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
45.52
The attendance at a seminar in year 1 was 500. In Year 2, the attendance changed by 100. What was the percent chang
in attendance?
O The percent change was 0.2%.
O The percent change was 0.4%.
O The percent change was 20%.
O The percent change was 40%.
Save and Exit
Next
Submit
Marke this and tu
Answers
Answer:
20%
Step-by-step explanation:
[tex]percent change = \frac{difference}{original value} * 100[/tex]
[tex]= \frac{100}{500} * 100\\= 20[/tex]
Which expression shows the COMMUTATIVE PROPERTY of addition?
A. 3 + 5 + 2 = 3 + (5 + 2)
B. 3 + 5 + 2 = 8 + 2
C. 3 + 5 + 2 = 5 + 2 + 3
D. 3 + 5 + 2 = 10
Answers
Answer:
C
Step-by-step explanation:
Commutative property means to add in a different order.
what is the constant in 15-8y
Answers
Answer:
15
Step-by-step explanation:
15 doesn’t have variable next to it
8 would be a coefficient
A scale drawing of an office space uses a scale of 1 in. : 6 yd. The scale drawing has an area of 5 square inches. What is the area of the actual office space?
Answers
Answer: 30
Step-by-step explanation:
The scale is 1 in : 6 yd. the drawing was 5 inches. Multiply the drawing measurement (5) times the yards cause that’s the measurement you want and you get 30 yards.
Which point lies on the line -x+4y=-3
Answers
Answer:
3x+4y
gyhhuhyyb buhhujnjjijnjijhu
A lot contains 12 items, and 4 are defective. If three items are drawn at random from the lot, what is the probability they are not
defective?
Answers
Answer:
ur nan
Step-by-step explanation:
Factorise 6x squares minus 14x
Answers
First, let's solve this using Bhaskara:
−
14
±
√
14
2
−
4
(
6
)
(
−
12
)
2
⋅
6
−
14
±
22
12
Roots:
x
=
−
3
, which is the same as the factor
x
+
3
=
0
x
=
2
3
, which is the same as the factor
3
x
−
2
=
0
Using these factors, we can rewrite the original function:
6
x
2
+
14
x
−
12
=
2
(
3
x
2
+
7
x
−
6
)
=
2
(
x
+
3
)
(
3
x
−
2
)
2
x
2
x
out of
6
x
2
6
x
2
.
2
x
(
3
x
)
+
14
x
2
x
(
3
x
)
+
14
x
Factor
2
x
2
x
out of
14
x
14
x
.
2
x
(
3
x
)
+
2
x
(
7
)
2
x
(
3
x
)
+
2
x
(
7
)
Factor
2
x
2
x
out of
2
x
(
3
x
)
+
2
x
(
7
)
2
x
(
3
x
)
+
2
x
(
7
)
.
2
x
(
3
x
+
7
)
can someone help me i don’t get this at all !!!! OLEASEEE
Answers
Answer:
A
Step-by-step explanation:
not enough info
What are the partial products that result from multiplying 15 x 32? (____ x ____) + (____ x ___) + (____ x ____) + (____ x ____)
Answers
Dividing both into this (15 x 32) below.
15=10+5
32=30+2 and both of the equations will give you the result of 4 partial products.
10x30=300
5x30=150
10x2=20
5x2=10
How many times greater is the product of 4 x 300 than the product 4 x 30
Answers
Answer:
10 times bigger
Step-by-step explanation:
because if you do 4 times 300 thats 1200
and if you do 4 times 30 then you get 120
and 120 times 10 is 1200 so there you go.
HOPED THIS HELPED!!!!!!!!! :D
) A watershed experiences a rainfall of 8 inches. What is the runoff volume when the curve number is 80
Answers
Answer:
5.625 inches
Step-by-step explanation:
Given that:
Total Rainfall in inches (P) = 8 inches
The runoff volume (in inches) Q = ???
