The difference between Z₁ and Z₂ is -10 + 0i.
Z₁ - Z₂ locates on the real axis, this is solved using the concept of complex numbers.
Option b is correct.
What is complex number?Real numbers and imaginary numbers combine to form complex numbers, which have two components. Complex numbers serve as the foundation for more complex arithmetic, including algebra.
Complex numbers are those that are represented as a+ib, where a and b are actual numbers and i is an imaginary number termed a "iota." i has the value (√-1).
From the graph we can know:
Z₁ (-5,2) = -5 + 2i
Z₂ (5,2) = 5 + 2i
The difference between Z₁ and Z₂ is Z₁ - Z₂
So, Z₁ - Z₂ = (-5 + 2i) - (5 + 2i)
Z₁ - Z₂ = - 10 + 0i
Thus, Z₁ - Z₂ locates on the real axis.
Correct option is: b
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Answer:
Option B
Step-by-step explanation:
I just finished the test on edge. confirmed correct
Please help. Solve the system of equations.
Y=2x
Y=x^2-8
The solution of the system of equation is as follows;
when x = -2 , y = -4
when x = 4, y = 8
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Let solve the system of equation by substitution method.
Therefore,
y = 2x
y = x² - 8
Using substitution,
2x = x² - 8
x² - 2x - 8 = 0
x² + 2x - 4x - 8 = 0
x(x + 2) - 4(x + 2) = 0
(x - 4)(x + 2) = 0
x = -2 or 4
Hence,
when x = -2
y = 2(-2) = -4
when x = 4
y = 2(4) = 8
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In triangle LMN, m∠L = (3c + 66)°. If the exterior angle to ∠L measures 72°, determine the value of c.
c = 72
c = 46
c = 14
c = 2
Answer:
c = 14
Step-by-step explanation:
Your algebra final exam is worth 150 points and contains 60 questions. Some of the questions are worth two
points and some are worth five points. How many two-point and five-point questions are on the test?
There are 50 two-point questions and 10 five-point questions on the test.
What is a linear equation in two variables?
A linear equation in two variables is an equation that can be written in the form Ax + By = C, where A, B, and C are constants and x and y are variables. The graph of a linear equation in two variables is a straight line, and the equation represents a linear relationship between the variables.
To solve this problem, you can use the fact that the total number of points on the test is 150 and that some of the questions are worth two points and some are worth five points.
Let x represent the number of two-point questions on the test, and let y represent the number of five-point questions on the test.
We can set up the following system of equations to represent the given information:
2x + 5y = 150
x + y = 60
To solve this system, you can use the substitution method. First, solve the second equation for y:
y = 60 - x
Substitute this expression for y into the first equation:
2x + 5(60 - x) = 150
This simplifies to:
2x + 300 - 5x = 150
Combine like terms:
-3x = -150
Divide both sides by -3:
x = 50
Substitute this value for x into the second equation to find the value of y:
y = 60 - 50 = 10
Hence, there are 50 two-point questions and 10 five-point questions on the test.
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Greg the doggo has a rectangular playpen that he and the other dogs can "chill" in. The playpen has an area of 32 square feet . The pen's length is 4 feet longer than its wide.
Include an equation to represent this situation.
The required equation for the width of the rectangular playpen is w² + 4w -32 = 0.
What is a rectangle?The rectangle is 4 sided geometric shape whose opposites are equal in lengths and all angles are about 90°.
here,
let the length be l and width be w,
According to the question,
l = w + 4
Now,
Area of the pen = length × width
Area of the pen = (w + 4) × w
32 = w² + 4w
w² + 4w -32 = 0
Thus, w² + 4w -32 = 0 is the required equation that represents the rectangular playpen.
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what is the greatest common factor of 18x^4y+3x^3y^2-39x^2y^3+12x^2y^4
The required greatest common factor in the given expression is 3x²y.
What is the greatest common factor?The greatest common factor is defined as a group of the set of numbers that is the most considerable and greatest factor that all the numbers include of.
here,
Given expression,
= 18x⁴y+3x³y²-39x²y³+12x²y⁴
Taking common 3x²y from every term,
= 3x²y(6x² + xy - 13y² + 4y³)
Where 3x²y id the greatest common factor,
Thus, In terms of the given expression 3x²y is the greatest common factor.
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a. 1 /2 + 5 12 greater than 1 less than 1 b. 2 7/8 – 1 7/9 greater than 1 less than 1.
Please HELP PLEASE PLEASE
Hillary makes two transactions while at the mall: • She returns an item to get $15 back at one store. • She buys an item for $15 at another store. Which is a correct description of the two quantities that represent these transactions? A The quantities have the same magnitude, but different signs. B The quantities have the same sign, but different magnitudes. C The quantities have different magnitudes and different signs. D The quantities have both the same magnitude and the same sign.
