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
There are 16 boys and 20 girls in a class. What part of the class is boys? What part girls?
Answers
Answer:
girls 4/9 or (Decimal: 0.444444) percent is 44.4%
boys 5/9 or (Decimal: 0.555556) percent is 55.5%
In a 20 item true-false examination, if 12 correct answers constitute a passing grade,
what is the probability that someone will pass, if they are guessing?
A. .8398
B. .2517
C. .1201
D. .1317
Answers
Answer:
The answer is B, I know this because I just took a test with this question lol
If 12 correct answers constitute a passing grade on a 20-item true-false exam, the probability that someone will pass is 1/2 if they are guessing.
What is meant by probability?Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring. Probability = the number of possible paths to success. The total number of possibilities For example, the probability of flipping a coin and getting heads is 12, because there is only one way to get a head and there are two possible outcomes.Therefore,
Let X denote the number of correctly answered questions out of a total of 20.
Bernoulli trails are formed by repeated coin tosses. Because the "head" on a coin represents the correct answer and the "tail" represents the incorrect answer, the questions that are correctly answered are Bernoulli trials.
[tex]$&\therefore \mathrm{p}=\frac{1}{2} \\[/tex]
[tex]&\therefore \mathrm{q}=1-\mathrm{p}=1-\frac{1}{2}=\frac{1}{2}[/tex]
X follows a binomial distribution with n = 20 and p = 1/2
[tex]&\therefore P(X=x)={ }^n C_x q^{n-x} p^x \\[/tex]
[tex]&={ }^{20} C_x\left(\frac{1}{2}\right)^{20-x} \cdot\left(\frac{1}{2}\right)^x \\[/tex]
[tex]&={ }^{20} C_x\left(\frac{1}{2}\right)^{20}[/tex]
P ( at least 12 questions answered correctly )= P (X ≥ 12)
[tex]&=\mathrm{P}(\mathrm{X}=12)+\mathrm{P}[/tex][tex](\mathrm{X}=13)+\ldots+\mathrm{P}(\mathrm{X}=20) \\[/tex]
[tex]&={ }^{20} \mathrm{C}_{12}\left(\frac{1}{2}\right)^{20}+{ }^{20}[/tex][tex]\mathrm{C}_{13}\left(\frac{1}{2}\right)^{20}+\ldots+{ }^{20}[/tex][tex]\mathrm{C}_{20}\left(\frac{1}{2}\right)^{20} \\[/tex]
[tex]&=\left(\frac{1}{2}\right)^{20} \cdot\left[{ }^{20} \mathrm{C}_{12}+{ }^{20} \mathrm{C}_{13}+\ldots+{ }^{20} \mathrm{C}_{20}\right][/tex]
Hence, If 12 correct answers constitute a passing grade on a 20-item true-false exam, the probability that someone will pass is 1/2 if they are guessing.
The complete question is:
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers 'true', if it falls tails, he answers 'false'. Find the probability that he answers at least 12 questions correctly.
To learn more about probability, refer to:
https://brainly.com/question/24756209
#SPJ2
explain the relationship between a strategy such as number sense and a written method such as partial products or area models for multiplying decimal numbers
Answers
Step-by-step explanation:Firstly, strategy are all in mind and not on paper while written methods are solid proofs that are written on paper. Strategies may or may not work out with respect to the situation, while Written method will always work. They are actually written after testing their reliability. As far as you multiply decimal numbers these will go in vain and you have to use your mind to solve these
The relationship between strategy and written method in mathematics is that;
Strategies can be changed or modified whereas written methods cannot be changed or modified because they have standards upon which such methods are based.
In mathematics, strategies are defined as the different ways in which a problem can be approached. For example;A student wants to perform addition of 19 and 46.
He could add the number straight away by doing 19 + 46 = 65or he can
take away 1 from 46 to become 45 and add that 1 to 19 to become 20 and
then sum 45 and 20 together as 20 + 45 = 65.
So we can see that the two strategies used to add 19 and 46 gave the same result.
In contrast, when dealing with written methods like partial products one cannot use any other method apart from that stated in the written method.For example, we want to use partial products to multiply 13 x 52.
The solution would become (10 × 50) + (10 × 2) + (3 × 50) + (3 × 2) = 676.
In this method, there cannot be another way used as the standard for using partial products is written and fixed.
Read more at; https://brainly.com/question/18884089
plssssssssssssssssssssssss help for test
Your math class is collecting canned food for a local food drive. The goal is to collect at least 130 cans but no more than 250 cans due to space limitations. There are 24 students in your math class and your teacher has promised to bring in 10 cans. Select which inequalities represent the possible numbers n of cans that each student should bring in.
Answers
the first thing we must do is define variables.
We have then:
n: number of cans that each student must bring.
