Answers
[tex]\left(\dfrac{1}{1+2i}+\dfrac{3}{1-i}\right)\left(\dfrac{3-2i}{1+3i}\right)=\\\\\left(\dfrac{1-2i}{(1+2i)(1-2i)}+\dfrac{3(1+i)}{(1-i)(1+i)}\right)\left(\dfrac{(3-2i)(1-3i)}{(1+3i)(1-3i)}\right)=\\\\\left(\dfrac{1-2i}{1+4}+\dfrac{3+3i}{1+1}\right)\left(\dfrac{3-9i-2i-6}{1+9}\right)=\\\\\left(\dfrac{1-2i}{5}+\dfrac{3+3i}{2}\right)\left(\dfrac{-3-11i}{10}\right)=\\\\\left(\dfrac{2(1-2i)}{10}+\dfrac{5(3+3i)}{10}\right)\left(\dfrac{-3-11i}{10}\right)=[/tex]
[tex]\dfrac{2-4i+15+15i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{17+11i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{-51-187i-33i+121}{100}=\\\\\dfrac{70-220i}{100}=\\\\\dfrac{70}{100}-\dfrac{220i}{100}=\\\\\boxed{\dfrac{7}{10}-\dfrac{11}{5}i}[/tex]
Related Questions
Evaluate f (x) = 2 x torx =-5.
Answers
Answer:
-10.
Step-by-step explanation:
f(x) = 2x, x = -5.
f(-5) = 2(-5)
= 2 * (-1) * 5
= 10 * (-1)
= -10.
Hope this helps!
The sum of two consecutive cube numbers is 341. Work out the two numbers. (2 marks)
Answers
Answer:
63 and 53
Step-by-step explanation:
you could use trail and error. So:
13+23=9
33+43=91
63+73=559
53+63=341
Giving brainliest!!!! Plzz put the correct answers.
2^(10)= 2x...x2 how many times
15^(57)= 15x...x15 how many times
(-4)x...x(-4) 7 times =
(1.5)x...x(1.5) 12 times =
If you give me the answer after like an hour i willl report you!!
Answers
Answer:
See below
Step-by-step explanation:
aⁿ = a×a×a×....×a (power n of the number a = number a multiplied by itself n times)2^(10)= 2x...x2 how many times = 10 times 2
15^(57)= 15x...x15 how many times = 57 times 15
(-4)x...x(-4) 7 times = (-4)^(7)
(1.5)x...x(1.5) 12 times = (1.5)^(12)
A bookstore decides to divide its space into three sections: nonfiction books, novels, and stationery. The bookstore wants to devote 1/6 of its space to stationery. If the total area of the bookstore is 288 square feet, and the stationery section will be 12 feet long, how wide will the stationery section be?
Answers
Answer:
Stationery section will be 4 feet wide.
Step-by-step explanation:
Total area of bookstore = 288 sq ft
Area to be devoted to stationery = [tex]\frac{1}6[/tex] of total area = [tex]\frac{1}{6} \times 288 = 48\ sq\ ft[/tex]
Length of stationery section = 12 ft
To find:
Width of stationery section = ?
Solution:
First of all, let us have a look at the area of rectangle:
[tex]A = Length \times Width[/tex]
Here, we are given the length for stationery section and area of stationery section has been calculated above.
And we have to find the Width of stationery section.
So, let us put the two values to find the third value.
[tex]\Rightarrow 48 = 12 \times Width\\\Rightarrow Width = \dfrac{48}{12}\\\Rightarrow \bold{Width = 4\ ft}[/tex]
So, the answer is:
Stationery section will be 4 feet wide.