Answer:
the correct answer to this question would be D
Giovanni works as a tour guide during the summer. He earns $45 a day and $14 for each tour that he leads. Which function is used to find the total amount of money Giovanni will earn each day
The function that is used to find the total amount of money Giovanni will earn each day is; A = 14 + 45d
How to solve algebra word problems?The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
Now, we are told that;
Giovanni works as a tour guide during the summer.
Amount he earns daily = $45
Amount earned for each tour = $14
Now, if the number of days he spends as a tour guide is d, then we can say that the total amount of money Giovanni will earn each day is expressed as;
A = 14 + 45d
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. Stanley needs to get 12 gallons of gas. He finds a gas station that is advertising their price at $3.479/gallon.
A. What will the cost be if the gas station rounds the final cost of gas (to the nearest hundredth) after all calculations?
B. What will the cost be if the gas station rounds their price per gallon (to the nearest hundredth) and then calculates the total price?
C. Which option will save Stanley money?
In case A:
The amount to be paid = $41.75
In case B :
The amount to be paid = $41.76
So, the Case A is better option.
Finding the right answer using the round off to nearest hundredth.
How to change any value to it's nearest hundredth ?
Rounding to the nearest hundredth means the rounding of any decimal number to its nearest hundredth value. In decimal, hundredth means 1/100 or 0.01. For example, the rounding of 2.167 to its nearest hundredth is 2.17.
Steps to find nearest hundredth of any value:
Step 1:
Since we need to round the given decimal number to the nearest hundredth, we mark the digit at the hundredths place.
Step 2:
Then, we observe the 'thousandths' place digit, which lies to the right of the hundredths column.
Step 3:
If the digit at the thousandths place is less than 5, we write the hundredths place digit as it is and remove all the digits to its right.
Step 4:
If the digit at the thousandths place is 5 or more than 5, we add 1 to the digit at the hundredths place, that is, we increase the hundredths place by 1 and remove all the digits to its right.
Case A :
The price for each gallon = $3.479
So, the total price for 12 gallon = $41.748
In case A total amount is rounded off
So, the price = $41.75
Case B :
The price for each gallon = $3.479
Rounding off the price for each gallon = $3.48
So, the total amount for 12 gallon = $41.76.
So, the case A is better option.
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A car dealership pays $8350 for a car. They mark up the price by 17.4% to get the retail price. What is the retail price of the car at this deallership
The retail price of the car is $ 9802.9.
What is percent?In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.A percentage is a figure or ratio that shows a portion of one hundred. A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals. The symbol "%" is frequently written after the number to indicate percentages.A car dealership pays $8350 for a car.
They mark up the price by 17.4%
8350 * 17.4% = 1452.9
retail price = 8350 + 1452.9 = $ 9802.9
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What is the vertical asymptote of the function? x = –3 x = –2 x = 0 x = 3
Answer:4
Step-by-step explanation:i did the quiz
If the price of a certain stock is $55.00 per share and its earnings are $2.75 per share, what is the ratio of the earnings to the stock’s price in lowest terms?
The earnings-to-stock-price ratio in simplest terms is 20.
What is PE ratio?A stock's P/E ratio is calculated by dividing its price by its annual earnings per share.The P/E ratio assists investors in determining whether a company's stock is overvalued or undervalued in relation to its earnings. The ratio measures what the market is willing to pay for the company's current operations as well as its potential growth. If a company has a high P/E ratio, the market believes in its growth potential and is willing to overspend today based on future earnings.
Here given,
Stock price = $55.00
Earnings per share = $2.75
We have to find ratio od earnings,
The formula is,
Ratio is : P/E
By substituting the values,
Ratio = $55.00 / $2.75
= 20
I NEED ANSWERS ASAP please guys this is due tomorrow and I have no idea what to do! Help!!
You could pick the question you want to answer..
The total time taken is 24 hours.
What is total time?
Total refers to a whole or full amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A automobile that has been totalled in an accident is irreparably damaged. Total Time is the result of multiplying the number of minutes in a day by the number of days in a given calendar month.
An inlet pipe takes 8 hours to fill a tank. An outlet pipe takes 12 hours to empty.
[tex]$\Rightarrow$[/tex] Time is taken to fill in 1 hour =1 / 8
[tex]$\Rightarrow$[/tex] Time taken to empty in 1 hour =-1 / 12
[tex]$\Rightarrow$[/tex] If both pipes are opened simultaneously tank be filled in 1 hour =1 / 8-1 / 12 =1 / 24 hours
[tex]$\therefore$[/tex] The total time taken is 24 hours.
