Multiplying a complex number by -1 flips it across the origin on the complex plane, changing its direction by 180 degrees but not its magnitude, resulting in a point directly opposite to the initial position.
Explanation:The question asks about the effect of multiplying a complex number by -1 in the complex plane. Multiplying a complex number by -1 essentially flips the point representing the complex number across the origin. If Point A represents a complex number on the complex plane, multiplying that complex number by -1 will result in a point that lies exactly opposite of Point A with respect to the origin. This operation does not change the magnitude of the complex number but changes its direction by 180 degrees. This is because the complex plane is analogous to a two-dimensional Cartesian coordinate system where complex numbers are represented as vectors. The multiplication by -1 is a reflection across the origin in such a plane.
For example, if a complex number z is represented by the point (a, b) where a is the real part and b is the imaginary part, then multiplying z by -1 gives us the point (-a, -b). This operation is similar to rotating the vector z 180 degrees around the origin or mirroring it across both the x and y axes.
If x varies inversely as y, and x = 11 when y = 15, find x when y = 3.
a:11/5
b:33/15
c:55
Answer:
55
Step-by-step explanation:
The equation of inverse variation is
y = k/x,
where k is a constant.
We can use the given x- and y-coordinates to find k.
y = k/x
15 = k/11
k = 165
The inverse variation equation for this problem is
y = 165/x
For y = 3,
3 = 165/x
3x = 165
x = 55
Answer:
C
Step-by-step explanation:
given x varies inversely as y then the equation relating them is
x = [tex]\frac{k}{y}[/tex] ← k is the constant of variation
To find k use the given condition x = 11 when y = 15
k = xy = 11 × 15 = 165 , hence
x = [tex]\frac{165}{y}[/tex] ← inverse variation equation
when y = 3, then
x = [tex]\frac{165}{3}[/tex] - 55 → C
Please help simple math problem.
Answer:
the answer is x=5 for a fact
Step-by-step explanation:
Answer:
the answer would be x=5
Anna baked 33 batches of cookies with cc cookies in each batch. She then ate 88 cookies! How many cookies does Anna have left?
Roberto'S puppy weighed 4.5 pounds at the end of May during June and July the puppy gained 18.63 pounds how much did Roberto's puppy weight at the at the end of July
Answer: 23.13 lbs
Step-by-step explanation:
Weight in May + Weight gained = Weight in July
4.5 + 18.63 =
23.13 =
NOTE: Make sure to line up the decimal point when adding decimals:
4.50
+ 18.63
23.13
It takes terrel 69 minutes to weed his garden if he does it every 2 weeks, while his wife can get it done in 49 minutes. How long would it take them working together? Round to the nearest tenth of a minute
Answer: 28.7 minutes
Step-by-step explanation:
Terrel: [tex]\dfrac{1}{69}[/tex] of job per minute
Wife: [tex]\dfrac{1}{49}[/tex] of job per minute
Together: [tex]\dfrac{1}{x}[/tex] of job per minute
Terrel + Wife = Together
[tex]\dfrac{1}{69}+\dfrac{1}{49}=\dfrac{1}{x}[/tex]
[tex]\dfrac{1}{69}(69*49*x)+\dfrac{1}{49}(69*49*x)=\dfrac{1}{x}(69*49*x)[/tex]
49x + 69x = 69 * 49
118x = 3381
x = 28.7
Determine the standard form of the equation of the line that passes through (-6,6) and (3,-2)
Considering the expression of a line, the equation of the line that passes through the pair of points (-66) and (3,-2) is 8/9x +y= 2/3.
Linear equation
A linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using:
m= (y₂ - y₁)÷ (x₂ - x₁)
Substituting the value of the slope m and the value of one of the points in the expression y = mx + b, the value of the ordinate to the origin b can be obtained.
The standard form of the line is Ax +By= C
Equation in this case
In this case, being (x₁, y₁)= (-6, 6) and (x₂, y₂)= (3, -2), the slope can be calculated as:
m= (-2 - 6)÷ (3 - (-6))
m= (-2 - 6)÷ (3 + 6)
m= (-8)÷ 9
m= -8/9
Considering point 2 and the slope, you obtain:
-2= (-8/9)×3 + b
-2= -8/3 + b
-2 +8/3= b
2/3= b
The equation of the line is y= -8/9x +2/3.
