Answers
Answer:
z1(z2 + z3) = z1 z2 + z1 z3 ⇒ verified down
Step-by-step explanation:
∵ z1 = 4 + 3i
∵ z2 = 3 - 2i
∵ z3 = i + 5
→ Find the left side
∵ z1(z2 + z3) = (4 + 3i)[3 - 2i + i + 5]
∴ z1(z2 + z3) = (4 + 3i)[(3 + 5) + (-2i + i)]
∴ z1(z2 + z3) = (4 + 3i)(8 - i)
∴ z1(z2 + z3) = (4)(8) + (4)(-i) + (3i)(8) + (3i)(-i)
∴ z1(z2 + z3) = 32 - 4i + 24i - 3i²
→ Remember that i² = -1
∴ z1(z2 + z3) = 32 - 4i + 24i - 3(-1)
∴ z1(z2 + z3) = 32 - 4i + 24i + 3
→ Add the like terms
∴ z1(z2 + z3) = (32 + 3) + (-4i + 24i)
∴ z1(z2 + z3) = 35 + 20i
→ Find the right side
∵ z1 z2 + z1 z3 = (4 + 3i)(3 - 2i) + (4 + 3i)(i + 5)
∴ z1 z2 + z1 z3 = [(4)(3)+(4)(-2i)+(3i)(3)+(3i)(-2i)] + [(4)(i)+(4)(5)+(3i)(i)+(3i)(5)]
∴ z1 z2 + z1 z3 = [12 -8i + 9i -6i²] + [4i + 20 + 3i² + 15i]
→ Replace i² by -1
∴ z1 z2 + z1 z3 = [12 -8i + 9i -6(-1)] + [4i + 20 + 3(-1) + 15i]
∴ z1 z2 + z1 z3 = [12 -8i + 9i + 6] + [4i + 20 - 3 + 15i]
→ Add the like terms
∴ z1 z2 + z1 z3 = [12 + 6 + 20 - 3] + [-8i + 9i + 4i + 15i]
∴ z1 z2 + z1 z3 = 35 + 20i
∵ The left side = 35 + 20i
∵ The right side = 35 + 20i
∴ The left side = the right side
∴ z1(z2 + z3) = z1 z2 + z1 z3
Related Questions
Question 61 point)
Chip earns a base salary of $500 per month as a salesman. In addition to the base salary, he earns $100 per product that he sells. If his
goal is to earn $5000 per month, how many products does he need to sell?
Answers
1. Maya has 24 baseball cards, and her grandfather gives her 6 baseball cards per week for earning good grades. Her brother, Marcus, has 0 baseball cards, but his grandfather gives him 12 baseball cards per week. After how many weeks will Maya and Marcus have the same number of baseball cards?
Answers
What is the solution to this equation?
8x - 5(x-3) = 18
O A. x = 7
O B. x= 11
O C. x = 5
O D. x= 1
Answers
Answer:
D x = 1
Step-by-step explanation:
Samantha is training for a race. The distances of her training runs form an arithmetic sequence. She runs 1 mi the first day and 2 mi the seventh day.
a. What is the explicit definition for this sequence?
b. How far does she run on day 19?
Answers
бx + 8 = 50
I need that answer
Answers
Answer:
=
7
Step-by-step explanation:
Jacob is training for a marathon. His plan is to run the same distance for 3 days a week, then increase that distance
by the same amount each week of training. During week 6, Jacob runs 14 miles per day, which is 1.5 miles more per
day than he ran during week 5. Which equation represents the daily running distance, in miles, as a function of time,
t, in weeks?
f(t) = 0.5t + 7
f(t) = 0.5t + 11
f(t) = 1.5t + 5
f(t) = 1.5t + 12.5
Answers
Answer:
f(t) = 1.5t + 5
Step-by-step explanation:
each week he will run an extra 1.5 miles and one the first week he started off running 5 miles. 1.5 is your slope and 5 is the y-intercept.
Answer:f(t) = 1.5t + 5
Step-by-step explanation:
Edg 2020
How many quarts does a 100 liter tank hold?
Answers
Answer: 84.535 Quartas.