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Victoria is paid $40 to lay mulch in the garden 5 times. At This rate, how many times must she lay mulch to earn $100?
Answer:
13 jobs
Step-by-step explanation:
if 40 dollars are made for 5 jobs you have to find what was made for one job which is 8 dollars
then you have to divide 100 by the 8 to find how many 8 dollar jobs it will take to make the 100 dollars.
you get 12.5 whuch beace you cant do half a job, you round it up to 13 jobs.
nj bought a car for $20,000. two years later, the car has depreciated to a value that is 81% of what he paid. which equation(s) represent the exponential relationship?
V = 20,000 * 0.81^2 and V = 20,000 * (1 - 0.19)^2 are the equation(s) that represent the exponential relationship.
The value of the car two years later is represented by the variable V. The initial value of the car is represented by the constant 20,000. The relationship between the value of the car two years later and the initial value of the car is exponential, because the value of the car decreases by a fixed percentage each year.
One equation that represents this relationship is:
V = 20,000 * 0.81^2
This equation says that the value of the car two years later is equal to the initial value of the car multiplied by the decay factor of 0.81 raised to the power of 2. The decay factor represents the percentage by which the value of the car decreases each year.
Another equation that represents this relationship is:
V = 20,000 * (1 - 0.19)^2
This equation says that the value of the car two years later is equal to the initial value of the car multiplied by (1 - 0.19) raised to the power of 2. The term (1 - 0.19) represents the percentage by which the value of the car remains after it has depreciated.
Both of these equations represent the exponential relationship between the value of the car two years later and the initial value of the car.
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-2y + 3 =21 solve linear equations
Answer:
y= -9
Step-by-step explanation:
Subtract 3 from both sides
-2y + 3-3= 21-3
-2y=18
Divide both sides by the same factor
-2y/-2 = 18/-2
y= -9
Answer: y = -9
Step-by-step explanation:
-2y+3=21
-2y=21-3
-2y=18
Divide that by -2:
y=-9
if 87.5 percent of a sample of pure 131i decays in 24 days, what is the half-life of 131i?
If 87. 5 percent of a sample of pure 131 I decays in 24 days, then the half-life of 131 i is 8 days.
In this question we have been given 87.5 percent of a sample of pure 131i decays in 24 days
We need to find the the half-life of 131i
We know that the rate constant expression is given as :
k = (2.303/t)*(log (a / a-x))
where, t = 24 days
a = 100
a -x = 100 - 87.5
= 12.5 g
From the rate constant expression,
k = (2.303 / 24) * (log(100/12.5))
k = 0.0866
Now, the half life is given as :
k = 0.693 / t(1/2)
t1/2 = 0.693 / 0.0866
t1/2 = 8 days.
Therefore, the half-life of 131 i is 8 days.
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HELP ME PLEASE!!!!!!!!!
The length of a cell phone is 1.41.4 inches and the width is 3.43.4 inches. The company making the cell phone wants to make a new version whose length will be 1.541.54 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
Step-by-step explanation:7.48521878104
These box plots show daily low temperatures for a sample of days in two
different towns.
Town A
15 20
30
HHH
Town B
15 20 25 30
58
HH
0
5
10
15 20 25
30
35
40
45 50 55 60
Degrees (F)
Compare the shapes of the box plots.
• A. The distributions for both towns are symmetric.
B. The distribution for town A is symmetric, but the distribution for
town B is negatively skewed.
C. The distributions for both towns are positively skewed.
• D. The distribution for
town A is symmetric, but the distribution for
town B is positively skewed.
The distribution for town A is symmetric, but the distribution for town B is positively skewed.
Define skew.Skewed lines are two lines that are not parallel to one another, neither do they intersect. Only dimensions greater than two-dimensional space can have skew lines. They must be non-coplanar, which means that they must exist in various planes. Two lines in a two-dimensional space can either intersect or run parallel to one another. Skew lines can never exist in 2D space as a result. Skew lines occur frequently in real-world circumstances. Let's say there is a line on the ceiling and a line on the wall. These lines can be skew lines because they lie in distinct planes if they are not parallel to one another and do not meet.
Given
By comparing the shapes of the box plots,
D. The distribution for town A is symmetric, but the distribution for town B is positively skewed.
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Please please please help me I need it asap! Please!!
Point A, located at (-11, -7) on the coordinate plane, is reflected over the x-axis to form point B. Then point B is reflected over the y-axis to form point C.
What are the coordinates of points B and C?
