Simplify the coefficient of z on the left side. We do this by rationalizing the denominators and multiplying them by their complex conjugates:
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3-2i}{1+i}\cdot\dfrac{1-i}{1-i} - \dfrac{5+3i}{1+2i}\cdot\dfrac{1-2i}{1-2i}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{(3-2i)(1-i)}{1-i^2} - \dfrac{(5+3i)(1-2i)}{1-(2i)^2}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 2i - 3i + 2i^2}{1-(-1)} - \dfrac{5 + 3i - 10i - 6i^2}{1-4(-1)}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{3 - 5i + 2(-1)}2 - \dfrac{5 - 7i - 6(-1)}5[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2 - \dfrac{11 - 7i}5[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{1 - 5i}2\cdot\dfrac55 - \dfrac{11 - 7i}5\cdot\dfrac22[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = \dfrac{5 - 25i - 22 + 14i}{10}[/tex]
[tex]\dfrac{3-2i}{1+i} - \dfrac{5+3i}{1+2i} = -\dfrac{17 + 11i}{10}[/tex]
So, the equation is simplified to
[tex]-\dfrac{17+11i}{10} z = \dfrac12 - \dfrac{2i}5[/tex]
Let's combine the fractions on the right side:
[tex]\dfrac12 - \dfrac{2i}5 = \dfrac12\cdot\dfrac55 - \dfrac{2i}5\cdot\dfrac22[/tex]
[tex]\dfrac12 - \dfrac{2i}5 = \dfrac{5-4i}{10}[/tex]
Then
[tex]-\dfrac{17+11i}{10} z = \dfrac{5-4i}{10}[/tex]
reduces to
[tex]-(17+11i) z = 5-4i[/tex]
Multiply both sides by -1/(17 + 11i) :
[tex]\dfrac{-(17+11i)}{-(17+11i)} z = \dfrac{5-4i}{-(17+11i)}[/tex]
[tex]z = -\dfrac{5-4i}{17+11i}[/tex]
Finally, simplify the right side:
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{5-4i}{17+11i} \cdot \dfrac{17-11i}{17-11i}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{(5-4i)(17-11i)}{17^2-(11i)^2}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44i^2}{289-121(-1)}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{85 - 68i - 55i + 44(-1)}{410}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 123i}{410}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{41 - 41\cdot3i}{410}[/tex]
[tex]-\dfrac{5-4i}{17+11i} = -\dfrac{1 - 3i}{10}[/tex]
So, the solution to the equation is
[tex]z = -\dfrac{1-3i}{10} = \boxed{-\dfrac1{10} + \dfrac3{10}i}[/tex]
$250, 3.4%, 3 years what would my interest be?
Mr. Wilhelm got a $2 discount on
the purchase of 5 bags of peat moss.
If he paid $7.40, what was the price
for a bag of peat moss before the
discount?
Answer:
9.40
Step-by-step explanation:
7.40+2.00=9.40
A gopher lives in an underground burrow. It starts at a certain point, p, underground and digs straight down to triple its distance under
the surface. It then climbs straight down another 2 feet. Its final position is deeper than 8 feet under the surface.
What was the gopher's original position, p, relative to the surface?
Enter your answer in the box to complete the inequality.
р
Answer:
The answer is <-2
Step-by-step explanation:
Answer: I'm late but here you go
Step-by-step explanation:
Juan wants to buy a video game for $63. He saves $12 every Friday. Part A. Create an equation to represent Juan's total savings, y, in dollars, after x Fridays. y
Answer:
Answer in explanation.
Step-by-step explanation:
An equation to represent Juan's total savings y, in dollars, after x Fridays will be;
⇒ y = 12x
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Juan wants to buy a video game for $63.
And, He saves $12 every Friday.
Now,
Let total dollars after x Friday = y
And, He saves $12 every Friday.
So, We can formulate;
⇒ Total money (y) = 12x
⇒ y = 12x
Thus, An equation to represent Juan's total savings y, in dollars, after x Fridays will be;
⇒ y = 12x
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
This circle is centered at the point (3,2) and the length of its radius is 5 what is the equation of the circle
Answer:(x-3)² + (y-2)² = 25
Step-by-step explanation:
A circle's equation is (x-h)² + (y-k)² = r². When centered at the origin, h and k equal 0. If you shift the circle, say, one unit up, then k equals 1, and the equation is x² + (y-1)² = r².
So for your circle, the equation would be (x-3)² + (y-2)² = 5² or (x-3)² + (y-2)² = 25.