The curve number CN = 80
Recall that: The runoff volume can be calculated by using the formula:
[tex]Q = \dfrac{(P-0.2S)^2}{(P+0.8S)}[/tex] for P > 0.2S
Q = 0 for P < 0.2S
[tex]S = \dfrac{1000}{CN}-10[/tex]
where:
curve number CN = 80
[tex]S = \dfrac{1000}{80}-10[/tex]
S = 2.5 inches
Since the rainfall (P) is greater than 0.25
Then:
[tex]Q = \dfrac{(P-0.2S)^2}{(P+0.8S)}[/tex]
[tex]Q = \dfrac{(8-0.2(2.5))^2}{(8+0.8(2.5))}[/tex]
[tex]Q = \dfrac{(8-0.5)^2}{(8+2)}[/tex]
[tex]Q = \dfrac{(7.5)^2}{(10)}[/tex]
[tex]Q = \dfrac{(56.25)}{(10)}[/tex]
Q = 5.625 inches
Thus, the runoff volume = 5.625 inches
Ritika bought 5 meters of cloth from the market. She cut off 2 3/4 meters and gave it to Aditi. What length of cloth is left with her?
Answers
Answer:
I think its 3/2
hope it will help you
One number exceeds another by 1. The sum of the numbers is 23. What are the numbers?
Answers
Answer:
the numbers are 11 and 12
Step-by-step explanation:
Ethan bought 4 packages of pencils. After he gave 8 pencils to his friends, he had 40 pencils
left over. How many pencils were in each package? Use the drop-down menus to solve the
problem arithmetically and algebraically.
Answers
He had 40 pencils left after he gave away 8, so originally he had 40 + 8 pencils, which is 48.
Now, he bought 4 packages, which had a total of 48 pencils, so divide 48 by 4, which is 12. He had 12 pencils in each package.
To determine the solution arithmetically, first add 8 to 40, then divide 48 by 4.
To determine the solution algebraically, set up and solve the equation 40 = 4x - 8.
Each package contained 12 pencils.
Hope this helps
Hey now please just anser if itnus a try i will still give 5 stars. THE Question is what is the most easy way to SOLVE THE NINES TABLE IK THIS BUT I WANT to see who else knows sorry fir the big ketters i did not means to put that
Answers
Answer:
Tbh, I think the easiest way is to count on your fingers. I still do it, however I can now do my chart tables to 17x17 by using fingers. People may tease, however, it is a good way to make sure you do not mess up as much as memorizing. You should memorize, and count on your fingers at the same time to solve extremely fast.
Step-by-step explanation:
9x4
You can pretend that your thumb equals nine, and count 9 plus 9 plus 9 plus 9, with each other finger, such as your ring finger, pointer, middle, and pinky , which equals 36. 5x9, you have five fingers on each hand, so each finger can equal nine (I don't care if people say that your thumb isn't a finger, just take it and move on lol).
Define cross-multiplication property
Answers
Answer: Not to be confused with Cross product.
In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable.
The method is also occasionally known as the "cross your heart" method because a heart can be drawn to remember which things to multiply together and the lines resemble a heart outline.
The expression 34−10+3+2=78 is an example of
Answers
Answer: simplifying expression
Step-by-step explanation:
What’s the difference between m=change in y and change in x and m =y2-y1and x2-x1
Answers
it's the same thing
[tex]slope = \frac{Δy}{Δx} or \frac{change \: in \: y}{change \: in \: x} = \frac{y2 - y1}{x2 - x1} = \frac{rise}{run} [/tex]
With the money she had saved by working, Jennifer wanted
Answers
Answer:a car
Step-by-step explanation:
SOMEONE PLEASE PLEASE HELP!!!!
Answers
Answer:
49[tex]\sqrt{21}[/tex]
Step-by-step explanation:
You multiply the two sevens to get the 49, and the square root of three has to be multiplied as well
Answer: 49 √3 or 84.87049
Step-by-step explanation:
If lim f(x)=5 g(x)=0 and h(x)=-2 then find (3h/2f+g)(x)
Answers
Answer:
B
Step-by-step explanation:
edg 2021 unit test review
To show that the triangles are congruent, triangle ABC could be transformed by which movement(s) to fit exactly on triangle XYZY
a rotation of 180° clockwise about the origin followed by a dilation of 1.2 with the center of dilation at the origin
a rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units
a rotation of 270° clockwise about the origin followed by translations left 1 unit and up 10 units
a reflection over the x-axis followed by a reflection over the y-axis
Answers
Answer:
a rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units
Step-by-step explanation:
Rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units is the required transformation.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Graph transformation is the process by which an existing graph, or graphed equation, is modified to produce a variation of the proceeding graph.
We have to show that triangle ABC could be transformed by which movement(s) to fit exactly on triangle XYZ.
Rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size
So if triangle ABC is rotated about 90 degrees clockwise about the origin followed by translated down 1 unit and left 10 units we get XYZ.
Hence, rotation of 90° clockwise about the origin followed by translations down 1 unit and left 10 units is the required transformation.