We know that:
The teacher will bring 5 cans
There are 20 students in the class
At least 105 cans must be brought, but no more than 205 cans
Therefore the inequation of the problem is given by:
105 < 20n + 5 <205
Answer:
the possible numbers n of cans that each student should bring in is: 105 < 20n + 5 < 205
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:
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
I don’t understand what this means
Answers
Answer:
This means that if you have that amount of those and you do whatever the rest of the question is.
Step-by-step explanation:
Answer:
120 different ways
Step-by-step explanation:
So Fundamental Counting Principle helps understand probability. So for this question, they are asking how many different ways there are.
To do that, we have to split into sets.
Set A: 4 Theme Parks
Set B: 6 Passes
Set C: 5 Food Options
Now we have to multiply the sets.
4 x 6 x 5 = 120
Therefore, the answer is 120 different ways.
How do you do this question?
Answers
Answers:
[tex]\displaystyle \lim_{n \to \infty} \frac{a_n}{b_n} = 6[/tex]
Based on the limit comparison test, the series is convergent
========================================================
Explanation:
As n gets really large, the terms [tex]3^n[/tex] and [tex]3^n-2[/tex] are effectively the same. Taking the limit to infinity of the ratio leads to 1.
In other words,
[tex]\displaystyle \lim_{n \to \infty} \frac{3^n}{3^n-2} = \lim_{n \to \infty} \frac{3^n}{3^n} = 1[/tex]
That -2 doesn't really play a role when n gets very large.
This result is then multiplied by the 6 in the [tex]a_n[/tex] sequence, getting 6 as the final limit we want.
So,
[tex]L = \displaystyle \lim_{n \to \infty} \left(a_n \div b_n\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6}{3^n-2} \div \frac{1}{3^n}\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6}{3^n-2} \times \frac{3^n}{1}\right)\\\\\\L = \displaystyle \lim_{n \to \infty} \left(\frac{6*3^n}{3^n-2}\right)\\\\\\[/tex]
[tex]L = \displaystyle 6*\lim_{n \to \infty} \left(\frac{3^n}{3^n-2}\right)\\\\\\L = \displaystyle 6*\lim_{n \to \infty} \left(\frac{3^n}{3^n}\right)\\\\\\L = \displaystyle 6*\lim_{n \to \infty} (1)\\\\\\L = \displaystyle 6*1\\\\\\L = \displaystyle 6\\\\\\[/tex]
Since the limiting value is positive and not infinity, this means that both series [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] converge or they both diverge.
----------------------------
If we plug n = 2 into the [tex]b_n[/tex] sequence, we get
[tex]b_n = \frac{1}{3^n}\\\\b_2 = \frac{1}{3^2}\\\\b_2 = \frac{1}{9}[/tex]
The first term is a = 1/9
If we plugged n = 3, we would get [tex]b_3 = \frac{1}{27}[/tex]
This shows that the common ratio is r = 1/3
Because -1 < r < 1 is true, we know that the infinite geometric series converges. Therefore, [tex]\sum b_n[/tex] converges. We don't need to find the converging value.
Going back to the limit comparison test, we stated that both [tex]\sum a_n[/tex] and [tex]\sum b_n[/tex] either diverge together or converge together.
We've shown that the b series converges, so the 'a' series must converge as well.
John had a baseball cards until he gave x cards away. How many cards does he have now?
Answers
Answer:
I don’t think the question makes sense
write an equation that represent the table
Answers
Answer:
y equals 5x + 20
The length of a rectangle is 4 more than the width. The area is 357 square centimeters.
Find the length and width of the rectangle
Answers
Answer:
17*21 = 357
Step-by-step explanation:
Firstly, set up your equation.
x*(x+4)=357
Multiply X by (x+4)
x^2+4x=357
You then subtract 357 from both sides
x^2+4x-357=0
Simplify using the quadratic formula shown, if you need assistance on solving this equation put it into a online calculator, or photomath as it shows the steps taken to solve it.
[tex]\frac{-4+\sqrt{4^2-4\cdot \:1\cdot \left(-357\right)}}{2\cdot \:1}\\[/tex]
My question is
4(2 - W) + w = 20
Answers
Answer:
- 4
Step-by-step explanation:
Step 1:
4 ( 2 - w ) + w = 20 Equation
Step 2:
8 - 4w + w = 20 Multiply
Step 3:
8 - 3w = 20 Combine Like Terms
Step 4:
- 3w = 12 Subtract 8 on both sides
Answer:
w = - 4
Hope This Helps :)
Answer:
w = -4
Step-by-step explanation:
4(2 - W) + w = 20
Distribute:
8 - 4w + w = 20
Subtract 8 from both sides:
-4w + w = 12
Simplify:
-3w = 12
Divide:
w = -4
Double check your work by substitution:
4(2 - W) + w = 20
4(2 - (-4)) + (-4) = 20
4(6) + (-4) = 20
24 + (-4)= 20
20 = 20
Since we know that 20 does equal 20, we can conclude that the final answer is:
w = -4
Combine Like Terms. -13x + 14a - 12x + 7x - 4x *
Answers
Answer:
4a - 22x
Step-by-step explanation:
-13x +14a - 12x + 7x - 4x = 4a - 22x
hope this helps :)
Calculate the vertices
(x+3, y + 1)
Answers
Answer:
A' (4,4), B' (5,7), C' (9,7)
Step-by-step explanation:
- Karan has n chocolates. He gave his younger brother 5 chocolates and distributed the remaining is
equally between his friend and himself. How many chocolate did his friend get in terms of n?
Answers
Answer:
4 chocolates
Step-by-step explanation:
n-c
brother-5n
5n-n=4
=4
If the bother has 5, then that leaves the rest to be 12 which is evenly distributed among his friends
N=4
3.A normal bus carries x passengers.
A large bus will carry twice as many passengers than the normal bus
A small bus will carry 8 passengers less than the normal bus.
Altogether the buses carry 128 passengers.
(a) Form a simplified equation in terms of x
Answers
Answer: A) 4x -8 = 128
Step-by-step explanation:
We will represent the amount that the normal bus carries by n= x
We will represent the amount that the large bus carries by l = 2x
We will also represent the amount that the small bus carries by s = x-8
Now add them to equal to 128.
x + 2x + x -8 = 128
4x -8 = 128
Measures of the missing numbered angles
Answers
Answer:
23
Step-by-step explanation:
is this correct or not
Answers
Answer:
yes it is u did a good job
Find the distance between each pair of points in the coordinate plane.
(3,-2) and (2,-1)
Answers
Answer:
1.41
Step-by-step explanation:
Solve the literal equation xy - 4xz = 5 for x.
X=
Answers
Answer:
x = 5/(-4 z + y)
Step-by-step explanation:
Solve for x:
x y - 4 x z = 5
Hint: | Write the linear polynomial on the left-hand side in standard form.
Collect in terms of x:
x (-4 z + y) = 5
Hint: | Solve for x.
Divide both sides by -4 z + y:
Answer: x = 5/(-4 z + y)
-7+8
what is negative 7 plus 8?
Answers
Answer:
1
Step-by-step explanation:
You could have just used a calculator tard lol
Answer:
1
Step-by-step explanation:
-7 +8=1 cause you have 1 positive left over
Why is the percent increase from 45 to 75 not equal to the percent decrease from 75 to 45? Select three options
Answers
Answer:
the answer is 2,3,and 5
Step-by-step explanation:
Answer:
2, 3, and 5
Step-by-step explanation:
Classify the following triangle. Check all that apply.
A. Right
B. Isosceles
C. Obtuse
D. Acute
E. Equilateral
F. Scalene
Answers
Answer:
is there a chart to this question?
because I can't tell the answer just by looking at it
Step-by-step explanation:
it's a b c d and f are all the correct answers
What is f(3)?
o 9
0 -1
O 1
O 9
Answers
Answer:
C.
Step-by-step explanation:
f(3) is referring to 3 on the left side and it is beside 1 which is on the left so it's 1.
Write each prime factorization using exponents.
1. 2×2×2×7
2. 2×3×3
3. 7×7×7×7
Answers
2). 2 x 3²
3). 7⁴
Human hair has an average diameter of about 0.000017 meters. Write this measurement in scientific notation
Answers
Answer:1.7 x 10 ^ -5
Step-by-step explanation:
Answer:1.7 x 10-5
hope this helps
Deandre pays $15.20 for a pack of 8 towels.
Find the unit price in dollars per towel.
If necessary, round your answer to the nearest cent.
Please help
Answers
Answer: Each towel costs $1.90
Step-by-step explanation:
$15.20 divided by 8 = $1.90
The grandpapa car traffic function is shown check although following statements are true of the function
Answers
HELP ME PLS ITS DUE TODAY :((
Answers
Answer:
3 8
18 48
22.5 60
27 72
Step-by-step explanation:
3:8 ratio
18/3=6
8*6=48
Answer:
48
60
72
Step-by-step explanation:
1. Find the number of times x or the first column numbers are multiplied to get y or the second column numbers.
2. Equation: 3*?=8, ? = 8/3
3. Multiply all of the other numbers by 8/3 to get the answers.
4. 3*8/3=8, 18*8/3=48, 22.5*8/3=60, 27*8/3=72.
Answers: 48, 60, 72
PLSSSS HELLPPPP MEEEEEEE ASAPPPP I WIILL GIVE BRAINLIEST!!!!!!!!! PLS SHOW WORK STEP BY STEP
Answers
Answer:
y = -3x + 3
Step-by-step explanation:
Slope = -3
y-intercept = 3
Substitute values into slope intercept form :
y=mx + b
Where :
m= Slope
b = y-intercept
[tex]y = - 3x + 3[/tex]