Explore sums of complex
numbers by moving points A
and B and noticing how the
sum of those points written
in the expression below
corresponds to the sum
shown geometrically.
Drag the points, A and B, to
produce a result of -3 + 4i.
Answers
The two-point A and B will be -1+2i and -2+2i respectively.
What is the complex number?A complex number is one that has both a real and an imaginary component, both of which are preceded by the letter I which stands for the square root of -1.
The complex number is given as;
x+iy
Where x is the real part and iy is the imaginary part.
The two points added to obtained -3 + 4i are;
A = -1+2i
B= -2+2i
The sum of the two points is;
⇒A+B;
⇒-1+2i + -2+2 i
⇒-3 + 4 i
Hence the two-point A and B will be -1+2i and -2+2i respectively.
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Related Questions
A pair of equations is shown below.
Answers
Answer: (2,5)
Step-by-step explanation: Step 1: Identify key concepts for Part A
y=7x-9
Slope: 7
y int. : -9
y=3x-1
Slope: 3
y int. : -1
Since you know this information, you can plot the points and graph it.
Part B
To solve a system of equations, you need to identify the point whereby the two graphs intersect, and since you're solving it graphically, just find the point of intersection. You should get an answer of: (2,5)
(x=2) and (y=5)
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
Answer:
Step-by-step explanation:
f(x) = x^2 – 5x + 12
The value of f(–10) = 82? NO
f(-10) = (-10)^2 – 5(-10) + 12
f(-10) = 100 + 50 + 12
f(-10) = 162
NO
The graph of the function is a parabola. YES
See attached graph.
YES
The graph of the function opens down. NO
See attached graph.
The graph contains the point (20, –8). NO
See graph
----
Plus we can use x=20 in the function and see if it returns -8:
f(x)=x^2-5x+12
f(20)=(20)^2-5*(20)+12
f(20) = 400 - 100 + 12
f(20) = 312 It does not result in -8
The graph contains the point (0,0). NO
See graph
The time spent dancing (minutes) and the amount of calories burned can be modeled by the equation c = 5.5t. Which table of values matches the equation and includes only viable solutions?
Answers
The table that matches the equation is:
Time Calories
-20 -110
-10 -55
-15 - 82.50
-5 -27.50
What is the correct table?The correct table would contain values that are multiples of 5.5t
For example:
Total calories burned at 20 seconds : 5.5 x 20 = 110
Total calories burned at 10 seconds : 5.5 x 10 = 55
Total calories burned at 15 seconds : 5.5 x 15 = 82.50
Total calories burned at 5 seconds : 5.5 x 5 = 27.50
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Answer:
The 2nd one
Step-by-step explanation:
its the right one
Solve:
x-1
——— < 0
x²-4
Answers
Answer: x≠±2, x<±2, x>1, x<1, and x>±2
explanation:
for this equation to be true
Case 1
either (x-1) should be a negative while (x²-4) should be positive
which gives:-
x-1<0
so, x<1
also, x²-4>0
so, x²>4
⇒x>±2
Case 2:-
x-1>0 and x²-4<0
which gives
x>1 and x²-4<0
so, x>1 or x<±2
Case 3:-
either way, the denominator can't be 0
so, x²-4≠0
which gives,
x≠±2
compiling all, we have,
x≠±2, x<±2, x>1, x<1, and x>±2
These solutions can be pointed to as points on a number line and the behavior shows their discontinuity.
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Please help me!! matrices question! ASAP
Answers
Write the equation of the line in slope-intercept form Slope=5/3 Y-Intercept=4
Answers
Answer:
y=5/3x+4
Step-by-step explanation:
Slope intercept formula: y=mx+b
m=slope
b=Y-Intercept
Answer:
[tex]\sf y=\dfrac{5}{3}x+4[/tex]
Step-by-step explanation:
Given:
[tex]\textsf{slope of $\dfrac{5}{3}$, and a y-intercept of $4$}[/tex]
⇒ Slope-Intercept Form: y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Substitute the given values:
[tex]\sf\\ \implies y=mx+b\\\\\implies y=\dfrac{5}{3}x+4[/tex]
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is n÷12=36,n=108 true or false
Answers
Answer:
False
Step-by-step explanation:
n÷12=36
n=36*12
hence n=432
hope it helps you and give me a brainliest
Answer:
(redacted answer - it was wrong - moderator please delete)
false
what is the slope of the line that is perpendicular to the line 3y=-5x+21
a -5/3
b -3/5
c- 3/5
d- 5/3
Answers
Step-by-step explanation:
the slope is the factor of x in an equation
y = ax + b
we have here
3y = -5x + 21
to get to the general format above we need to divide everything by 3 :
y = -5/3 x + 7
so, we see, the slope is -5/3.
the perpendicular (angle of 90°) slope is the original slope turned upside-down and with flipped sign :
3/5
so, I guess the correct answer option is c.
but it is not clear what you wrote there, as there is a "-" sign somehow in all 4 answers.
A single die is rolled. How many ways can you roll a number that is prime,
followed by a number less than 6? (Remember that 1 is not a prime number.)
Answers
Answer:
3 different ways
Step-by-step explanation:
2, 3, and 5 are all prime numbers under 6
What is the original price of an item that is being charged a tax of 20%, and
the total price is $144?
Points 1
Answers
So 144-28.80= 115.20
$115.20
So 144 minus 28.80 equals 115.20
The answer is 115.20
A.P.E.X Algebra 1 Sem 2
Answers
Answer:
Data Set C
Step-by-step explanation:
You can see that the data is best fit and better looking and fitting to the line in the data set C.
Find the value of x ??
A. 31
B. 5
C. 11
D. 25
Answers
Answer: 11
Step-by-step explanation:
By the trapezoid midsegment theorem, x = (9+13)/2 = 11
Find the sum :
3/8 + 22.5
Answers
Answer:
183/8 or 22.875
Step-by-step explanation:
Take 22.5 and put it over 1 so 22.5/1
And then multiply by 8 to get a common denominator (180/8) then add the 3/8 and you get 183/8 or 22.875
The vertical walls of two buildings are 50 m and 30 m tall. A vertical flagpole [XY] stands between the buildings such that B, Y, and C are collinear, and A, Y, and D are collinear. The vertical walls of two buildings are 50 m and 30 m tall . A vertical flagpole [ XY ] stands between the buildings such that B , Y , and C are collinear , and A , Y , and D are collinear . find the height of the flagpole
Answers
Answer:
which class of this exam
In a group of 36 pupils, 6 play the flute only.
6 play the piano only.
13 play neither instrument.
A student is selected at random.
What is the probability the student plays both instruments?
Help please
Answers
36-(6+6+13)/36
Hope this helped
5
·?
16. Which of the following is equivalent to 49
05-7²
O 5(7²)
O 5(72)
1
5(7²)
O
Answers
Step-by-step explanation:
[tex] = 49[/tex]
[tex] = 7 \times 7[/tex]
[tex] = {7}^{1 + 1} [/tex]
[tex] = {7}^{2} [/tex]
please help
Find the sum or type
“impossible”
Answers
Answer:
finished this question is from matric it is very easy
What are the solutions of the equation (x 2)2 – 2(x 2) – 15 = 0? use u substitution to solve.
Answers
The solution of the equation is x=3 or x=-5.
Given that the equation is (x+2)²-2(x-+2)-15=0 and use u substitution method to solve.
Let's assume that the (x+2)=u.
The given equation is rewritten as u²-2u-15=0.
Factorize the quadratic equation by adding or subtracting two number that gives the sum of -2u and product 15u² as
u²-5u+3u-15=0
u(u-5)+3(u-5)=0
Taking out (u-5) as common and get
(u-5)(u+3)=0
Compare each equation with 0 and get
u-5=0 or u+3=0
u=5 or u=-3
Performing back substitution by substituting the values of u in x+2
when u=5 then x is
x+2=5
x=3
And when u=-3 then x is
x+2=-3
x=-5
Hence, the solutions of the (x+2)²-2(x-+2)-15=0 is x=3 and x=-5.
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Answer:X=-5 and X=3
Step-by-step explanation:
Ramon has $80.00 saved from mowing yards and raking leaves. If half of his money came from mowing yards, how much money came from raking leaves?
Answers
Answer:
$40
Step-by-step explanation:
Ramon has $80 saved
half of it came from mowing yard
therefore 80/2 = 40
the rest from raking leaves
80-40=40
what are the roots of the polynomial below. x^3-3x^2+2
Answers
Polynomial is an expression that consists of indeterminates(variable) and coefficients. The roots of the polynomial are 1, 2.7321, and -0.7321.
What are polynomials?Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.
The roots of the polynomial are:
x³ - 3x² + 2
If we divide the polynomial by (x-1), then
(x³ - 3x² + 2)/(x-1) = x² - 2x - 2
now, factorize the given polynomial,
x² - 2x - 2
x = 1 ± √3
x = 1, 2.7321, -0.7321
Hence, the roots of the polynomial are 1, 2.7321, and -0.7321.
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A friend of yours, a senior, took the Graduate Record Exam in September and scored in the 99th percentile. In February, your friend took the same exam over again. This time your friend scored in the 90th percentile. As a research methods student, you told your friend that his/her lowered score was most likely due to:
Answers
His/her lowered score was most likely due to statistical regression.
How to determine the reason?The missing options in the question are:
A. compensation rivalry B. Demoralization C. Differential selection
D. Testing E. Statistical regression
From the question, we have:
September = 99th percentileFebruary = 90th percentileA change (whether higher or lower) in the score is caused by statistical regression.
This is so because several variables could attribute to the change in the score.
The relationship between these variables is referred to as statistical regression
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Ryan fills a bath with
22.6 litres of hot water
and 18.7 litres of cold.
He spills 2.5 litres
getting in.
How much water is in
the bath now?
Answers
Answer:
38.8 litres
Step-by-step explanation:
22.6 + 18.7 = 41.3
41.3 - 2.5 = 38.8
38.8 litres
Answer:
38.8 liters.
Step-by-step explanation:
Word problems with addition and subtraction:
To find the quantity of water inside the bath tub, add the quantity of hot water and cold water. Then from this subtract the water that is spilled.
Quantity of water in the bathtub = 22.6 + 18.7 - 2.5
= 41.3 - 2.5
= 38.8 liters
There are only red sweets and yellow sweets in a bag.
There are n red sweets in the bag.
There are 8 yellow sweets in the bag.
Sajid is going to take at random a sweet from the bag and eat it.
He says that the probability that the sweet will be red is
7
10
(a) Show why the probability cannot be
7
10
Answers
Red sweets
_______
Total number =
N÷n+8
Probility is 7/10=n÷n+8
10n= 7n+56
3n=56
N= 56/3 but it has to be a whole number so 7/10
Find x, y, and z. Help me please :)
Answers
Answer:
x = 58°
z = 60°
y = 29( 58°)
Step-by-step explanation:
The arrows on the lines are trying to tell you that these lines are parallel to each other, whenever you see parallel lines think of *FUN* method
2y = 58° (alternate angles)
y = 29
x = 58° (alternate angles)
62° + 58° + z = 180° (sum of angles on a triangle)
120° + z = 180°
z = 60°
PLS HELP
What is the factored form for the quadratic function below?
y = 7x² - 2x - 5
Oy
(7x+5)(x - 1)
Oy
(7x - 5)(x - 1)
Oy (7x + 1)(x + 5)
Oy (7x+5)(x + 1)
Answers
Answer: y = (x - 1) (7x + 5)
Step-by-step explanation:
y = 7x² - 2x - 5 Use the slip and slide method.
y = x² - 2x - 35 Factor
y = (x - 7) (x + 5) Slide 7 back in, divide -7 by 7 to get -1. Slip 7 into (x + 5).
y = (x - 1) (7x + 5)
The factorized form of the quadratic equation is y = (7x+5)(x - 1).
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.
To factor the quadratic function, we need to find two binomials whose product is equal to the given quadratic. Here's one way to factor y = 7x² - 2x - 5:
First, we need to find two numbers whose product is 7(-5) = -35 and whose sum is -2. These numbers are -7 and 5, since (-7)(5) = -35 and (-7) + 5 = -2.
Next, we use these two numbers to split the middle term of the quadratic:
y = 7x² - 7x + 5x - 5
Notice that we have a common factor of 7x in the first two terms and a common factor of 5 in the last two terms. We can factor these out to get:
y = 7x(x - 1) + 5(x - 1)
Now, we have a common factor of (x - 1), which we can factor out to get the factored form:
y = (7x + 5)(x - 1)
Therefore, the correct answer is: y = (7x+5)(x - 1).
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y=-6x-8
y=-6x+8
Solve the system of linear equations
Answers
Answer: No solution
Step-by-step explanation:
Both of these equations have the same number as to coefficient of x (-6) but have a different constant (-8 and 8). This means that there are no solutions to this system of equations.
Which of the following is equivalent to the sum of expressions 2a^2 + 2 and a – 2
A = 2a^2+a
B = a^3-2
C = 2a^2
D = a^2-2
Answers
Answer:
A
Step-by-step explanation:
2a² + 2 + a - 2
+2 and -2 cancel
a² and a aren't like terms
final = 2a² + a
-16p+37=49-21p what is the answer
Answers
Answer:
p = 12/5Step-by-step explanation:
-16p+37=49-21p what is the answer?
-16p + 37 = 49 - 21p
-16p + 21p = 49 - 37
5p = 12p =
p = 12/5
Tristan has a points card for a movie theater.
He receives 25 rewards points just for signing up.
He earns 8.5 points for each visit to the movie theater.
He needs at least 110 points for a free movie ticket.
Write and solve an inequality which can be used to determine vv, the number of visits Tristan can make to earn his first free movie ticket.
Answers
You would have to visit the movies 10 times to get your first free ticket
Tristan needs to make at least 10 visits to the movie theater to earn his first free movie ticket.
Let v be the number of visits Tristan makes to the movie theater.
He receives 25 rewards points just for signing up, and he earns 8.5 points for each visit. So, the total rewards points he will have is
25+8.5v.
He needs at least 110 points for a free movie ticket. Therefore, we can write the inequality:
25+8.5v≥110
To solve for v, we can subtract 25 from both sides of the inequality and then divide by 8.5:
8.5v≥85
v≥85/8.5
v≥10
So, Tristan needs to make at least 10 visits to the movie theater to earn his first free movie ticket.
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Mila is designing a necklace with 12 platinum spherical beads that each have a radius of 7 millimeters. she has 350 grams of platinum to use. if pure platinum has a mass of 21.5 grams per cubic centimeter, does she have enough to make the 12 spherical beads? explain how you found your answer.
Answers
Volume is a three-dimensional scalar quantity. Mila only has 350 grams of platinum, therefore, she does not have enough platinum to make a necklace.
What is volume?A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of 12 bead = 12 × (4/3) × π × R³
= 12 × (4/3) × π × (0.7)³
= 17.241 cm³
Given the density of platinum as 21.5 grams per cubic centimeter, therefore,
Mass = density × Volume = 370.682
Since Mila only has 350 grams of platinum, therefore, she does not have enough platinum to make a necklace.
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