To learn more on Graph click:
https://brainly.com/question/17267403
#SPJ2
By the end of Tina’s bike ride, she traveled a distance of 40 kilometers. How many miles did Tina ride? (1 mile ≈ 1.6 kilometers)
help plz brainless you help me
Answers
Answer:
24.85 or rounded to 24.9
Step-by-step explanation:
Conversion
K H D____D C M
The number of miles did Tina ride when (1 mile ≈ 1.6 kilometers) so it should be considered as the 25 miles.
Calculation of the number of miles:Since
By the end of Tina’s bike ride, she traveled a distance of 40 kilometers.
And we know that
1 mile ≈ 1.6 kilometers
So,
[tex]= 40 \div 1.6[/tex]
= 25 miles
hence, The number of miles did Tina ride when (1 mile ≈ 1.6 kilometers) so it should be considered as the 25 miles.
Learn more about miles here: https://brainly.com/question/13208356
What are the domain and range of f (x)= -27
Answers
Answer:
Domain: (-∞,∞)
Range: {−27}
HELP ME PLEASE IM ALMOST TO 100
Answers
Answer:
= 3/4
Step-by-step explanation:
Find 2 points on the graph
(2,3) and (6,6)
Using the slope formula
m = (y2-y1)/(x2-x1)
= ( 6-3)/(6-2)
= 3/4
Date:10/16/20
1. The largest river in the world is the Nile River. It is 4,132 miles long. The
longest river in the United States is the Missouri River. It is 2,540 miles long.
Which is the best estimate of the difference in the lengths of the Nile and
the Missouri rivers?
a. 1,000 miles
b. 1,600 miles
c. 2,000 miles
d. 6,600 miles
2. Each year, the NYC Humane Society works to raise as much money as
possible for the animal shelters. Last month, they raised $14,392 from donations
and $456,892 from pet adoptions. About how much money did they raise
altogether?
Answers
the answer to 1 is d and the answer to 2 is 471,284. Please review this topic when you get time.hope this helps
An item has a listed price of $80. If the sales tax rate is 8%, how much is the sales tax (in dollars)?
Answers
Answer:
$6.40
Step-by-step explanation:
u have to multiply 80 by 0.08 (tax percent in decimal form)
Answer:
$6.4
Step-by-step explanation:
all you have to do is find 8% of 80 by doing 8x8, which equals 64, then dividing by 10. That gives you 6.4. Then check it on a calculator to make sure you did it correctly
HELP WITH MATH!!! 20 points
the questions are solving systems by substitution
Answers
Answer: 1. 2x-3y=-1 y=x-1 2. y=6x-11 -2-3y=-7 3. y=3x+5 5x-4y=-3
#1. 2x-3y=-1 and y=x-1
#2. y=6x-11 and -2x-3y=-7
#3. y=-3x+5 and 5x-4y=-3
the ray XZ is the angle bisector of WXY and m WXY = 125°. Enter m WXZ
Answers
PLEASE HELP WORTH 40 POINTS FOR WHOEVER ANSWERS CORRECTLY!!!! PLEASE HELP
1. Refer to the equation 3x − 5y = 15.
(a) Create a table of values for at least 4 points. Show your work on how you found the values for each coordinate pair and validated the points were on the line.
Answers
Answer:
x = 1 ⇔ y = -2.4
x = 2 ⇔ y = -1.8
x = 3 ⇔ y = -1.2
x = 4 ⇔ y = -0.6
Step-by-step explanation:
[tex]3x-5y=15[/tex]
→ Rearrange to make y the subject
[tex]-5y=-3x+15[/tex]
→ Multiply everything by -1
[tex]5y=3x-15[/tex]
→ Divide everything by 5
[tex]y=0.6x-3[/tex]
⇒ Substitute x = 1, 2, 3 and 4
[tex]y=0.6x-3\\ y=(0.6*1)-3\\ y=0.6-3\\ y=-2.4\\(1,-2.4)[/tex]
[tex]y=0.6x-3\\ y=(0.6*2)-3\\ y=1.2-3\\ y=-1.8\\(2,-1.8)[/tex]
[tex]y=0.6x-3\\ y=(0.6*3)-3\\ y=1.8-3\\ y=-1.2\\(3,-1.2)[/tex]
[tex]y=0.6x-3\\ y=(0.6*4)-3\\ y=2.4-3\\ y=-0.6\\(4,-0.6)[/tex]