Finally, the standard form of the line is 8/9x +y= 2/3
Write a function rule for the given graph identify the value of y when x=12
write out the steps
Answer:
y=8
Step-by-step explanation:
We need to find the equation for the line.
The first step is to find the slope
We need 2 points (0,2) (2,3)
slope = (y2-y1)/(x2-x1)
= (3-2)/(2-0)
= 1/2
We know the y intercept ( where it crosses the y axis) at 2
Lets use the slope intercept form of the line
y= mx+b
y = 1/2 x+2
If we want to find the value of y when x =12 , substitute the value of x=12
y =1/2 * 12 +2
y = 6+2
y=8
HELP please explain to me how to get this.
Which of the following represents a function?
Answer:
option A : graph is a function
Step-by-step explanation:
(a) option is given is a graph
For graph , the function should pass vertical line test
Draw vertical line for every value of x
The vertical lines cross only one red point at a time
So the graph is a function
(b) When each input has only one output then it is a function
in option B , input 3 has two output -5 and 0
so it is not a function
(c) in option C , input 3 has two output 14 and 19
so it is not a function
(d) in option d , input -1 has two output -11 and 5
so it is not a function
The Ebbinghaus model of human memory may be used to model the amount of acquired knowledge a college student will retain after “cramming” for a final exam. The formula is p=(100-a)e^-b(0.07), where a and b vary from one person to another, and p is the percent of retained knowledge 1/2 day later when the student actually takes the final exam. If a = 20 and b = 1.2 for a typical student, how much of their “crammed” knowledge will that student retain at the moment of taking the final exam?
Answer: 73.55%
Step-by-step explanation:
p = (100-a) e^-b(0.07)
we have a = 20 and b =1.2
= (100-20) e^-(1.2)(0.07)
= 80(e^-0.084)
= 80(0.919431)
= 73.55%
Answer:
The correct answer is 93.6%
Step-by-step explanation:
Got it right on Edge 2020
look at attachment 10 POINTS!!!
Answer:
The midpoint of TS is (-1,-3)
The coordinates of M should be (8,18)
Step-by-step explanation:
1. Amanda tells you that because a variable is in the denominator, the equation three over x plus one over three equals five over six becomes unsolvable. Amanda explains, "There is a value for x that makes the denominator zero, and you can't divide by zero." Demonstrate to Amanda how the equation is still solvable and explain your reasoning.
2. When looking at the rational function f of x equals the quantity x minus one times the quantity x plus two times the quantity x plus four all divided by the quantity x plus one times the quantity x minus two times the quantity x minus four, Bella and Edward have two different thoughts. Bella says that the function is defined at x = –1, x = 2, and x = 4. Edward says that the function is undefined at those x values. Who is correct? Justify your reasoning.
Answer: x = 6
Step-by-step explanation:
[tex]\dfrac{3}{x}+\dfrac{1}{3}=\dfrac{5}{6}[/tex]
[tex](6x)\dfrac{3}{x}+(6x)\dfrac{1}{3}=(6x)\dfrac{5}{6}[/tex] multiplied by common denominator
18 + 2x = 5x
-2x -2x
18 = 3x
÷3 ÷3
6 = x
Since "x" is in the denominator, the restriction is that x ≠ 0. If the solution was x = 0, then the solution would not be valid and would be eliminated as an answer.
Remember that "x" is just an unknown value. It is possible to add two fractions together and have their sum be a fraction.
For example: [tex]\dfrac{1}{5} + \dfrac{2}{5} = \dfrac{3}{5}[/tex] could be written as [tex]\dfrac{1}{5} + \dfrac{2}{x} = \dfrac{3}{5}[/tex]. When we solve it, we will get x = 5.