Step-by-step explanation:
The graph shows the relationship between the United States dollar and the euro, the currency of the European Union, in December 2011. Part A: What is the constant of proportionality shown in the graph? *
Answers
The graph is missing, so i have attached it;
Answer:
Constant of proportionality = 0.75
Step-by-step explanation:
From the graph attached, we are given 3 coordinate points of (x, y) namely;
(120, 90), (250, 187.5), (400, 300)
Now, constant of proportionality for each coordinate point is simply;
k = y/x
Thus, for first coordinate point (120, 90),
k1 = 90/120
k1 = 0.75
For 2nd coordinate point (250, 187.5),
k2 = 187.5/250
k2 = 0.75
For third coordinate point (400, 300),
k3 = 300/400
k3 = 0.75
From each of the 3 points, we can see the constant of proportionality is the same and equal to 0.75.
If the area of the base of the box is 112 square inches and the height is 3.5 inches, what is the volume of the box?
Answers
Answer: uh i think its 392 inches squared
Step-by-step explanation:
The volume of the box whose area is 112 inch² and height 3.5 inch is
392 inch³
What is the Volume of a Rectangle?
The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle
Volume of Rectangle = Length x Width x Height
Volume of Rectangle = Area of Rectangle x Height
Given data ,
The area of the box = 112 inch²
The height of the box = 3.5 inch
Now , the volume of the box is given by the equation
Volume of the box = Area of the box × Height of the box
Volume of the box = 112 inch² x 3.5 inch
Volume of the box = 392 inch³
Therefore , the volume of the box is 392 inch³
Hence , the volume of the box whose area is 112 inch² and height 3.5 inch is 392 inch³
To learn more about volume of rectangle click :
https://brainly.com/question/25422723
#SPJ2
What kind of sequence is this? 1, 8, 64, 512, ...
arithmetic, geometric, neither or both
Answers
Answer:
Geometric
Step-by-step explanation:
It has a consistent multiple-factor by which it increases (8).
will mark brainliest:) helppppp -7x + y = -19 -2x+ 3y = -19 solve the system of equations
Answers
Answer:
X=2, Y=-15
Step-by-step explanation:
-7x+y=-19
-2x+3y=-19
------------------
-3(-7x+y)=-19
-2x+3y=-19
---------------------
21x-3y=57
-2x+3y=-19
---------------------
19x = 38
19x/19=38/19
x=2
now plug 2 into x of the second equation to get y=-15
What does h(40) = 1700 mean in terms of the problem?
Hours of
Training
10
20
30
40
50
60
70
Monthly
Pay
1250
1400
1550
1700
1850
2000
2150
Answers
Answer:
40 hours of training=h(40)
Monthly Pay=1700
Step-by-step explanation:
For 40 hours of training, you will receive $1700 for the month.
Will Give Branieliest!!!!!!!
A farmer placed an order for 11 tons of fertilizer. He calculates that the corn fields will require 6 5/8 tons of it. How much fertilizer will the farmer have left for his other crops?
Write your answer as a fraction or as a whole or mixed number.
Answers
Answer:
4.375
Step-by-step explanation:
11 tons
He needs 6 5/8
Convert 11 tons to a fraction with the same denominator:
[tex]\frac{11}{1} *\frac{8}{8} =\frac{88}{8}[/tex]
Now calculate 6 5/8:
[tex]\frac{6}{1} *\frac{8}{8} =\frac{48}{8}[/tex] and add [tex]\frac{5}{8}[/tex]
[tex]\frac{48}{8} +\frac{5}{8} =\frac{53}{8}[/tex]
Now subtract
[tex]\frac{88}{8} -\frac{53}{8} =\frac{35}{8}[/tex]
As a mixed number:
[tex]\frac{35}{8} = 4 \frac{3}{8}[/tex]
As a fraction:
4.375 is how much he has left for his other crops.
Enter your answer and show all the steps that you use to solve this problem in the space provided.
Use cross products to demonstrate whether or not the two ratios are equivalent:
4/6 and 14/21.
Answers
so, essentially you’re just drawing two diagonal lines from one side to the other, multiplying those numbers together, and setting them equal
so: 4/6 and 14/21 = (4*21 = 6*14) = (84 = 84)
84 is equal to 84 so these two ratios are equivalent.
