Write the equation for whose roots are 3,0,1,i,-i
Answers
Given the roots: 3,0,1,i,-i
We will write the equation for whose roots are
As we were given the roots, we can write the factors
so, we have the following factors:
\(\begin{gathered} x=3\rightarrow(x-3) \\ x=0\rightarrow x \\ x=1\rightarrow(x-1) \\ x=i\rightarrow(x-i) \\ x=-i\rightarrow(x+i) \end{gathered}\)So, the equation will be:
\(f(x)=x(x-1)(x-3)(x-i)(x+i)\)Related Questions
Find the regression line associated with the set of points. (Round all coefficients to four decimal places.) HINT (See Example 2.]
(1, 2), (4,4), (9,9)
y(x) =
Answers
The equation of the regression line is : Ŷ = 0.8571+0.8878X
Given the set of points :
(1, 2), (4,4), (9,9)
X axis : ___ Y axis
1 ___________2
1 ___________2 4 __________ 4
1 ___________2 4 __________ 4 9 __________ 9
The regression line associated could be obtained using technology such as excel, linear regression solvers or a graphing calculator.
Using technology :
Input the values of X and Y into their appropriate column and plot :
The regression equation obtained is :
Ŷ = 0.8571 + 0.8878X
Where :
Ŷ = predicted value of Y(dependent variable)
X = Independent variable
Slope = 0.8878
Intercept = 0.8571
The regression plot is attached below
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It took 35 seconds for 5 songs to download to Rebecca’s computer. The next day, it took 42 seconds for 6 songs to download. Write an equation in point-slope form to represent the time y it took to download x songs.
NEEDS TO BE STEP BY STEP
Answers
The equation in point-slope form to represent the time y it took to download x songs is; (y - 35) = 7(x - 5)
Since it took 35 seconds for 5 songs to downloadand it took 42 seconds for 6 songs to downloadIn essence, we can represent the information as;
(5, 35) and (6,42)To find the slope of the equation; we have;
Slope, m = (42-35)/(6-5)m = 7In essence, the equation in point-slope form to represent the time y it took to download x songs is;
(y - 35) = 7(x - 5)Read more:
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m NEED HELP ON THIS ONE
Answers
The following measurements on a semi circle are
m< S = 47 degree
m< U = 90
x = 6.78
What are angles on a semicircle?The angle inscribed on a semicircle is equal to 90 degrees. This makes the triangle SUT a right triangle
How to find the angle on the semicircleThe angle at U is the inscribed angle and this is equal to 90 degrees
m< U = 90 degrees
m< S + m< U + m< T = 180 - sum of angle o a triangle
m< S = (9x - 14)
m< U = 90
m< T = 43
substitute the values
9x - 14 + 90 + 43 = 180
9x - 14 = 180 - 90 - 43
9x - 14 = 47
9x = 47 + 14
9x = 61
x = 61/9
x is solved to be 61/9
m< S = 9x - 14
substitute the value of x
m< S = 9 * 61/9 - 14
m< S = 47 degree
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Phil has completed 1/4 of his shift; Darren has completed 3/7 of his shift; Alice has finished 1/8 of her shift; Lisa has 1/5 of her shift remaining. Out of the four employees, who has completed the least work time?
Answers
Answer:
Out of the four employees, Alice is the one who has completed the least work time, since she only completed 12.5% of it.
Step-by-step explanation:
Since Phil has completed 1/4 of his shift; Darren has completed 3/7 of his shift; Alice has finished 1/8 of her shift of her; and Lisa has 1/5 of her shift remaining, to determine, out of the four employees, who has completed the least work time, the following calculation must be performed:
Phil: 4 - 1/4 = 3/4 = 0.75
Darren: 7 - 3/7 = 4/7 = 0.57
Alice: 8 - 1/8 = 7/8 = 0.875
Smooth: 5 - 1/5 = 4/5 = 0.8
Thus, of the four employees, Alice is the one who has completed the least work time, since she only completed 12.5% of it.
Which statement describes volume?
A) measures the space inside in cubic units
B) measures the space inside in square units
C) measures the outside surface in cubic units
D) measures the outside surface in square units
Answers
Answer:
A) measures the space inside in cubic units
Step-by-step explanation:
-1/4 plus 3/5
Answer or else
Answers
The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.
To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.
The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:
-1/4 = -5/20
3/5 = 12/20
Now that the fractions have the same denominator, we can add them:
-5/20 + 12/20 = (-5 + 12)/20 = 7/20
Therefore, -1/4 + 3/5 is equal to 7/20.