******************************************************************************************
Answer: Edward
Step-by-step explanation:
[tex]f(x)=\dfrac{(x-1)(x+2)(x+4)}{(x+1)(x-2)(x-4)}[/tex]
The denominator cannot equal zero, so:
x + 1 ≠ 0 → x ≠ -1x - 2 ≠ 0 → x ≠ 2x - 4 ≠ 0 → x ≠ 4Those x-values are the asymptotes, which is where the function is undefined.
plz no one ever helps me I need the answer
Which statement is TRUE about 131 ? A) It lies between 12 and 13 on a number line. B) It lies between 11 and 12 on a number line. C) It lies between 10 and 11 on a number line. D) It lies between 9 and 10 on a number line.
Answer:
B
Step-by-step explanation:
The square root of 131 is 11.445 and so it lies between 11 and 12 on a number line.
See where it goes on a number line below:-
Thomas earns 15 per hour if he recurved a 10% per hour pay increase how much does Thomas now make per hour
Answer:
He now makes 16.50 per hour
Step-by-step explanation:
15.00 x .10 = 1.50
15.00 + 1.50 = 16.50
Please help me out, I really could use it
Answer:
No real solutions
129
Step-by-step explanation:
The quadratic formula is
-b ± sqrt(b^2 -4ac)
----------------------------
2a
3x^2 =2x-1
Lets get the equation in proper form
3x^2 -2x+1 = 2x-1-2x+1
3x^2 -2x+1 =0
a=3 b=-2 c=1
Lets substitute what we know
2 ± sqrt((-2)^2 -4(3)(1))
----------------------------
2(2)
-2 ± sqrt(4-12)
----------------------------
2(2)
-2 ± sqrt(-8)
----------------------------
4
No real solutions
The quadratic formula is
-b ± sqrt(b^2 -4ac)
----------------------------
2a
2x^2 -10= 7x
Lets get the equation in proper form
2x^2 -7x-10 = 7-7x
2x^2 -7x-10 =0
a=2 b=-7 c=-10
Lets substitute what we know, we are only looking for what is inside the radical
(b^2 -4ac)
((-7)^2 -4(2)(-10))
(49 +80)
129
Please help! 70 points :)
Will award brainliest
Answer:
38 = FH
Step-by-step explanation:
Because this is a rectangle, IG = FH
We know that IE + EG = FH
We also know that IE = EG (perpendicular bisectors)
IE = EG
3x+4 = 5x-6
Subtract 3x from each side
3x-3x+4 = 5x-3x-6
4 = 2x-6
Add 6 to each side
4+6 =2x
10 =2x
Divide by 2
10/2 =2x/2
5=x
Now lets find FH
IE + EG = FH
3x+4 + 5x-6 = FH
Combine like terms
8x-2 = FH
Substitute in x =5
8*5-2
40-2
38 = FH
Answer:
40-2
38 = FH
Step-by-step explanation:
Please answer this question correctly!!
f(x) + n - translate the graph n units up
f(x) - n - translate the graph n units down
f(x + n) - translate the graph n units left
f(x - n) - translate the graph n units right
|f(x)| - reflect over x-axis for x < 0.
[tex]f(x)=|x+2|-5[/tex]
Graph g(x) = x
g(x + 2) = x + 2 → translate 2 units left
|g(x + 2)| = |x + 2| → reflect over x-axis for x < 0
|g(x + 2)| - 5 = |x + 2| - 5 → translate 5 units down
Which points are on the graph of f(x)=(1/3)x ?
Select each correct answer.
(0, 1)
(3, 27)
(−2, 9)
(−1, −1/3)
Answer:
the only point is (0,1) if u would look at the graph i post
Step-by-step explanation:
The point which lies on the graph of f(x) = (1/3)x will satisfy the function thus point (-1, -1/3) will lie on the graph thus option (D) is correct.
How to plot a graph?A graph is a diagram that shows the fluctuation of one variable in relation to one or more other variables.
In order to plot the graph, we need to find out y's values corresponding to x's value
As per the given function,
f(x) = (1/3)x
Substitute, x = 0,
y = f(0) = (1/3)0 = 0
So,(0,1) will not lie on the graph.
