Answers
Answer:
20 - i
Step-by-step explanation:
Addition of complex numbers:In complex number addition/subtraction, add the imaginary part and add the real part separately.
The error is while adding imaginary part, you have to combine the coefficients of the imaginary numbers. So, -3 +2 will give us -1. So, the result is -i.
16 - 3i + 4+ 2i = 16 + 4 -3i + 2i
= 20 - i
Answer:
20 - i
Step-by-step explanation:
The error made during second step:
When adding or subtracting expression, we add or subtract like terms.
(16 - 3i) + (4 + 2i) get rid of parenthesis
16 - 3i + 4 + 2i add/subtract like terms
20 - i (the mistake is made here, instead of "i" they typed i^2)
Related Questions
< Question 7, 1.5.25 >
The line graph to the right indicates that in 1960, 21% of taxes came from corporate income tax. For the period from 1960 through 2010,
this percentage decreased by approximately 0.32 each year. If this trend continues, by which year will corporations pay zero taxes?
Answers
The 21% of taxes and annual percentage decrease of 0.32, using arithmetic progression gives;
The year corporations will pay zero taxes as 2025How can arithmetic progression be used to find the required year?The percentage of tax that comes from corporate income tax = 21%
Amount by which the percentage decreased each year = 0.32
Period during which the tax reduced = Between 1960 and 2010
Required;
The year corporations pay zero taxes.
Solution;
The amount of tax paid each year can be given by the arithmetic progression formula,
[tex] a_{n} = a + (n - 1) \cdot d[/tex]
Where;
a = The first term = 21
[tex] a_{n} = value \: on \: the \: nth \: year[/tex]
d = The common difference = -0.32
When [tex] a_{n} = 0 [/tex], we have;
[tex] 0 = 21 + (n - 1) \times (-0.32) [/tex]
0.32•(n - 1) = 21
n - 1 = 21/0.32 = 65.625
n = 65.625 - 1 = 64.625 ≈ 65
The year the corporations will pay no taxes is 1960 + 65 = 2025
Corporations will pay no taxes in the year 2025
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You are lubricating several motors in the shop. One motor must be lubricated with of 3/16 an ounce of grease, and one larger motor must be lubricated with 3/8 of an ounce of grease. How many ounces of grease will you require? Your answer should be a fraction of an ounce, reduced to its lowest terms.
Answers
3/16 + 6/16 = 9/16 of an ounce
help me with this precal
Answers
Answer: Ok
Step-by-step explanation:
9-0-0
Mark Ogara rented a truck from Avis Rent-A-Car for the weekend (2 days). The base rental price was $30.45 per day plus 15 3/4 cents per mile. Mark drove 415.85 miles.
How much does Mark owe?
ound your answer to the nearest cent.
Answers
The amount that he owes will be $6610.54.
How to compute the value?From the information, the base rental price was $30.45 per day plus 15 3/4 cents per mile. Mark drove 415.85 miles.
Therefore the amount that will be paid will be:
= ($30.45 × 2) + (15.75 × 415.85 miles)
= $60.90 + $6549.64
= $6610.54
The cost is $6610.54.
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←
Assume log x=0.27 and log by = 0.81. evaluate the following expression logb x/y
Answers
By evaluating following logarithm equation and we we get the value of required expression is -0.54.
What is logarithm?
The logarithm is the opposite of exponentiation as a function. This indicates that the base b of another fixed number, the logarithm of a given number x, is the exponent that must be raised in order to obtain the given number x.
As per the question
we have to assume x
log x=0.27
log by=0.81
We have to calculate log bx/y by following expression
We know loge (a/b)= log_e a-log_e b
We know (x)= logb y
=0.27-0.81
= -0.54
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How do you find the range and domain of this graph?
Answers
Answer: Domain {-4,-2,2}
Range{4,6}
Step-by-step explanation:
To make barstools, Federico rents a shop for $1510 a month and calculates the materials for each stool are $45. Find the total cost for him to make 98 stools in a month.
Answers
Answer:
4410
Step-by-step explanation:
45 x 98 = 4410
PLS CHECK IF THIS ANSWER IS CORRECT
WILL MARK BRAINLIEST
Answers
Answer:
I'm pretty sure the answer is 6.
Step-by-step explanation:
Labeling the rooms A, B, and C makes it easier.
Room A - All BUT 4
Room B - All BUT 4
Room C - All BUT 4
Since you can see each room is all but four, you can split the 4 into 2 into 2 OTHER rooms than the one stated. For example, Room A is all but 4, so 2 go to Room B and the other 2 go to Room C because each room is all BUT 4.
Basically, 2+2+2 = 6
Triangle XYZ has translated 4 units up and 3 units left to yield ΔX'Y'Z'. What is the distance between any two corresponding points on ΔXYZ and ΔX'Y'Z′?