2y² +4y-48=0
solve the equation
Answers
Answer:
y = - 6, y = 4
Step-by-step explanation:
Given
2y² + 4y - 48 = 0 ( divide through by 2 )
y² + 2y - 24 = 0
Consider the factors of the constant term (- 24) which sum to give the coefficient of the y- term (+ 2)
The factors are + 6 and - 4 , since
6 × - 4 = - 24 and 6 - 4 = + 2 , thus
(y + 6)(y - 4) = 0
Equate each factor to zero and solve for y
y + 6 = 0 ⇒ y = - 6
y - 4 = 0 ⇒ y = 4
Answer:
Step-by-step explanation:
2y² + 4y - 48 = 0
2y² + 12y - 8y + (-8)* 6 = 0
2y(y + 6) - 8(y + 6) =0
(y + 6) (2y - 8)= 0
y + 6 = 0 ; 2y- 8 = 0
y = -6 2y = 8
y = 8/2
y = 4
Solution: y = -6 , 4
Bryan completed a 100-meter race in 11.74 seconds. Luis completed the same race in 11.69 seconds. What was the difference between their times, expressed as a fraction of a second?
Answers
Answer:
[tex]\frac{1}{20}[/tex] of a second
Step-by-step explanation:
We can convert each time into fractions.
11.74 is the same thing as [tex]11 \frac{74}{100}[/tex]
and 11.69 is the same thing as [tex]11 \frac{69}{100}[/tex].
We know that 11 - 11 = 0, so we can focus on the fractions for now.
Let's subtract [tex]\frac{69}{100}[/tex] from [tex]\frac{74}{100}[/tex].
[tex]\frac{74}{100} - \frac{69}{100} = \frac{5}{100}[/tex].
We can now simplify [tex]\frac{5}{100}[/tex] by dividing both the numerator and denominator by 5.
[tex]\frac{5\div5}{100\div5} = \frac{1}{20}[/tex].
Hope this helped!
What is the value of 1/4m +n 8 - 6 = 12 *
Answers
Answer:
i dont know if you want me to solve for m
Step-by-step explanation:
Let's solve for m.
Which of the following is true? Tangent is positive in Quadrant I. Sine is negative in Quadrant II. Cosine is positive in Quadrant III. Sine is positive in Quadrant IV.
Answers
Since sine and cosine are both positive in Quadrant I and tangent is the ratio of sine to cosine, tangent is positive in Quadrant I
Answer:
A
Step-by-step explanation:
I had this question and got it right the user above explains it in detail
plz help asap i have limited time i will give brainliest
Answers
Answer:
358
Step-by-step explanation:
In 1995, the boys were 50 %
Take the number of people at the convention in 1995 ( 716)
and multiply by 50%
716 * 50%
716 * .50
358
Answer:
b. 358
Step-by-step explanation:
First, find what percentage of attendees were boys in 1995:
By reading the graph, we can see 50% were boys.
In the table, we can see that there were 716 attendees in 1995.
To find how many boys attended in 1995, find 50% of 716.
716(0.5) = 358
Write this expression as a complex number in standard form
Answers
Answer:
[tex]81+144i[/tex]
Step-by-step explanation:
We want to simplify:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i[/tex]
Recall that:
[tex]\displaystyle \sqrt{-a} = i\sqrt{a}[/tex]
Therefore:
[tex]\displaystyle \begin{aligned} (-3\sqrt{-81})(-5+\sqrt{-9}) + 9i & = (-3i\sqrt{81})(-5+i\sqrt{9})+9i \\ \\ &= -(3i(9))(-5+i(3))+9i \\ \\ & = -27i(-5+3i)+9i \\ \\ & = 135i -81i^2 + 9i \\ \\ & = 144i - 81i^2 \\ \\ & = 81+144i\end{aligned}[/tex]
Note that i² = -1.
In conclusion:
[tex]\displaystyle (-3\sqrt{-81})(-5+\sqrt{-9})+9i = 81 + 144i[/tex]
If f(x)= Square root of X +12 and g(x)= 2 Square root of X what is the value of (f-g)(144)
Answers
Answer:
0
Step-by-step explanation:
Find the sum and express it in simplest form.
(6u - 7c - 6) + (-2u + 4c)
Answers
Answer:
4u - 3c - 6
Step-by-step explanation:
Remove the parentheses and combine like factors.
(6u - 7c - 6) + (-2u + 4c)
6u - 7c - 6 - 2u + 4c
4u - 3c - 6
If the production rate is 975 brownies per hour at a bakery, how many brownies will be produced in an 8 hour shift?
Answers
Answer:
[tex]\large \boxed{\mathrm{7800 \ brownies}}[/tex]
Step-by-step explanation:
975 brownies are produced per 1 hour.
To find how many brownies are produced in 8 hours, multiply the brownies amount by the hours.
975 × 8 = 7800
7800 brownies will be produced in an 8 hour shift.
Answer:
the answer is 7800
Step-by-step explanation:
975 brownies are created per 60 minutes.
To discover what number of brownies are created in 8 hours, duplicate the brownies sum continuously.
975 × 8 = 7800
7800 brownies will be created in a 8 hour move.
How do u find the area of a rectangle?
Answers
Answer:
6x-21
Step-by-step explanation:
Area of a rectangle is length times width.
3*(2x-7)-
6x-21
Answer:
6x - 21
Step-by-step explanation:
Since area = L x W (Length x Width)
--> 3(2x - 7)
6x - 21
Find an equation of the line with x-intercept 8 and y-intercept 4
Answers
Answer:
y = -1/2x + 4
Step-by-step explanation:
We have two points ( 8,0) and ( 0,4)
We can find the slope
m =(y2-y1)/(x2-x1)
= (4-0)/(0-8)
4/-8
-1/2
We can use the slope intercept form
y = mx+b where m is the slope and b is the y intercept
y = -1/2x + 4
Answer:
Step-by-step explanation:
eq. of line with intercepts a and b is
[tex]\frac{x}{a} +\frac{y}{b} =1\\here ~eq. ~of ~line~ is ~ \frac{x}{8} +\frac{y}{4} =1\\or x+2y=8\\[/tex]
Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
square root of the quantity x minus 3 end quantity plus 5 equals x
Answers
Answer:
Step-by-step explanation:
[tex]\sqrt{x-3} +5=x\\\sqrt{x-3} =x-5\\squaring ~both~sides\\x-3=x^2-10x+25\\x^2-10x-x+25+3=0\\x^2-11x+28=0\\x^2-7x-4x+28=0\\x(x-7)-4(x-7)=0\\(x-7)(x-4)=0\\x=7,4[/tex]
put x=7 in the given equation
[tex]\sqrt{7-3} +5=7\\\sqrt{4} +5=7\\2+5=7\\7=7[/tex]
which is true .
∴ x=7 is a solution of the given eq.
now put x=4 in the given eq.
[tex]\sqrt{4-3} +5=7\\1+5=7\\6=7\\[/tex]
which is not true.
∴x=4 is an extraneous solution.
WILL MARK BRAINLIEST FOR CORRECT ANSWER. <3 <3 The area of the following rectangle is 24 square units. A. Write an equation that can be used to find the value of n. B. Solve the equation to find the value of n. In your answer, show all of your work.
Answers
Because area is multiplication lets multiply the sides and make an equation:
A 2(n-3) = 24
n-3=(12)
B n= 15
15-3 = 12
12 x 2 = 24
Answer:
2(n-3)=24
n=15
Step-by-step explanation:
2(n-3)=24
2n-6=24
2n=30
n=15
Find the volume of a pyramid with a square base, where the side length of the base is 17 in 17 in and the height of the pyramid is 9 in 9 in. Round your answer to the nearest tenth of a cubic inch.
Answers
Answer:
The volume of the pyramid is 867 inch^3
Step-by-step explanation:
Here in this question, we are interested in calculating the volume of a square based pyramid.
Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.
V = a^2h/3
where a represents the length of the side of the square and h is the height of the pyramid
From the question, the length of the side of the square is 17 in while the height is 9 in
Plugging these values, we have ;
V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch
How many 1-foot rulers laid end to end would
it take to equal 3 yards?
Answers
Answer:
9
Step-by-step explanation:
A farmer has 2000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this. 4.
Answers
Answer:
500 plantsStep-by-step explanation:
Step one:
given that the number of plants the farmer has is 2000
for him to plant in equal rows and column he needs an amount of plant the is a perfect square.
The closest number to a perfect square is 2500
Step two:
From the above figure which is 2500 plants, the farmer is able to plant 50 rows and 50 columns.
multiplying these values together will amount to 2500
Hence the farmer needs at least 500 plants to achieve this
Answer:
25
Step-by-step explanation:
Number of plants = 2000
He wants to plant such that number of rows and column of plants remain the same, Find the minimum number of plants he needs more for this:
To obtain this,
We take the square root of 2000
Sqrt(2000) = 44.721359
Therefore, the number of columns and rows we need is a natural number whereby the square root of its square is perfect (that is leaves no remainder).
The minimum number will thus be ; the next natural number or integer after 44.721359, whish is 45
Taking the square of 45
45^2 = 2025
The minimum number of plants needed more is :
2025 - 2000 = 25 plants
Add the matrices to find the answer.
Answers
Answer:
[tex]\large \boxed{\mathrm{Option \ C}}[/tex]
Step-by-step explanation:
[tex]{\mathrm{view \ attachment}}[/tex]
How many solutions does the nonlinear system of equations graphed below
have?
y
10+
-10
10
-10
A. One
B. Two
0
O
C. Four
O
D. Zero
Answers
Answer:
D. zero
Step-by-step explanation:
Since the graphs do not intersect, there are zero solutions.
The number of solutions on the graph is zero
How to determine the number of solutions?The graph shows a linear equation (the straight line) and a non linear equation (the curve)
From the graph, we can see that the straight line and the curve do not intersect
This means that the graph do not have any solution
Hence, the number of solutions on the graph is zero
Read more about non-linear graphs at:
https://brainly.com/question/16274644
#SPJ5
how many eighth rests are in a half rest?
Answers
find the sum of partial fraction for x^4/(x-1)(x²-4)
Answers
Answer:
see attachment
Step-by-step explanation:
Use the number line to plot –3, 1, and 3.
Which statements are true? Select all that apply.
–3 > 1
–3 = 3
1 < 3
–3 < 1
Answers
Answer:
Options 3 and 4 are correct
Step-by-step explanation:
-3>1 is false bc a positive is always greater than a negative
-3=3 is false because a positive is not equal to a negative
1<3 is correct because 1 is less than 3
-3<1 is correct because a negative is always less than a positive.
Answer:
1 < 3
–3 < 1
Step-by-step explanation:
Mrs.magar sold 40 kg of fruits at rate of RS 60 per kg and gained Rs 600 . calculate purchasing rate and profit percent.
Answers
Answer:
Purchasing rate = ₹45 per kg
Profit percent = 33.33%
Step-by-step explanation:
Selling price of 1 kg fruit = ₹60
Therefore, S. P. of 40 kg fruits = 40*60 = ₹2400
Gain = ₹ 600 (given)
Cost price (C. P.) = S. P. - Gain
= ₹2400 - ₹600
= ₹ 1800
Rate of purchasing
= C. P. /quantity of fruits
= 1800/40
= ₹45 per kg
Profit percent
= (Gain* 100)/C.P.
= (600*100)/1800
= 60000/1800
=33.33%
how many are 5 raised to 3 ???
Answers
Answer:
[tex]\boxed{125}[/tex]
Step-by-step explanation:
Hey there!
Well 5 raised to the 3 can be written as,
[tex]5^3[/tex]
This is 5*5*5
= 125
Hope this helps :)
A timeline. 27 B C E to 180 C E PAX ROMANA. 44 B C E The Roman Empire was founded. 80 C E The Colosseum was built. 121 C E Hadrian's Wall was built in England to keep out enemies. 306 C E Constantine became emperor.
How many years passed between the building of the Colosseum and the building of Hadrian’s Wall?
201
121
41
36
Answers
Answer:
the answer is 41
Step-by-step explanation:
C. 41
Step-by-step explanation:
I REALLY NEED HELP WITH THESE 5 QUESTIONS!!!!!!!!!
Answers
Answer:
is -5,-3
Step-by-step explanation:
set up the tablet and done
Point E is on line segment DF. Given DE=9 and DF=11, determine the length EF.
Answers
Answer: Line EF=2
Step-by-step explanation: 11 minus 9 is equal to 2. So line EF is equal to 2.