Similarly, (3, 27) and (−2, 9) also do not lie on the graph.
Substitute (-1,-1/3)
-1/3 = (1/3)(-1) = -1/3
Thus, it will be the point of the function.
Hence "The point which lies on the graph of f(x) = (1/3)x will satisfy the function thus point (-1, -1/3) will lie on the graph".
For more information about the graph of a function,
brainly.com/question/27757761
#SPJ3
In ∆PQR, PQ = 39 cm and PN is an altitude. Find PR if QN = 36 cm and RN = 8 cm.
Use the Pythagorean theorem two times:
[tex]NQ^2+NP^2=QP^2\\\\36^2+h^2=39^2\\\\1296+h^2=1521\qquad\text{subtract 1521 from both sides}\\\\h^2=225\to h=\sqrt{225}\\\\\boxed{h=15\ cm}[/tex]
second time:
[tex]PR^2=RN^2+NP^2\\\\x^2=8^2+15^2\\\\x^2=64+225\\\\x^2=289\to x=\sqrt{289}\\\\\boxed{x=17\ cm}[/tex]
Answer: PR = 17 cm.Answer:
17 cm
Step-by-step explanation:
We must first find the length of the height, PN. Since PN is an altitude, it makes a right angle with QR; this means that PNQ will be a right triangle, as will PNR. This means we will use the Pythagorean theorem:
a²+b² = c²
Letting h represent PR (since it is the height),
h²+36² = 39²
h²+1296 = 1521
Subtract 1296 from each side:
h²+1296-1296 = 1521-1296
h² = 225
Take the square root of each side:
√(h²) = √(225)
h = 15
PN is 15 cm.
Now we will use it and the other "base," RN, to find PR:
15²+8² = x²
225+64 = x²
289 = x²
Take the square root of each side:
√(289) = √(x²)
17 = x
Your mother asked you to turn the oven down to 325 degrees Fahrenheit This is 75 degrees fahrenheit less than it was. What was the original temperature
PLEASE HELP PLEASE PLEASE
Answer:
2.5 rad ( to the nearest tenth )
Step-by-step explanation:
the time difference between the given times is 24 minutes
In 1 hour the hand moves 2π radians, hence in 1 minute moves
[tex]\frac{2\pi }{60}[/tex], thus in 24 minutes moves
[tex]\frac{2\pi }{60}[/tex] × 24 ≈ 2.5 radians
144 flowers in a vase the ratio of yellow to pink flowers is 5 to 6 how many yellow flowers are in the vase
y = 2x + 3
2y = 4x + 6
The system of equations has _____ solution(s).
A.no
B.one
C.infinite
divide. simplify your answer (2x^4-6x^3+4x^2-3x)*(2x) pls show work
Distribute
2x × 2x^4 + 2x × -6x^3 + 2x ×4x^2 + 2x × - 3x
Take out the constants
(2 × 2)xx^4 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x
Simplify 2 × 2 to 4
4xx^4 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x
Use Product Rule: x^a x^b = x^a + b
4x^1 + 4 + 2x × -6x^3 + 2x ×4x^2 + 2x × -3x
Simplify 1 + 4 to 5
4x^5 + 2x × -6x^3 + 2x × 4x^2 + 2x × -3x
Take out the constants
4x^5 + (2 × -6)xx^3 + 2x × 4x^2 + 2x × -3x
Simplify 2 × -6 to -12
4x^5 - 12xx^3 + 2x × 4x^2 + 2x × -3x
Use the Product Rule: x^a x^b = x^a + b
4x^5 - 12x^1 + 3 + 2x × 4x^2 + 2x -3x
Simplify 1 + 3 to 4
4x^4 - 12x^4 + 2x ×4x^2 + 2x × -3x
Take out the constants
4x^5 - 12x^4 + (2 × 4)xx^2 + 2x × -3x
Simplify 2 × 4 to 8
4x^5 - 12x^4 + 8xx^2 + 2x × -3x
Use the Product Rule: x^a x^b = x^a + b
4x^5 - 12x^4 + 8x^ 1 + 2 + 2x × -3x
Simplify 1 + 2 to 3
4x^5 - 12x^4 + 8x^3 + 2x × -3x
Take out the constants
4x^5 - 12x^4 + 8x^3 + (2 × -3)xx
Simplify 2 × -3 to -6
4x^5 - 12x^4 + 8x^3 - 6xx
Use the Product Rule: x^a x^b = x^a + b
4x^5 - 12x^4 + 8x^3 - 6x^2
Answer:
4x^5 - 12x^4 + 8x^3 - 6x^2
Step-by-step explanation:
Please answer both questions and show all your work. I am in a hurry... please...
