The simplification of the given expression is 0.6i.
What are complex numbers?Complex numbers are those numbers that contain the imaginary and the real part.
A Complex value z is written in a rectangular form as z = x+iy where (x, y) is the rectangular coordinates.
where r is the modulus of the complex number and θ is the argument
r =√x²+y² and θ = tan⁻¹y/x
Usually the simplification involves proceeding with the pending operations in the expression.
We need to simpify the 0.4i - i
= i(0.4-1)
= 0.6i
Therefore, the simplification of the given expression is 0.6i.
Learn more about cube root of complex numbers here:
https://brainly.com/question/16048106
#SPJ2
The table below shows some values of f(x) and g(x) for different values of x.
x f(x) = 9x + 7 g(x) = 5x
-2 -11
-1 -2
0 1
1 5
2
Complete the chart and determine the solution of the equation f(x) = g(x)?
A.) x = -1
B.) x = 0
C.) x = 2
D.) x = 25
Answer:
x = -1.75 makes f(x) = g(x)
Step-by-step explanation:
See the attached for a table. You will notice that for x=-1.75, the values of f(x) and g(x) are the same. That means x = -1.75 is the solution to f(x)=g(x).
Upon calculating the values for f(x) and g(x), it's determined that f(x) = g(x) when x = -7/4. The options provided do not include this answer, suggesting a possible typo in the question or answer choices.
Completing the Values and Finding the Solution for f(x) = g(x)
To complete the given table, we need to apply the functions f(x) = 9x + 7 and g(x) = 5x to the missing x values. For x = -2, g(x) equals -10 (since 5 * -2 = -10). For x = 0, f(x) is 7 (since 9 * 0 + 7 = 7), and for x = 2, f(x) equals 25 (since 9 * 2 + 7 = 25) and g(x) equals 10 (since 5 * 2 = 10).
To determine the solution for the equation f(x) = g(x), we set the two expressions equal to each other:
9x + 7 = 5x
By subtracting 5x from both sides, we get:
4x + 7 = 0
Now, subtracting 7 from both sides, we find:
4x = -7
Finally, by dividing both sides by 4, we get:
x = -7/4
None of the given options A, B, C, or D match x = -7/4, which might indicate there could be a typo in the question or answer choices.
On the first 4 quizzes of her chemistry class, nadia got an average score of 88. what does she need on the next quiz to have an overall average of 90?
Use the trapezoid rule to estimate the area under the graph of y = x2 + 2 for values of x from 0 to 3.
Which of the following is a feature of debit card?
A. Interest charge
B. Paying off purchases over time
C. More flexibility
D. Requires a linked bank account
Option D - Requires a linked bank account
Step-by-step explanation:
A debit card is an ATM card that is linked with the bank account of the same bank of which the card is issued from.
This works on debit mode like when it is swapped, immediate cash is deducted from your account. If your account is empty, it cannot be used.
Hence, the feature of the debit card out of all the options is option D - Requires a linked bank account.
If the area of a circle is 16pi what is the circumference of the circle, circle b, if its radius is 1/2 that of the circle a
find the inverse function for f(x)=square root 2x-6
The length of a photograph is 1 cm less than twice the width. The area is 91cm^2. Find the width and length.
The length of the photograph is 13 cm and the width is 7 cm.
What is a rectangle?
A rectangle is a quadrilateral having the four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.
Given that:-
The length of a photograph is 1 cm less than twice the widthThe area is 91 cm²The length and the width will be calculated as:-
let the width = x
length = 2x - 1
91 = x ( 2x - 1 ) = 2x² - x
2x² - x - 91 = 0
= ( 2x + 13 ) ( x - 7 )
x = - 13 / 2
x = 7 cm
Length will be = 2x - 1 = 2 x 7 - 1 = 13 cm
Therefore the length of the photograph is 13 cm and the width is 7 cm.
To know more about rectangles follow
https://brainly.com/question/25292087
#SPJ2
Carrie works in a clothing store. Every day before her shift ends, she folds the clothes that customers have tried on and puts them back on the racks. Today, she needs to fold 180 T-shirts and place them evenly on 9 racks. How many T-shirts does she place on each rack?
a. 15
b. 35
c. 44
d. 20
Answer: correct answer is D
180 shirts÷ by 9 racks=20
Carys is checking her tax bill for the last year.
The tax rates were as follows:
No tax of the first £11 000 of earnings.
Earnings in excess of £11 000 and up to £43 000 taxed at a rate of 20%.
Earnings in excess of £43 000 and up to £150 000 taxed at a rate of 40%.
Earnings over £150 000 taxed at a rate of 45%.
Last year Carys earned £45 600 before tax.
How much tax did she pay in total?
Show your working.
I am having a lot of trouble finding the answer to this. I looked it up on this website hoping I could find how to solve it but unfortunately that didn't happen. Can anyone help ?!!! Anxious to know!!!!!
Answer:
£7,440
Step-by-step explanation:
We have been given the tax rates as follows:
$0-$11,000 = No tax.
$11,000-$43,000 = 20%.
$43,000-$150,000 = 40%.
Earnings over $150,000 = 45%.
Since last year Carys earned $45,600, so we will have to find the tax paid by her for 11,000-43,000 at rate of 20%, then the tax for amount over 43,000 at the rate of 40%
Therefore, Carys paid an amount of $7,440 in tax.
Carys paid no tax on the first £11,000 of her income. She paid £6,400 in tax on her earnings between £11,000 and £43,000, and £1,040 on her earnings between £43,000 and £45,600. The total tax paid was £7,440.
Explanation:To calculate how much tax Carys paid on her earnings of £45,600, we need to apply the given tax rates to the appropriate segments of her income. Here is the step-by-step working:
She pays no tax on the first £11,000.Earnings between £11,000 and £43,000 are taxed at 20%. To find the tax for this bracket, we subtract £11,000 from £43,000 to get the taxable amount, which is ¤32,000. Then we calculate 20% of ¤32,000, which amounts to £6,400.Earnings above £43,000 up to £150,000 are taxed at 40%. Carys earned ¤2,600 in this bracket (because £45,600 - £43,000 = ¤2,600). The tax on this amount is 40% of ¤2,600, which is £1,040.Since Carys did not earn over £150,000, she does not pay any tax at the 45% rate.We now add the tax from the second and third bullet points to get the total tax that Carys pays: £6,400 + £1,040 = £7,440.
Therefore, Carys paid a total of £7,440 in tax for the last year.
Learn more about Tax Calculation here:https://brainly.com/question/34140086
#SPJ3
A culture of 1.75×1018 bacteria is in petri dish A. A culture of 6.25×1015 bacteria is in petri dish B. How many times greater is the number of bacteria in petri dish A than petri dish B? Enter your answer, in standard notation, in the box.
This is a point at which a graph intersects the y-axis. Example: (0, 5) for the equation y = x + 5.
The graph intersects the y-axis the y-coordinate is known as the y-intercept and this can be determined by using the definition of the y-intercept.
Given :
This is a point at which a graph intersects the y-axis. Example: (0, 5) for the equation y = x + 5.
The following steps can be used in order to determine a point at which a graph intersects the y-axis:
Step 1 - According to the example (0, 5) for the equation y = x + 5.
Step 2 - When the graph intersects the y-axis the value of the x-coordinate is zero.
Step 3 - When the graph intersects the y-axis the y-coordinate is known as the y-intercept.
For more information, refer to the link given below:
https://brainly.com/question/329422
JL is a diameter of circle K. If tangents to circle K are constructed through points L and J, what relationship would exist between the two tangents? Explain. ( I am falling behind on my online classes because this question is holding me back... I cannot compute anymore.... uuuurrghh)
What is the initial value of the exponential function shown on the graph
Answer:
The initial value of the exponential function is 2
Step-by-step explanation:
A function is a mathematical relation in which we input the values of a domain that generate the output values of a range.
Initial value of the function is the output value of the function when the input is x =0.
As shown in the graph:
The exponential function cut at the point (0, 2)
where;
y=2 when x=0.
Therefore, the initial value for the exponential as shown in the figure is, 2.
A local reader's club has a set of 12 hardback books, a set of 18 paperbacks, and a set of 36 magazines. each set can be divided equally among the club members. what is the greatest possible number of club members?
The greatest possible number of club members is the greatest common factor of 12, 18, 36 since all of these quantities of books have to be distributed evenly:
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 18 are 1, 2, 3, 6, 9, 18
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36.
The greatest common factor for this three numbers is 6.
As a result, the greatest possible number of club members is 6.
You have set up a webpage for your company. your logo took up 2/7 of your allotted space on the main page and the location information takes up 1/10 of the allotted space on a page. how much more space did the logo use than the location information? please express your answer as a fraction and percent.
Compute the exact value of the function for the given x-value without using a calculator. You must show your work for full credit. f(x) = 5x for x = 2
The equation y= 3x relates the number of points resulting from three-point baskets.
What is the constant of proportionality in this equation?
A.1
B.3
C.x
D.y
Answer:
3
Step-by-step explanation:
Andrew took a math test with 40 questions. If he scored an 85%, how many questions did he get correct?
Answer:
34 is my answer
In a bag there are 13 red marbles, 5 blue marbles, and 7 green marbles. what percent of the marbles are green?
(1 pt) which point represents the origin? number line from minus5 to 5 with point s at minus2, t at 0, u at 1, and v at 3.
Find the 10th term of the sequence defined by the given rule:f(n)=sqrt n+2
We are given the equation:
f(n)=sqrt n+2
To get the 10th term of the series, we simply have to substitute the value of 10 into the equation, n = 10. So that:
f (10) = sqrt (10 + 2)
f (10) = sqrt (12)
f (10) = 3.46
The measurement of the supplement of an angle is 7 times the measure of the complement. find the measure of the complement
Answer:
15⁰
Step-by-step explanation:
Angke = x
Complement = 90 - x
Supplement = 180 - x
Given:
180 - x = 7 (90 - x)
180 - x = 630 - 7x
6x = 450
x = 75
Complement = 90 - 75 = 15⁰
Write an equation of a line that goes through point (4, -5) and is parallel to line y = 2x + 8. Show all work.
I really need help with this.
Mr frost typed for 12 minutes at a constant rate of 50 words per minute. Mrs. grey typed the same number of words at a constant rate of60 words per minute how many minutes did it take Mrs. Grey to type the same amount as mr frost?
Find the equation of the line l where l is perpendicular to y=2/5x and passes through the points (5,2)
The temperature in degrees Celsius, c, can be converted to degrees Fahrenheit, f, using the equation mc026-1.jpg. Which statement best describes the relation (c, f)? It is a function because –40°C is paired with –40°F. It is a function because every Celsius temperature is associated with only one Fahrenheit temperature. It is not a function because 0°C is not paired with 0°F. It is not a function because some Celsius temperatures cannot be associated with a Fahrenheit temperature.
Answer:
B is true.
Step-by-step explanation:
given that the temperature in degrees Celsius C can be converted to degrees Fahrenheit F
For every Celsius temperature we get only one value of Fahrenheit .
Function: function is a mapping between two sets .Each member of set is mapped with one value of set B.
Given function is one-one because for every value of Celsius we get a unique value of Fahrenheit
Hence, it is a function because every Celsius temperature is associated with only one Fahrenheit temperature.
Therefore, option B is true.
1. What is the difference between –4 and 6?
1) –10
2) –2
3) 2
4) 10
2. What is the first step in solving the equation 4.2y -5.2=18.5
1. Add 5.2 to each side of the equation.
2. Subtract 5.2 from each side of the equation.
3. Multiply each side of the equation by 4.2.
4. Divide each side of the equation by 5.2.
Which table represents a linear function?
The cost of a classified ad is based on a daily rate plus a flat service fee. One day cost $3.50 and four days cost $800 write and solve a linear equation to find the cost of a 7-day ad.
x= 11
hope this helped :)
The linear equation that gives the cost in dollars, y, in terms of the number of days the ad appears, x is: y = $1.50x + $2.00
The cost of a 7-day ad is $12.50.
Let, the daily rate is "d" dollars and the flat service fee is "f" dollars.
We are given two pieces of information:
One day costs $3.50.
Four days cost $8.00.
Using this information, we can set up two equations:
For one day: d + f = $3.50
For four days: 4d + f = $8.00
Now, we need to solve this system of linear equations to find the values of "d" and "f."
Subtract Equation 1 from Equation 2 to eliminate "f":
(4d + f) - (d + f) = $8.00 - $3.50
3d = $4.50
Now, divide both sides by 3 to solve for "d":
d = $4.50 / 3
d = $1.50
Now that we have the value of "d," we can find the value of "f" by substituting "d" into Equation 1:
d + f = $3.50
$1.50 + f = $3.50
Now, subtract $1.50 from both sides to solve for "f":
f = $3.50 - $1.50
f = $2.00
So, the daily rate (d) is $1.50, and the flat service fee (f) is $2.00.
We get, a linear equation that gives the cost in dollars, y, in terms of the number of days the ad appears, x is: y = $1.50x + $2.00
Now, to find the cost of a 7-day ad, we can use the daily rate and multiply it by the number of days (7):
Cost of a 7-day ad = 7 * $1.50 + $2.00
Cost of a 7-day ad = $10.50+ $2.00 = $12.50
The cost of a 7-day ad is $12.50.
To learn more on equation click:
https://brainly.com/question/14468218
#SPJ5
Rajesh wakes up at 7:00 a.m. and takes a walk for half an hour. He then spends 30 minutes bathing and eating breakfast. After watching the morning news on TV for a while, Rajesh leaves for school at 9:30 a.m. How many hours does Rajesh spend watching the news? 1 and 1/2 hours 2 hours 2 hours and 30 minutes 120 minutes 130 minutes