A: Point B: (-11, 7) Point C: (11, -7)
B: Point B: (11, -7) Point C: (11, 7)
C: Point B: (11, -7) Point C: (-11, 7)
D: Point B: (-11, 7) Point C: (11, 7)
Rewrite in simplest terms: -3(7f+3f+9) -4f
-3(7f + 3f + 9) - 4f
Distribute.
(−3)(7f) + (−3)(3f) + (−3)(9) + −4f
−21f + −9f + −27 + −4f
Combine like terms.
−21f + −9f + −27 + −4f
(−21f + −9f + −4f) + (−27)
−34f + −27
-34f + -27
The sum of two numbers is 57 and the difference is 3. What are the numbers?
Answer:
The 2 numbers are 27 and 30
Step-by-step explanation:
Let call them x and y where x is the larger number and y is the smaller number :
x + y = 57 (obtained from the first line of the question)
x - y = 3 (obtained from the second line of the question)
Now we are going to use the rules of simultaneous equations to find x and y :
I will use elimination method :
Add the 2 equations to eliminate the y :
2x = 60
x = 30
Substitute x into equation 1 :
(30) + y = 57
Subtract 30 from both sides :
y = 57 - 30
y = 27
So
x = 30 and y = 27
As you can see the difference is also 3
The 2 numbers are 27 and 30
Hope this helped and have a good day
11.3 is 7% of what?
Answer: 157.14
Step-by-step explanation: SDHU IK
What is right ?
Please help !!!!
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The true statements about the circle are
The radius of the circle is 3 units.The center of the circle lies on the x-axis.The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. How to determine the true statements about the circle?From the question, we have the following parameters that can be used in our computation:
x² + y² - 2x - 8 = 0
Generally, To convert this equation to standard form, we need to complete the square.
First, we can rearrange the terms on the left-hand side of the equation so that all the x terms are together and all the y terms are together:
x² - 2x + y² - 8 = 0
Then, we need to add and subtract a value that allows us to rewrite x² - 2x term as a perfect square.
To do this, we take half of the coefficient of the x term (which is -2), square it, and add it to both sides of the equation:
So, we have
x² - 2x + (1²) + y² - 8 = 0 + (1²)
Evaluate
(x - 1)² + y² - 8 = 1
Finally, we can rearrange the terms
So, we have
(x - 1)² + y² = 9
Express 9 as the square of 3
(x - 1)² + y² = 3²
So, the standard form of the equation is (x - 1)² + y² = 3²
The standard equation of a circle is represented as
(x - a)² + (y - b)² = r²
Where
Center = (a, b)
Radius = r
When these equations are compared, we have
Center = (a, b) = (-1, 0)
Radius = r = 3
The point (-1, 0) lies on the x-axis
This means that the center is on the x-axis.
Also, it means that the radius of the circle is 3 units
This radius is the same for a circle that has the form x² + y² = 9
This is so because 9 can be expresses as the square or 3, and r = 3
Hence, the correct statements are (a), (b) and (e)
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Complete Question
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true?
Select three options.
The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.Assume that when adults with smartphones are randomlyselected, 45% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find the probability that exactly 2 of them use their smartphones in meetings or classes. Round to 4 decimals
P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.
what is probability?The possibility or likelihood of an event occurring is expressed numerically as probability. Probabilities are expressed as ratios (0 to 1) and percentages (0 to 100). It is founded on the likelihood that something will occur. The theoretical probability is built on the fundamental principle of probability justification. For instance, there is a 12 percent chance of receiving heads while flipping a coin.
P(X=12) is the needed probability. P ( X = 12 ) . There is a 0.0042 percent chance that all 12 of them will use their smartphones during courses or meetings.
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A man spends 70% of his income and craves rs 2580 What is his income? Full explanation please
Answer:
• Statement of the given problem,
⚫ A man spends 70% of his income and saves Rs. 2550. What is his income?
According to above data,
⚫ the required income of the
given man
= 2550/(1 - 70/10)
☐ = 2550/0.30
= 8,500 (Rs) [Ans]
what is the difference between a squared number and a cubed number
this is the explanation above with some examples
one characteristic of quality data which pertains to the expectation for the time between when data are expected and when they are available for use is:
A characteristic of quality data which pertains to the expectation for the time between when data are expected and when they are available for use is timeliness of information.
Information's timeliness is a crucial aspect of data quality since incomplete or outdated information can influence people's actions. That consequently costs businesses time, money, and reputational harm.
The term "completeness" describes how thorough the information is. Consider if all the information you require is there when evaluating data completeness; for example, you might just require a customer's first and last name, but their middle initial might be optional.
Reliability in the context of data quality traits refers to the absence of contradiction between one piece of information and another piece of information from a different source or system.
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