The equation of line g is y = -6/7x + 3 line h is parallel to line g what is the slope of line h
Answers
Answer:
It should be -6/7 because parallel lines have the same slope
To which subsets of the real numbers does the numbers -57 belongs?
Answers
Answer:
integer, rational number
Step-by-step explanation:
-57 is an integer because integers include negative and positive numbers that are not decimals or fractions. it is also a rational number because it can be converted into a fraction. these are subsets of the real numbers category.
-cz+6z= tz+83
solve for z
Answers
Answer:
z = 83 /( -c+6-t)
Step-by-step explanation:
-cz+6z= tz+83
Subtract tz from each side
-cz+6z -tz= tz-tz+83
-cz+6z- tz=83
Factor out a z
z( -c+6-t) = 83
Divide by ( -c+6-t)
z( -c+6-t)/( -c+6-t) = 83 /( -c+6-t)
z = 83 /( -c+6-t)
4 1/8÷2 3/4 convert the mixed numbers to improper fractions
Answers
Answer:
Check picture
Step-by-step explanation:
9514 1404 393
Answer:
1 1/2
Step-by-step explanation:
[tex]\dfrac{4\dfrac{1}{8}}{2\dfrac{3}{4}}=\dfrac{\left(\dfrac{4\cdot8+1}{8}\right)}{\left(\dfrac{2\cdot4+3}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{11}{4}\right)}=\dfrac{\left(\dfrac{33}{8}\right)}{\left(\dfrac{22}{8}\right)}=\dfrac{33}{22}=\dfrac{3}{2}[/tex]
Then the improper fraction 3/2 can be written as the mixed number 1 1/2.
(4 1/8) / (2 3/4) = 1 1/2
_____
Comment on division of fractions
Fractions can be divided several ways. Two ways that are commonly taught are "invert and multiply", or "match denominators". Here, we have used the second of these methods.
If we were to "invert and multiply", the computation would be ...
(33/8)(4/11) = (33/11)(4/8) = 3(1/2) = 3/2
Instead, we multiplied 11/4 by 2/2 to make it be 22/8, so having a denominator of 8 matching that of the numerator. Then the value of the compound fraction is the ratio of the numerators:
(33/8)/(22/8) = 33/22 = (3/2)(11/11) = 3/2
Which of the following statements correctly uses the distributive property?
-2(15 - 3) = -2(15) + (-2)(3)
0719- 8) = 7(9) - 8
91-7 + 6) = 9(-7) + 9(6)
-3(12 + 5) = -3(12) - (-3)(5)
Answers
-3(12+5) = -3(12)-(-3)(5)
Step-by-step explanation:
the distributive property is distributing the -3 to each number
Solve the proportion.
Thursday
Friday
Classes
6
Hours
8
4
Hellppppp it’s a testttt!
Answers
Ratio of number of classes and the time taken to conduct each one of them on Thursday = 6 : 8
Ratio of number of classes and the time taken to conduct each one of them on Friday = c : 4
Which means :-
6 : 8 :: c : 4
6/8 = c/4
= 6 × 4 = c × 8
= 24 = 3 × 8
c = 3
The ratio = 6 : 8 :: 3 : 4
Which means that C = 3 .
What is the value of j
Answers
180- 82= 98
98 - 32 = 66
So it’s 66
Triangle A B C is reflected across the line of reflection m to form triangle A prime B prime C prime. Triangle A prime B prime C prime is rotated about point B prime 270 degrees to form triangle A double-prime B double-prime C double-prime.
Which rule describes the composition of transformations that maps ΔABC to ΔA"B'C"?