Answer:
(x - 3)² + (y - 2)² = 25
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
Here (h, k ) = (3, 2 ) and r = 5 , then
(x - 3)² + (y - 2)² = 5² , that is
(x - 3)² + (y - 2)² = 25 ← equation of circle
-3y<-14 i dont get the dam question
Answer:
Step-by-step explanation:
-3y<-14
divide both sides by -3
y<4.67
i’m not exactly sure what the question is asking or what you’re trying to find, but this is what i could figure out.
Answer:
y>14/3
I'll provide the step by step solution too.
=3y÷(-3)>-14÷(-3)
y>-14÷(-3)
y>14÷3
turn it into a fraction
y>14/3
hence your given answer above
There are 564 men and women working in a factory.
There are twice as many women as men.
How many men are working in the factory?
Answer:
564x2=1128 men
Step-by-step explanation:
Answer:
there are1139 women are working in the factory
what is the intercepts of the line?
x-intercept and y-intercept
4x-1=3y+5
Answer: X (3/2,0) Y (0,-2)
Step-by-step explanation:
what is the estimate of 45.15
Answer:
The estimate would be:
(one of them :)
45 (if your doing the entire number)
0 (if your rounding out of 100)
45.2 (nearest hundredth)
45.0 (nearest tenth)
50 (nearest tens)
Hopefully one of these works for you.
AYUDA!!!!!!! Pls help me answer
You don't mention what's the question
The diagram below shows two parallel lines, m and n, cut by a transversal, k. Angles A, B, and C are shown in the diagram
A student writes a proof to show that the corresponding angles, A and B, are congruent. The student's proof is shown below
A. Both reason 2 and Reason 3 are correct as shown in the table
B. Reason 2 is correct, but Reason 3 should "Alternate interior angles are congruent"
C. Reason 2 should be "Alternate interior angles are congruent," but Reason 3 is correct
D. Both Reason 2 and Reason 3 should be "Alternate interior angles are congruent"
(look at picture to understand better)
9514 1404 393
Answer:
B
Step-by-step explanation:
Angles A and C are vertical angles; angles B and C are alternate interior angles. Only line 3 of the proof is in error.
The applicable description is found in choice B.
What is the value of g(1)? What is the value of g(-12)? For which of the following x-values is g(x)=-6
The numeric values of the function are given as follows:
g(1) = 4.g(-12) = -10.g(x) = -6 for -8 ≤ x < -1.g(1)When x = 1, the function has a closed value on the graph at y = 4, hence:
g(1) = 4.
g(-12)When x = -1,2 the function is passing through y = -10, hence the numeric value is given as follows:
g(-12) = -10.
g(x) = -6The function is passing through the horizontal line y = -6 when -8 ≤ x < -1, hence:
g(x) = -6 for -8 ≤ x < -1.
Learn more about the numeric values of a function at https://brainly.com/question/28296698
#SPJ1
The graph of f(x) = x2 has been shifted into the form f(x) = (x - h)2 + k:
5
365
What is the value of k? (1 point)
0 1
0-1
O-2
O 2
maya picks 16 vegetables 6 of them are carrots the rest are cucumbers then she gives away 5 cucumbers how many cucumbers does maya have now
Answer:
5
Step-by-step explanation:
First subtract 6 from 16 to find how many cucumbers she has,
16 - 6 = 10
Now we know she has 10 cucumbers.
Subtract 5 from the 10 cucumbers to find out how many she has after giving away 5.
10 - 5 = 5
After subtracting the 5 cucumbers she gave away, we are left with 5
This means Maya has 5 cucumbers now
Please solve for a: b = 2 - (1/a)
[tex]b = 2 - \dfrac 1a\\\\\implies ab = 2a -1\\\\\implies 2a -ab = 1\\\\\implies a(2-b) =1\\\\\implies a = \dfrac 1{2-b}[/tex]
Apply the distribute property, substitute the given numerical value given:
9(-3r -11), r=10
Answer:
-369
Step-by-step explanation:
Replace r with 10.
9(-3(10)-10))
9(-30-11)
9*-30+9*-11
-270+ -99
-369
Hope this helped. :)
Abigail earned $10.26 for babysitting her cousin for 3 hours. How much did she earn in each hour?
Divide total earned by number of hours:
10.26/3 = $3.42
She earned $3.42 per hour
Solve the right triangle. a = 2.2 m, B = 37.7°, C = 90° 4) A) A = 52.3°, b = 0.6 m, c = 2.3 m B) A = 52.3°, b = 1.7 m, c = 2.8 m C) A = 52.3°, b = 3.2 m, c = 3.9 m D) A = 52.3°, b = 3.2 m, c = 2.8 m
Answer:
B) A = 52.3°, b = 1.7 m, c = 2.8 m
Step-by-step explanation:
We know that it is a right angle triangle because C = 90°
because of that we can do 180 - 90 + 37.7
which is a=52.3
Because it is a right angle triangle, we can use sin, cos,tan
I will use sin to find the side of c
2.2 is a
sin 52.3 = 2.2/x
x= 2.2/ sin 52.3
x=2.78
You could do cos or tan but the pythagorean theorem for me is much faster
so it looks like this, a^2+b^2 =c^2
in this case we have both a and c we want b
so we rearrange
c^2-a^2=b^2
2.78^2-2.2^2= b^2
[tex]\sqrt{2.89}[/tex]=b
1.7=b
therefore it would be this option B) A = 52.3°, b = 1.7 m, c = 2.8 m
Is x = 1 a function?
Answer:
Yes
Step-by-step explanation:
It is a constant linear function, which is in fact a function.
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
f(x)= -2x^3 +14x -8
g(x)= 2x+6
Answer:
F(2x+6)=-16x^3-144x^3-404x-356
Step-by-step explanation:
no link fast but righ and if you get the answer right can you help me with other question
Answer:
12 inches
Step-by-step explanation:
The volume of a cone is given by
V = 1/3 pi r^2 h where r is the radius and h is the height
113.04 = 1/3*3.14 ( 3)^2 h
113.04 = 9.42 h
Divide each side by 9.42
113.04/9.42 = h
12 = h
12 inches
Answer:
Height = 12 in
Step-by-step explanation:
Volume Cone = 1/3(πr²h)
113.04 = 1/3(3.14)(3²)(h) [tex]\longmapsto[/tex] Note that the 1/3 and 9 simplify
113.04 = 3.14(h)(3)
37.68 = 3.14(h)
h = 12
-Chetan K
The cost of a ride in a taxi is $2.50 for the first half-mile plus a constant amount per half-mile after that. The sequence below shows the pattern of numbers that appear on the driver's screen.
2.50, 2.75, 3.00. 3.25, 3.50, 3.75
Part A: Write a recursive function that can be used to determine f(x), the cost in dollars, for a ride in the taxi of, x, half-miles.
Answer: 2.50 + 0.35(15.75-1)*4 = $23.15 is the answer
Step-by-step explanation: Hope this helps!
Leah's bill for breakfast at a restaurant was $68. She left an 18% tip. What was the amount of the tip?
Answer:
55.76
Step-by-step explanation:
55.76
what would be the volume of the cone that has the same measurement as the cylinder above in the pic
do the working also
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
Volume of cone will be ~
[tex]\fbox \colorbox{black}{ \colorbox{white}{volume} \: \: \: \: \: \colorbox{white}{=} \: \: \: + \colorbox{white}{462 \: cm³ }}[/tex]
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let's find the volume of cone with ~
radius (r) = 7 cmheight (h) = 9 cmAnd as we know, volume of cone is equal to ~
[tex] \dfrac{1}{3}\pi {r}^{2} h[/tex]now, let's plug in the values and find the volume ~
[tex] \dfrac{1}{ \cancel{3} }\times \dfrac{22}{\cancel{7}} \times \cancel{7 }\times 7 \times \cancel{9}[/tex][tex]1 \times 22 \times 7 \times 3[/tex][tex]462 \: \: {cm}^{3} [/tex]Volume of cone is 462 cm³ = 462 ml
Is 6,702,512 divisible by 9?
What is 34÷18? Explain or show your reasoning.
Answer:
1.8889
Step-by-step explanation:
A bag contains 11 apples and 6 oranges. If you select 6 pieces of fruit without looking, how many ways can you select exactly 5 apples
Answer:
you have a 11/17 percent chance of getting an apple
Step-by-step explanation:
if there are 11 apples and 6 oranges. 11 out of 17 times you will get an apple
geomtry plzzz help 15 points
Answer:
19
Step-by-step explanation:
they give you xz, and they want half, so just divide 38 by 2
The price of an item has been reduced by 85%. The original price was $37.
Answer: Multiply the original price by the decimal form of the percent and subtract that from the original price.
37*0.85=31.45
37-31.45=5.55
Answer: New price is $5.55
Pease someone help me with this.
I just need two more tiles to create but I don't know how they would look like.
I will show below what I have filled and what the question is asking.
Question: How many different layouts are possible for a path that is five feet long? Draw them all here:
Answer:
go get that girl
Step-by-step explanation:
sike you use what you got the first time
Answer:
If the path is 5 feet long, then you could only have a limited amount of layouts...so- you could only have 5 limited spaces in one layout, making it 5 DIFFERENT LAYOUTS.
(I don't know what they're really asking, but I did what makes sense, SORRY if I'm wrong, I'm going to try and solve it better/draw it.)