Answers
The distance between any two point is 5 unit.
What is distance?
The measurement of distance between two objects or points can be quantitative or occasionally qualitative. Distance in physics or common language can refer to a physical length or an assumption based on other factors.
As per the question
Triangle xyz is translated = 4units
And triangle xyz left to yield=3 unit
The distance between the corresponding is hypotenuse of the triangle is-
Buy applying Pythagorus theorem we can get C^2=a^2+b^2
As we know a,b=legs
c=hypotenus
C^2=a^2+b^2C^2
=3^2+4^2
=9+16
=25C =√25 =5 unit
Therefore, the distance between any two point is 5 unit.
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Solve for x.
12x + 7 < -11
OR 5x8 > 40
Answers
Answer:
-3/2
Step-by-step explanation:
x < -3/2
Which transformation would take Figure A to Figure B?
Answers
Answer:.......................
Which of the following systems of equations has the same
solution as
-2x+2y=-2;3x-y=9
a.
A. 4x = 16;3x-y=9
B. [-2x+2y=-2;16x-2y = 9
C. -3x-7y=3;3x-y=9
D. [-2x+2y=-2;x+y=11
Answers
Answer:
Step-by-step explanation:
16/4
2.5 of what is 3?
Need help ASAP
Answers
Step by step
2.5 of (multiply) x (unknown) is (=) 3
2.5 x = 3
Divide both sides by 2.5 to solve
2.5 / 2.5 x = 3/ 2.5
X = 1.2
Check your work, sub 1.2 in for x
(2.5) (1.2) = 3
3 = 3
Problem solved!!
denny is in the car repair business. Denny recently calculated his total cost conditions. He found that the total cost of repairing s cars is TC(s)=2s^2+10
If the market price is $20, how many cars will Denny be willing to repair?
Answers
When the market price is $20, the number of cars that Denny will be willing to repair is 5 cars.
How to calculate the value?It should be noted that the total revenue will be:
= price × quantity
= 20 × s
= 20s
where s = number of cars
The marginal revenue will be 20.
The total cost is given as:
= 2s² + 10
The marginal cost will be 4s
We will equate the marginal. This will be:
4s = 20
Divide
s = 20/4
s = 5
Therefore, the number is 5.
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can someone help me with this
Answers
⇒
s=kt^2
condition –> 64 feet in 1 second
s=kt^2
64=k(1)^2
64=k
s=64t^2
first part (how far will it fall in 5 seconds)
s=64(5)^2
s=1600
second part(how long will it take an object to fall 256 feet)
256=64t^2
256/64=t^2
4=t^2
√4=t
2=t
Brock, age 50, and Erin, age 49, are married with three dependent children. They file a joint return for 2021. Their income from salaries totals $50,000, and they received $8,000 in taxable interest, $5,000 in royalties, and $3,000 in other ordinary income. Brock and Erin's deductions for adjusted gross income amount to $2,500, and they have itemized deductions totaling $19,250.
Answers
Based on the filing status of Brock and Erin, their itemized deductions, and their income from their salaries, their income tax liability is $4,250.
What is the income tax liability?First, find the taxable income:
= Adjusted gross income - larger of Itemized deductions or standard deductions
= (50,000 + 8,000 + 5,000 + 3,000 - 2,500) - 24,800
= $38,700
The tax rate is 10 % for income between $0 and $19,750 and 12% for salaries between $19,751 and $80,250.
Brock and Erin therefore have a tax liability of:
= (10% x 19,750) + (12% x (38,700 - 19,750))
= $4,252
Rest of the question is:
Find the Income tax liability before any credits
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a car rental company charges a daily rate of $26 plus $0.10 per mile for a certain car. Suppose that you rent that car for a day and your bill (before taxes) is $71. How many miles did you drive?
Answers
Answer: 450 miles
Step-by-step explanation: we can put the info we got from the question into an equation. since the car was only rented for a day, the daily rate that was paid was $26. and $0.10 for every mile the car was driven. So we can put into the equation 71 = 26 +0.10m, where m represents miles. Now subtract 26 from both sides and we get 45 = 0.10m. Divide both sides by 0.10 and we get m= 450
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!
Answers
Using the normal distribution, it is found that 55.7% of response times are between 4 and 6 minutes.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.For this problem, the mean and the standard deviation are given, respectively, by:
[tex]\mu = 4.5, \sigma = 1.2[/tex]
The proportion between 4 and 6 minutes is the p-value of Z when X = 6 subtracted by the p-value of Z when X = 4, hence:
X = 6:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (6 - 4.5)/1.2
Z = 1.25
Z = 1.25 has a p-value of 0.8944.
X = 4:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (4 - 4.5)/1.2
Z = -0.42
Z = -0.42 has a p-value of 0.3372.
0.8944 - 0.3372 = 0.5572 = 55.72%.
Hence:
55.7% of response times are between 4 and 6 minutes.
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Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson’s eventual profit function is given as: , where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson’s profit start decreasing
Answers
The company's profit will start to decline if it only produces one bag.
Given f(x) = 2x⁴ ₋ 4x³ ₊ 7
Differentiate it with respect to x.
therefore, f'x) = 8x³ ₋ 12x²
= 4x²(2x ₋ 3)
For decreasing, f'(x) ≤ 0
⇒ 4x²(2x ₋ 3) ≤ 0
⇒ 2x ₋ 3 ≤ 0
⇒ x ≤ 3/2
Since the number of bags are represented by x.
Hence, x ∈ N
Therefore, x = 1 is only possibility.
Therefore, if the company only produces one bag, its profit begins to decline.
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Your question was incomplete. Please find the missing the content here.
Wilson hires a financial analyst to analyse costs and profits for his cereal production business. The analyst determines that Wilson's eventual profit function is given as: pi = 2x⁴ ₋ 4x³ ₊ 7 where x is the number of bags of cereal produced. At what point or number of bags of cereal will Wilson's profit start decreasing?
High divers use the height of the diving platform to calculate the speed at which they enter the
water. The formula 58-34-12 models the diver's speed s (in miles per hour) and the height
h (in feet) of the platform.
a. Solve the formula for 3 and for h
b. At what speed does a diver enter the water when the platform is 82 feet tall?
c. A diver enters the water at 48 miles per hour. How tall is the platform?
Answers
a. 3h = -12 + 5s
b. Speed = 51. 6 miles per hour
c. Height = 76 feet
How to determine the valueGiven the function;
5s - 3h = 12
Where;
s is the speed in miles per hourh is the height in feeta. To solve for 3h
We have;
- 3h = 12 - 5s
3h = -12 + 5s
b. If the height is 82 feet , then
5s - 3(82) = 12
5s - 246 = 12
collect like terms
5s = 12 + 246
5s = 258
Make 's' the subject
s = 258/ 5
s = 51. 6 miles per hour
c. If the speed is 48 miles per hour, we have;
5(48) - 3h = 12
240 - 3h = 12
collect like terms
-3h = 12 - 240
-3h = -228
Make 'h' the subject
h = -228/ -3
h = 76 feet
Thus, the speed and height are 51. 6 miles per hour and 76 feet respectively.
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Use properties of operations to add (−3) and (−17)
14
20
-20
-14
Answers
Answer:
Step-by-step explanation:
-20
4x+3y=7 x+2y=-2
put both in slope-intercept form
Answers
Answer:
Second equation Answer: [tex]y=-\frac{1}{2}x-1[/tex]
First equation Answer: [tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]
Step-by-step explanation:
Concept:
The general equation of a line in slope-intercept form is given below as
[tex]y=mx+c[/tex]
where
[tex]m=slope[/tex]
[tex]c=intercept[/tex]
First equationThe first equation is given below as
[tex]4x+3y=7[/tex]
We will make y the subject of the formula to change the equation in slope-intercept form
[tex]4x+3y=7[/tex]
subtract 4x from both sides
[tex]4x-4x+3y=7=-4x[/tex]
[tex]3y=-4+7[/tex]
divide both sides by 3
[tex]\frac{3}{y} =\frac{-4x}{3} +\frac{7}{3}[/tex]
[tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]
Hence,
The equation of 4x+3y=7 in slope intercept form is given below as
[tex]y=-\frac{4}{3}x~+\frac{7}{3}[/tex]Second EquationThe second equation is given below as
[tex]x+2y=-2[/tex]Subtract x from both sides[tex]x-x+2y=-2-x[/tex][tex]2y=-x-2[/tex]divide through by 2[tex]\frac{2y}{2} =-\frac{x}{2} =-\frac{2}{2}[/tex][tex]y=-\frac{1}{2}x-1[/tex]Hence,
The equation of x+2y=-2 in slope-intercept form is
[tex]y=-\frac{1}{2}x-1[/tex]Hope this Helps! <3Answered by:AshTheNeko
At a local pizzeria, a pizza with one topping is 9.99. You can add additional toppings for 1.25 each. The pizzeria's menu lists 10 different toppings. Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings. Find the domain and range.