Answers
Answer:
it is D trust me
Step-by-step explanation:
Answer:
the answer is d
Step-by-step explanation:
the way you can figure this out is by looking at the figures and finding what transformation came first because of the number of prime notations on a letter in a figure. in this case is was ABC first then A'B'C' then A''B''C''
using that we can now determine the order of how the composition will be written. the first step of the composition is the left most part and the last part of the composition is the right most part. basicly the order is left to right.
we see that figure ABC is reflected across the line m to create the figure A'B'C' relections are written like r for the relection and the sub letter is the line the figure is reflected across to in this case it would be written as r sub m meaning that r sub m is the 2nd part of the composition.
the 2nd step in the composition is when figure A'B'C' turns into figure A''B''C'' the way we find out its transformation is determine whether it was slid or if it was rotated aroound a point of rotation. here we have a rotation. now we got to determine what the center of roation is. in this case its B'. looking at the options there is no negative -90 degrees which means that the rotation happened counter clockwise because all valuse are positive. counter clockwise is to the left. now simple math figure A'B'C 180 degrees would make it need 90 more degrees so 180+90=270 thats the degree of the roation around point B'
rotations are written as R sub point of rotation, __ degrees. in our case it is r sub B', 270 degrees. this is the second step so it will be on the right of the equation. the full equation turns out to be R sub B', 270 degrees composition of transformations r sub m.
it must be that way because if you rotated the figure first then reflected it it would look like an entirely different image.
pls give brainliest
Find the equation of a parabola with a focus at (–2,–3) and a directrix at y = –5.
A)
y = 1∕4(x – 2)2 – 4
B)
y = –1∕16(x + 2)2 – 4
C)
y = 1∕4(x + 2)2 – 8
D)
y = 1∕4(x + 2)2 – 4
Answers
Answer:
It"s (C) byeeee and ur welcome
someone pls help, find the length of the segment
Answers
the segment is 4 units long
hope this helps
Evaluate the expresion for x=6. -2x + 1/3(x2 + 6) - 36/6
Answers
Answer:
x=6/7 hope i did it right- im so sorry if thats wrong
Step-by-step explanation:
How much is one pound of oranges according the the chart?
Answers
Answer:
The retail price for bananas and seedless grapes has had a somewhat rockier track record over the past 25 years. Starting at 45 U.S. cents in 1995, the price of bananas per pound reached its peak in 2008, with 62 cents. In 2019, bananas cost consumers an average of 57 U.S. cents per pound. In recent years, the retail price of seedless Thompson grapes had decreased: the price stood at roughly 3 U.S. dollars per pound in 2014 and dropped to approximately 2.40 U.S. dollars in 2019.
Sales growth of fresh fruit
In 2019, sales numbers for papayas increased by roughly 15 percent in the United States, making it the type of fresh fruit that experienced the highest rate of sales growth that year. Kiwis, berries, and limes were some of the other fruit types that experienced growth in the United States, while sales percentages for apricots, oranges, and tangelos decreased considerably
Step-by-step explanation:
Answer:
1.50
Step-by-step explanation:
On the X-axis where oranges are graphed, you run until you get to 1 pound. Then you go up from the X-axis and see where it connects with the Y-axis (total cost)
What might be the result of sharing a link if it is pseudopsychology instead of accurate psychological science?
You would be unintentionally sharing inaccurate information.
You might get credit for the information in the article.
You would have an article you could cite for a class project,
You will find good evidence to back up the headline in the article
Submit
W
Answers
Answer:
You would be unintentionally sharing inaccurate information.
Step-by-step explanation:
i just read the book
A taxi company charges $3 per ride plus $1.50 for each mile traveled. Andrea wants to spend no more than $24 on a taxi ride. How many miles can Andrea travel? Select all that apply.
Answers
Answer:
x=14
Step-by-step explanation:
3+1.50x=24
24-3=21
21/1.50=14
Answer is C which is 14
is 10 15 18 equal to a right triangle
Answers
Answer:
no
Step-by-step explanation:
Right triangles follow the Pythagorean theorem:
[tex]a^2+b^2=c^2\\c=\sqrt{a^2+b^2}\\18=\sqrt{10^2+15^2} \\18=\sqrt{325} \\18 != 18.0277\\[/tex]
Because this statement isn't true, the side lengths are not for a right triangle.
Simplify the expression:
27
simplifying square roots
Answers
Answer:
3^2
Step-by-step explanation:
3x3x3 = 27
Because if you have 3^2 then that is 3 to the power of 2 and 3 to the power of 2 is 27.
Answer:
3 by the power of 2
Step-by-step explanation: