find out how many hours of sleep Tucker gets every night by counting in one-hour intervals.
One hour from 8:25 is 9:25.
9:25, 10:25, 11:25, 12:25, 1:25, 2:25, 3:25, 4:25, 5:25, 6:25.
This is 10 hours.
Now we count in ten-minute intervals to get to 6:45
6:35, 6:45.
This is 20 minutes.
Therefore, Tucker gets 10 hours and 20 minutes of sleep each night.
This is equivalent to 620 minutes.
===================================================
Explanation:
The user purrugh has a great answer. I'll provide a slightly different approach.
The timespan from 8:25 PM to 9:00 PM is 35 minutes. Note how adding 35 minutes to 25 past the hour gets us to 25+35 = 60 minutes, so we're at the top of the hour now, and at 9 o' clock on the dot.
Then from 9 PM to 12 midnight is a gap of 3 hours (because 12-9 = 3). From midnight to 6 AM is another 6 hours. So far we have 3+6 = 9 hours, plus the additional 35 minutes mentioned earlier. The duration so far is 9 hours, 35 minutes. We still have to account for another 45 minutes, since we want to get to 6:45 AM and not 6:00 AM.
Note how 35+45 = 80, which is over 60. This means 35 min + 45 min = 80 min = (60 min) + (20 min) = 1 hr, 20 min
That "1 hr, 20 min" is added onto the "9 hours" from earlier and we arrive at 10 hours, 20 minutes as the final answer
-----------------------------
Yet another approach is to do everything in minutes, and then convert to hours,minutes format at the very end.
Again the gap from 8:25 PM to 9:00 PM is 35 minutes. From 9 PM to midnight is 3 hours, or 3*60 = 180 minutes. We have a duration so far of 35+180 = 215 minutes.
From midnight to 6 AM is 6*60 = 360 minutes. The duration has been updated to 360+215 = 575 minutes. Finally, from 6 AM to 6:45 AM is the last gap of 45 min to get us to 575+45 = 620 minutes.
Tucker slept a total of 620 minutes. Let's convert that to hours,minutes format. Note how 620 = 600+20 and how 600/60 = 10. Meaning that 600 minutes = 10 hours. Therefore,
620 min = (600 min) + (20 min) = 10 hours, 20 minutes
A tank that holds 6000 gallons of water may be filled by two pipes. One pipe pours water into the tank at the rate of 80 gallons per minute. The other fills the tank at the rate of 120 gallons per minute.
(a) If the pipes run simultaneously, how long will it take to fill the tank?
(b) The small pipe is opened and water is run into the tank for a certain length of time. Then this pipe is shut off and the large one is used to finish filling the tank. How long was each pipe used if it took 60 minutes to fill the tank?
(c) The large pipe alone is opened for a certain time and then both pipes together are used to finish filling the tank. If it takes 34 minutes to fill the tank in this manner, how long was the small pipe used?
Answer:
Below.
Step-by-step explanation:
Working together the rate is 80 + 120 = 200 gallons per minute.
(a) Time to fill tank = 6000 / 200 = 30 minutes.
(b) Let length of time the small pipe was used be x minutes , the the large pipe was used for is 60-x minutes.
Volume delivered by small pipe = y gallons, and by large pipe = 6000-y gallons.
Rate for small pipe = 80 = y/x.
Rate for large pipe = 120 = (6000-y) / 60-x.
y/x = 80
(6000-y) / 60-x = 120
From first equation y = 80x so:
6000 - 80 x = 7200 - 120x
40x = 1200
x = 30
So time for small pipe = 30 and time for large on = 30 minutes also.
C. In a similar way to part B:
y/x = 120
(6000-y) / 34 - x = 200
(6000-120x) / 34 - x = 200
6000 - 120x = 6800 - 200x
80x = 800 so the large pipe on its own took 10 minutes and the small pipe was used for 34 - 10 = 24 minutes.
3a=12; a =
b+3.3=8.9; b =
1=14c; c =
512=d+14; d =
2e=6.4; e =
help? Please!
Answer:
a=4
Step-by-step explanation:
3a=12
a=12/3
a=4
b+3.3=8.9
b=8.9-3.3
b=5.6
1=14c
1/14=14c/14
1/14=c
512=d+14
512-14=d
498=d
2e=6.4
2e/2=6.4/2
e=3.2
would -60 be the opposite of 60?
Answer:
yes,please mark me brainlest
Step-by-step explanation:
Answer:
Yes.
Step-by-step explanation:
A negative number is the opposite of it's positive.
Juan decided to start savings for college. He deposited $500 into an account which earns 4% simple annual interest. At the end of each year, he will add $250 to this account. How much will he have in his account after the end of three years?
a
$550
b
$770
c
$1,050.80
d
$1,342.83
Answer
I am getting a different answer The reason being the first year we calculating the 4% of the initial amount of the $500 towards the end of the year if he deposits the 250 the second year he gets to have a 4% interest of the 750 in total If he deposits the 250 in the 3rd he gets to have a 4% of 1000 So if you actually calculate that and get the total of all the amount which is 1,000 plus the percentages of all that you get what I've shared
9514 1404 393
Answer:
d $1342.83
Step-by-step explanation:
At the end of the first year, the account balance will be $500 plus 4% interest on that amount, plus the $250 deposited at the end of the year:
$500(1.04) +250 = $770
At the end of the second year, the account balance will be $770 plus 4% interest on that amount, plus the $250 deposited at the end of the year:
$770(1.04) +250 = $1050.80
At the end of the third year, the account balance will be $1050.80 plus 4% interest on that amount, plus the $250 deposited at the end of the year:
$1050.80(1.04) +250 = $1342.83
_____
Additional comment
You can make an appropriate guess by realizing the total of the deposits is ...
$500 + 3×250 = $1250
Adding interest to that will increase the amount. The only answer choice greater than $1250 is $1342.83.
Find the solution for the system of equations using substitution.
Answer:
x= 7/3
Step-by-step explanation:
y=2x+5
5x-2=2x+5
transfer 2x to the left side and -2 to the right side you get
5x-2x=2+5
as it transfers the sign changes
3x=7
x=7/3
Please help will give brainliest
Answer:
C. 120
Step-by-step explanation:
B × H
(base) × (height)
15 × 8 = 120
Answer:
120
Step-by-step explanation:
Parallelogram= length times width so
15*8=120
PLEASE HELPP I NEED TO GET A GOOD GRADE :(((((((((((((((9
Answer:
circumference = 2 π r
perimeter = 41.1 ,
Step-by-step explanation:
Write an equation for this graph. (Use / for division and * for multiplication; do not include spaces in your answer)
Answer:
The equation of the line is;
y = 4x
Step-by-step explanation:
The general equation form of a straight line is;
y = mx + b
m
is the slope and b is the y-intercept
The graph passes through the origin and that means the y -intercept is 0
To get the value of the slope, we select any point on the graph and substitute its coordinates
Let’s select point (1,4)
Substitute this;
4 = m(1) + 0
m = 4
Thus, the equation of the line is;
y = 4x
I need help! Answer this please! I will give brainliest!! ASAP
Answer:
it's 9 or 21
Step-by-step explanation:
Given cos x = 3/5 and 3pi /2 < x < 2 and sin y = ─ square root 2/2,
and < y < 3pi /2; evaluate tan (x ─ y).
Answer:
Step-by-step explanation:
everyone do me a favor and nominate "thebecks" as the educator of th.e year!
Answer:
will do
Step-by-step explanation:
and hello friend lol :)
Answer:
imma bout to answer my own question
Step-by-step explanation:
You deposit $300 dollars in a savings account the account earns 10% simple interest per year whats the interest after 8 years
Answer:
$240
Step-by-step explanation:
Given data
Principal= $300
Rate= 10%
Time= 8 years
We know that the expression for the simple interest is given as
SI= PRT/100
Substitute
SI= 300*10*8/100
SI= 24000/100
SI= $240
Hence the interest is $240
6. You are planning a trip. You can go to Phoenix, Las Vegas, San Diego, or Los Angeles. You can
fly or drive. You can stay 3, 4, or 5 days. How many different trip possibilities are there?
How many different trip possibilities are there?
Answer:
There are 24 different trip possibilities.
Step-by-step explanation:
Here the first thing we need to find is all the individual events, such that each event (or selection) will have a given number of options.
The first event is the selection of the location.
Here the options are: Phoenix, Las Vegas, San Diego, or Los Angeles (4 options)
The second event is the selection of how you go there.
The options are flying or driving (2 options)
The third event is the selection of how many days you will stay there. The options are 3 days, 4 days, and 5 days (3 options).
The total number of different trip possibilities is equal to the product between the number of options for each event.
P = 4*2*3 = 24
There are 24 different trip possibilities.
4x > 20 Is x=12 a solution?
yes or no
no
Hope this helps
:T
:B
:D
From what we have, x can equal 12
4x > 20
20/4 = 5
x > 5
12 > 5
Consider the diagram below. Given tir tix til Which triangle was constructed congruent to the given triangle?
Answer: The anwser is Triangle 2
The given triangle is congruent to the second triangle because they same construction methods and the have same size and same shape.
What is the congruent triangle?Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.
We have given a congruent triangle in the picture.
After close observation, the second triangle has the same size and the same shape, and the same construction method by arc method.
Other triangles have different construction methods.
Thus, the given triangle is congruent to the second triangle because they same construction methods and the have same size and same shape.