To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.
Thus, the final answer is 7/20.
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according to a recent pew research center report, many american adults have made money by selling something online. in a random sample of 4579 american adults, 914 reported that they earned money by selling something online in the previous year. assume the conditions for inference are met. construct a 98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year. (0.1859, 0.2133) (0.1899, 0.2093) (0.1994, 0.1998) (0.1880, 0.2112) (0.1937, 0.2037)
Answers
98% confidence interval for the proportion of all american adults who would report having earned money by selling something online in the previous year by using z-score. The correct answer is (0.1859, 0.2133)
The point estimate for the proportion of American adults who earned money by selling something online in the previous year is:
p-hat = 914/4579 = 0.1995
To construct a 98% confidence interval for the population proportion, we can use the formula:
p-hat ± z*(sqrt(p-hat*(1-p-hat)/n))
where z is the z-score associated with the desired confidence level (98% corresponds to a z-score of 2.33), and n is the sample size. Plugging in the values, we get:
0.1995 ± 2.33*(sqrt(0.1995*(1-0.1995)/4579))
Simplifying this expression, we get:
(0.1859, 0.2133)
Therefore, the correct answer is (0.1859, 0.2133). This means we are 98% confident that the true proportion of American adults who earned money by selling something online in the previous year lies between 0.1859 and 0.2133.
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A circle with center Q located at (1, 2) is drawn on the coordinate plane below.
A(3,-2)
B (2,4)
C (-2, 2)
D(-1,1)
Which point is located on the edge of the circle?
Answers
https://lalinks.org/linksweb
PLZZZZ Hurry I’m in a rush
Answers
Answer:
y=10
Step-by-step explanation:
2y+3+9y-7+7y+4=180
18y=180
y=10
A bridge deck is suspended 215 feet above a river. If a stone is dropped over the side of the bridge, the height, in feet, of the stone above the water surface after consistency is given by y 215-16t
Answers
Thandi deposits 850 into a bank. the bank will pay a simple interest rate of 8% per year. how much money will Thandi get when she withdraws all her money after five years
Answers
Answer:
1084.83932813 which you would round to 1085
in a classroom there are 28 tablets which includes 5 that are defective. if seven tablets are chosen at random to be used by student groups. 12. how many total selections can be made? a. 140 b. 98280 c. 11793600 d. 4037880 e. 1184040 13. how many selections contain 2 defective tablets? a. 10 b. 21 c. 336490 d. 706629 e. 33649
Answers
Using the combination formula, it is found that:
The number of total selections that can be made is: e. 1184040.The number of selections that contain two defective tablets is: c. 336490.Combination formula\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula, involving factorials. It is used when the order in which the elements are chosen does not matter.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
In the context of this problem, we have that seven tablets are chosen from a set of 28 tablets, hence the number of selections that can be made is given by:
\(C_{28,7} = \frac{28!}{7!21!} = 1,184,040\)
For two defective tablets, the selections are given as follows:
Two defective from a set of five.Five non-defective from a set of 23.Hence the number of selections is calculated as follows:
\(C_{23,5}C_{5,2} = \frac{23!}{5!18!} \times \frac{5!}{2!3!} = 336,490\)
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HELPPP ME PLEASE IVE BEEN 2 hours IN THIS QUESTIONN
Answers
9514 1404 393
Answer:
12.9 square yards
Step-by-step explanation:
The base is an equilateral triangle, so we can assume that the three faces have the same dimensions. Each of those face triangles has an area of ...
A = 1/2bh
A = 1/2(3 yd)(2 yd) = 3 yd²
The base area is computed using the same formula and the given height:
A = 1/2(3 yd)(2.6 yd) = 3.9 yd²
Then the total surface area is that of the base and the three faces:
SA = (3.9 yd²) + 3(3 yd²) = 12.9 yd² . . . total surface area
Which of the following statements describes a rhombus?A. all sides are equalB. the opposite angles are equalC. the diagonals bisect each other at right anglesD. the adjacent angles are not supplementary
Answers
The Option B statement "the opposite angles are equal" accurately describes a rhombus, as each of the four angles of a rhombus are equal to each other. This means that the opposite sides of the rhombus have the same measure.
Which statement describes a rhombus?B. the opposite angles are equalA rhombus is a four-sided shape with all sides equal in length. It is also known as a diamond shape. The most important thing to remember about a rhombus is that the opposite angles are equal.
This means that the two angles across from each other on the rhombus have the same measure. This is what is meant by the statement "the opposite angles are equal," and it accurately describes a rhombus.