1) To finish an order in time the company had to produce 40 items daily, but it produced 20 items more daily and finished the order 3 days ahead of time. In how many days was the company supposed to finish the order?
2) If eight people share equally in an inheritance, what percent of the inheritance belongs to three people? What percent belongs to them if two of the people are disinherited? By what percent does each person’s share of the inheritance increase?
Answer: 1) 9 days
2) a)37.5%
b)50%
c) 33.33%
Step-by-step explanation:
1) - Let's call:
x: number of days the company supposed to finish the order.
- You know that the company had to produce 40 items daily, but it produced 20 items more daily and finished the order 3 days ahead of time. Therefore, you can express this as following:
[tex]40x=(40+20)(x-3)\\40x=60(x-3)[/tex]
- Solve for [tex]x[/tex]:
[tex]40x=60x-180\\-20x=-180\\x=9[/tex]
(The answer is 9 days)
2) a) The percent that belongs to three people if eight eight people share equally in an inheritance, can be calculated as following:
[tex]\frac{3}{8}*100=37.5[/tex]%
b) The percent that belongs to three people if six people share equally in an inheritance (because two of the people are disinherited) can be calculated as following:
[tex]\frac{3}{6}*100=50[/tex]%
c) - The increase goes from 1/8 to 1/6, therefore, you must subtract them:
[tex]\frac{1}{6}-\frac{1}{8}=\frac{1}{24}=0.04167[/tex]
- Divide the result by 1/8 and multiply by 100 to obtain the percent:
[tex]\frac{0.04167}{\frac{1}{8}}*100=33.33[/tex]%
What is the value of the function at x = 3?
Enter your answer in the box.
Answer:
4
Step-by-step explanation:
Recall a linear function, is a line on a graph made up of an infinite amount of points which satisfy the relationship. That means at x=3 there is a specific point on the line with an output. The value of a function at x=3 asks, what is the output y value for the input x value?
To find it, we locate 3 on the x-axis. We draw a vertical line directly to the line following the grid line. We mark the point on the line. We then draw a horizontal line directly to the y-axis following the grid line. The point we hit on the y-axis is the value of the function.
Here it is 4.
Answer:
4
Step-by-step explanation:
i took the test
Right triangle ABC has side lengths 3,4 and 5. Do the side lengths form a Pythagorean triple? Explain.
Answer:
Yes, the side lengths of ΔABC forms a Pythagorean triple
Step-by-step explanation:
Given : A right angled triangle ABC
Side lengths - 3,4 and 5
To Find: . Do the side lengths form a Pythagorean triple?
Solution :
Hypotenuse (longest side) = 5
To check we need to use Pythagoras theorem :
[tex]Hypotenuse^{2} =Perpendicular^{2} +Base^{2}[/tex]
[tex]5^{2} =3^{2} +4^{2}[/tex]
[tex]25 =9 +16[/tex]
[tex]25 =25[/tex]
Since Pythagoras theorem is verified . So, the side lengths form the Pythagorean triplet.
Hence the side lengths of ΔABC forms a Pythagorean triple
Bob has a standard deck of playing cards. If he randomly draws a J, K, 2, and 2, what is the probability that the next card he draws to add to his hand is a K? Please answer in fraction form.
Answer:
The correct answer has already been given (twice). I'd like to present two solutions that expand on (and explain more completely) the reasoning of the ones already given.
One is using the hypergeometric distribution, which is meant exactly for the type of problem you describe (sampling without replacement):
P(X=k)=(Kk)(N−Kn−k)(Nn)
where N is the total number of cards in the deck, K is the total number of ace cards in the deck, k is the number of ace cards you intend to select, and n is the number of cards overall that you intend to select.
P(X=2)=(42)(480)(522)
P(X=2)=61326=1221
In essence, this would give you the number of possible combinations of drawing two of the four ace cards in the deck (6, already enumerated by Ravish) over the number of possible combinations of drawing any two cards out of the 52 in the deck (1326). This is the way Ravish chose to solve the problem.
Another way is using simple probabilities and combinations:
P(X=2)=(4C1∗152)∗(3C1∗151)
P(X=2)=452∗351=1221
The chance of picking an ace for the first time (same as the chance of picking any card for the first time) is 1/52, multiplied by the number of ways you can pick one of the four aces in the deck, 4C1. This probability is multiplied by the probability of picking a card for the second time (1/51) times the number of ways to get one of the three remaining aces (3C1). This is the way Larry chose to solve the this.
Step-by-step explanation:
Hi There!
Answer:
4/52 (With cards picked before put back.)
3/48 (With cards picked before not put back.)
Step-by-step explanation:
A standard deck of cards is made up of 52 cards.
There are 4 kings in a deck.
4/52
Bob has a 4/52 chance of picking a king.
I don't know if the cards he picked prior to this he put back or not. If he didn't then it's 3/48.
Hope This Helps :)
math help please!!!!!!!!!!! will mark brainly
Answer:
B)3/8
Step-by-step explanation:
So there are 3 yellow or blue in total. So 3/8.
Answer:
3/8
Step-by-step explanation:
There are 8 pieces of equal size (and thus equal probability). 3 of them qualify as "success" (yellow or blue), so 3 out of 8 is the probability.
BRAINLIEST AND 39 POINTS
How many different 4-digit personal identification numbers (PINs) can be made from the digit 0 through 9 if no digits repeat?
You have 10 numbers to choose from, and you're choosing 4 from that pool. Order of the numbers matters, because having 1234 as a PIN is not the same having it be 1324, so we're counting the number of permutations of 10 digits taken 4 at a time. So there are
[tex]4!\dbinom{10}4=4!C(10,4)=4!C^{10}_4=\dfrac{10!}{(10-4)!}=5040[/tex]
possible PINs that can be made.
Answer:
5,040 PINs
Step-by-step explanation:
From the vast numbers from 1 to 10, the numbers can amount to over 5,040 PINs. Having to use the following equation in the attachment below (also found in the other question), the vast amount of numbers can either amount to 5,040 PINs, or possibly over that amount.
You need to have 10 numbers to choose from.
I hope this helps!
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year. Michigan's population was 9.9 million, increasing by 0.6 million each year. When will the two years have the same population? Let y represent the number of years.
Answer:-
[tex]11.4 + 0.5y = 9.9 + 0.6y[/tex] , then the two states have the same population.
Step-by-step explanation:
Let y represents the number of years
As per the statement:
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.
⇒ [tex]11.4 + 0.5y[/tex]
and
also, it is given that: Michigan's population was 9.9 million, increasing by 0.6 million each year.
⇒ [tex]9.9 + 0.6y[/tex]
When two states have the same population.
then the equation : [tex]11.4 + 0.5y = 9.9 + 0.6y[/tex].
Answer:
In 15 years the population will be same.
Step-by-step explanation:
Let y represent the number of years.
In 2000, Ohio's population was 11.4 million and and increasing by 0.5 million each year.
[tex]x=11.4+0.5y[/tex]
Michigan's population was 9.9 million, increasing by 0.6 million each year.
[tex]x=9.9+0.6y[/tex]
We have to tell that when will the two years have the same population, so we will put both equations equal.
[tex]11.4+0.5y=9.9+0.6y[/tex]
=> [tex]11.4-9.9=0.6y-0.5y[/tex]
=> [tex]0.1y=1.5[/tex]
So, y = 15
Therefore, in 15 years the population will be same.