Answers
The function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings is C(x) = 9.99 + 1.25x
The domain is x >= 0 and the range is c(x) >= 9.99
Write a function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.The given parameters are:
One topping = 9.99
Additional topping = 1.25 each
We have x to represent the number of toppings
This means that
C(x) = One topping + Additional topping * x
So, we have
C(x) = 9.99 + 1.25x
How to find the domain and range?We have
C(x) = 9.99 + 1.25x
The smallest number of topping is 0
So, the domain is x >= 0
Substitute 0 for x in C(x) = 9.99 + 1.25x
C(0) = 9.99 + 1.25(0)
This gives
C(0) = 9.99
So, the range is c(x) >= 9.99
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Answer:
C(x) = 8.74 + 1.25x
Domain: 1 ≤ x ≤ 10
Range: [9.99, 21.24]
Step-by-step explanation:
a) We need to find the function C(x) that represents the cost of a pizza with at least one topping, where x is the number of toppings.
We know that a pizza with one topping is $9.99 and that you can add additional toppings for 1.25 each.
So the equation is C(x) = 9.99 + 1.25x right?
Not really... Since $9.99 is the price of a pizza and 1 topping, we need to subtract 1 from x otherwise we would be paying for a pizza with 2 toppings when we had ordered a pizza with 1!
So the new equation is:
C(x) = 9.99 +1.25(x - 1)
or, C(x) = 9.99 + 1.25x - 1.25
or, C(x) = 1.25x + 8.74
b) We need to find the Domain of C(x).
We know that the pizzeria's menu lists 10 different toppings and that a pizza has at least one topping.
So we can choose up to 10 different toppings. And we need at least 1 topping.
∴ Domain is 1 ≤ x ≤ 10.
b) We need to find the Range of C(x).
We know that the domain of C(x) is 1 ≤ x ≤ 10, and that a pizza with 1 topping is $9.99.
Since we already know the minimum (9.99) all we have to do is find the maximum. We can do that by plugging in 10 into C(x) since it is the maximum of our domain.
C(10) = 1.25(10) + 8.74
or, C(10) = 12.50 + 8.74
or, C(10) = 21.24
∴ Range of C(x) = [9.99, 21.24]
Answer:
C(x) = 8.74 + 1.25x
Domain: 1 ≤ x ≤ 10
Range: [9.99, 21.24]
Three line segments form the letter Z. Rotate the letter Z counterclockwise around the midpoint of segment BC by 180 degrees. Describe the result.
Answers
Answer:
i don't known the question you are asking
Write down two prime numbers that have a sum of 20
Answers
3 and 17
7 and 13
Step-by-step explanation:
........
Ximena launches a toy rocket from a platform. The height of the rocket in feet
is given by h(t) = -16t² + 40t +96 where t represents the time in
seconds after launch. What is the appropriate domain for this situation?
Answers
The apprοpriate dοmain fοr this situatiοn is t ≥ 0.
What is Functiοn?In mathematics, a functiοn is a relatiοn between a set οf inputs and a set οf pοssible οutputs with the prοperty that each input is related tο exactly οne οutput. It can be thοught οf as a rule οr a machine that takes inputs and prοduces οutputs accοrding tο a specific set οf instructiοns οr οperatiοns.
The dοmain οf a functiοn represents the set οf all pοssible input values fοr which the functiοn is defined. In this case, the functiοn h(t) represents the height οf the rοcket as a functiοn οf time t after launch.
Since time cannοt be negative in this cοntext (we can't have negative secοnds), the apprοpriate dοmain fοr this situatiοn is t ≥ 0, which means the functiοn is defined fοr all nοn-negative values οf t after the rοcket is launched.
Therefοre, the apprοpriate dοmain fοr this situatiοn is t ≥ 0.
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Find the measure of KNM
Answers
Given: p: x is a perfect square. q: x is even
What is a value of x that makes p and q true?
16
30
81
99
Answers
Answer:
16
Step-by-step explanation:
16: 16=4^2 and is even. 16/2=8
30: 30 is even, 30/2=15. However, the square root of 30 is between 5 and 6([tex]\sqrt{25}[/tex]and [tex]\sqrt{36}[/tex]).
81: 81=9^2, but 81 is not even. 81/2=40.5.
99: 99 is not even and doesn't have a square root. The square root of 100 is 10, so the square root of 99 is around 9.9, slightly less than 10.
PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!!
Answers
The proportion of users that park bike on the trail is 0.1728
How to determine the proportion of users that park bike on the trail?The table represents the given parameters
From the table, we have the following parameters
Suburban total = 243
Users that park bike on the trail = 42
The proportion of users that park bike on the trail is then calculated as
P = Users that park bike on the trail/Suburban total
This gives
P = 42/243
Evaluate
P = 0.1728
Hence, the proportion of users that park bike on the trail is 0.1728
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PLSSS HELP ANSWER, THE QUESTION IS IN THE SCREENSHOT
Answers
[tex]y(\pi/3)=1 \implies 1=C-2\cos(\pi/3) \\ \\ 1=C-1 \\ \\ C=0 \\ \\ \therefore y=\boxed{-2\cos x}[/tex]