Learn more about the congruent triangle here:
https://brainly.com/question/12413243
#SPJ2
Use the distance formula to find the distance between each pair of points round to the nearest 10th if necessary
Given:
The pairs of points are:
a. A(-6,-4), B(-3,-1)
b. C(3.5,1), D(-4,2.5)
c. X(5,-5), Y(-5,5)
To find:
The distance between the pair of points by using the distance formula.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
a.
Using the distance formula, the distance between the points A(-6,-4) and B(-3,-1) is:
[tex]AB=\sqrt{(-3-(-6))^2+((-1-(-4))^2}[/tex]
[tex]AB=\sqrt{(3)^2+(3)^2}[/tex]
[tex]AB=\sqrt{2(3)^2}[/tex]
[tex]AB=3\sqrt{2}[/tex]
[tex]AB\approx 4.2[/tex]
Therefore, the distance between the points A(-6,-4) and B(-3,-1) is about 4.2 units.
b.
Using the distance formula, the distance between the points C(3.5,1) and D(-4,2.5) is:
[tex]CD=\sqrt{(-4-3.5)^2+(2.5-1)^2}[/tex]
[tex]CD=\sqrt{(-7.5)^2+(1.5)^2}[/tex]
[tex]CD=\sqrt{56.25+2.25 }[/tex]
[tex]CD=\sqrt{58.5 }[/tex]
[tex]CD\approx 7.6[/tex]
Therefore, the distance between the points C(3.5,1) and D(-4,2.5) is about 7.6 units.
c.
Using the distance formula, the distance between the points X(5,-5) and Y(-5,5) is:
[tex]XY=\sqrt{(-5-5)^2+(5-(-5))^2}[/tex]
[tex]XY=\sqrt{(-10)^2+(10)^2}[/tex]
[tex]XY=\sqrt{100+100}[/tex]
[tex]XY=\sqrt{200}[/tex]
[tex]XY\approx 14.1[/tex]
Therefore, the distance between the points X(5,-5) and Y(-5,5) is about 14.1 units.
Need help due in 20 mins
Answer: The slope is 0.
The slope is 0 because for something to have a slope, it either has to be going upward or downwards.
Choose the function whose graph is given by
Answer:
D
Step-by-step explanation:
I plugged each equation into a graphing calculator and compared them to see which one matched the one in the picture.
The value of the trigonometric equation after transformation is given by the value y = 3 [ sin ( x + 3 ) ] - 2
How does the transformation of a function happen?The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: y=f(x+c) (same output, but c units earlier)
Right shift by c units: y=f(x-c)(same output, but c units late)
Vertical shift:
Up by d units: y = f(x) + d
Down by d units: y = f(x) - d
Stretching:
Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)
Given data ,
Let the parent function be represented as f ( x )
Now , the value of the trigonometric function f ( x ) is
f ( x ) = 3sin ( x )
when the function is translated 3 units to the left and 2 units down , we get
y = 3 [ sin ( x + 3 ) ] - 2
Therefore , the transformed function is y = 3 [ sin ( x + 3 ) ] - 2 and the graph is plotted
Hence , the transformed function is y = 3 [ sin ( x + 3 ) ] - 2
To learn more about transformation of function click :
https://brainly.com/question/26896273
#SPJ7
Nalani says the expression 9+7r cannot be factored using the GCF. Is she correct? Explain why or why not
Answer:
Nalani is correct.
Step-by-step explanation:
Given - Nalani says the expression 9+7r cannot be factored using the GCF.
To find - Is she correct? Explain why or why not.
Proof -
GCF - Greater Common factor
Given that, the expression is - 9 + 7r
As
HCF(9, 7) = 1
So , we can not factor the expression.
i.e. there does not exist any number who is a multiple of 9 and 7 both.
So,
Nalani is correct.
Example -
Let the expression be 24 + 18x
HCF(24, 18) = 6
So,
24 + 18x = 6(4 + 3x)
Dominic spent $8 on a book. He made $6 doing chores for a neighbor. What numbers represent the situations?
–8 and –6
–8 and 6
8 and –6
8 and 6
Answer:
-8 and 6
Step-by-step explanation:
I need help! It is confusing, I need a little help
Help ASAP I’ll mark you as brainlister
Answer:
3/4[tex]\pi[/tex] x 180/[tex]\pi[/tex]= 135°
Step-by-step explanation:
What's the area of the composite figure below ?
Answer:
31.13
Step-by-step explanation:
If you look carefully, you will find a semicircle and a triangle.
The total area is =
[tex]\frac{\pi r^{2}}{2} + \frac{1}{2} \times base \times height\\[/tex]
r = 4 - 0 = 4base = |-4-0 | = 4height = 14 - 9 = 5So if we put the values:
[tex]\frac{\pi \times 4^{2}}{2} + \frac{1}{2} \times 4 \times 3\\= 31.13[/tex]