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Which expression is equivalent to 27 + 45?
Question options:
1)
8(3 + 6)
2)
8(19 + 37)
3)
9(3 + 5)
4)
9(18 + 36)
Answers
Answer:
Step-by-step explanation:
li boa yerrmeee
To estimate 179% of 41 by rounding, use the expression
.
Using the distributive property, the expression is equivalent to
.
179% of 41 is about
Answers
The estimate of 179% of 41 by rounding is about 73.19.
To find this estimate, first convert the percentage to a decimal by dividing it by 100: 179/100 = 1.79. Then, multiply this decimal by 41: 1.79 * 41 = 73.39.
Since we are rounding, we round this value to the nearest whole number, which is 73. Therefore, the direct answer is 179% of 41 is about 73.When estimating by rounding, we look at the decimal places. In this case, the hundredth place is 3. Since 3 is less than 5, we round down. Hence, the estimate is 73.19. It is important to note that rounding introduces some degree of error, as the actual value is 73.39. However, for most practical purposes, an estimate provides a close approximation that is quick and easy to calculate.For more similar questions on whole number
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Maximizing revenue. Edwards University wants to determine what price to charge for tickets to football games. At $18 per ticket, attendance averages 40,000 people per game. Every decrease of $3 to the ticket price adds 10,000 people to the average attendance. Every person at a game spends an average of $4.50 on concessions. What price per ticket will maximize revenue
Answers
Answer:
New price is $12.75
New attendance is 57500
Step-by-step explanation:
For starters, we use the relation.
18 - 3x
Since we don't know the number of times we're expected to deduct $3 from the price.
Again, we have 40000 + 10000x on another hand. Question says to add 10000 people everytime $3 is deducted.
Since (40000 + 10000x) is the number of people, we multiply it by $4.50, the average amount each person spends is then gotten to be
(18 - 3x) (40000 + 10000x) + (40000 + 10000x) (4.5) = 0
Expanding the bracket, we have
[720000 + 60000x - 30000x²] + [180000 + 45000x] = 0, solving further, we have
900000 + 105000x - 30000x² = 0 or
-30000x² + 105000x + 900000 = 0
Then, we find the maximum of a quadratic, by finding the axis of symmetry. Use x = -b/2a
x = -105000 / 2 * -30000
x = -105000 / -60000
x = 1.75
From our earlier equations, the new price then is
18 - 3(1.75) = 18 - 5.25 = $12.75
The new attendance also is
40000 + 10000(1.75) =
40000 + 17500 = 57500
What is one fifth of twenty more than half
of 80?
(A) 8
(B) 10
(C) 12
(D) 13
Answers
Answer:
(C) 12
Step-by-step explanation:
To solve this problem, we can use the following steps:
Find half of 80: 80/2 = 40
Add 20 to half of 80: 40 + 20 = 60
Find one fifth of the result: 60/5 = 12
Therefore, one fifth of twenty more than half of 80 is equal to 12. The correct answer is (C) 12.
Answer:
(C) 12
Step-by-step explanation:
What is one fifth of twenty more than half of 80
0.5 × 80 = 40
What is one fifth of twenty more than half of 80
40 + 20 = 60
What is one fifth of twenty more than half of 80
1/5 × 60 = 60/5 = 12
In the making of ball bearings, diameters vary from one bearing to the next because of minor variations in the
manufacturing process. The diameter of the ball bearings varies according to a distribution that is approximately Normal
with mean 11.5 mm and standard deviation 0.05 mm. Two ball bearings are randomly selected. Find the probability that the difference in the diameters of the two ball bearings is less than 0.06 mm.
Answers
On solving the provided questions, we can say that Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
he diameter of the ball bearings varies according to a distribution that is approximately Normal
mean 11.5 mm and standard deviation 0.05 mm
the probability that the difference in the diameters of the two ball bearings is less than 0.06 mm
Probability, P( -1.6 \(\leq\) Z \(\leq\) 1.6 ) = 89.04%
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△TOPtriangle, T, O, P is rotated − 18 0 ∘ −180 ∘ minus, 180, degrees about the origin. Draw the image of this rotation
Answers
A graph of the resulting triangle after a rotation of -180° about the origin is shown below.
What is a rotation?In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).
Furthermore, the mapping rule for the rotation of triangle TOP 180° counterclockwise or -180° about the origin is given by this mathematical expression:
(x, y) → (-x, -y)
Coordinates of point T (6, 0) → Coordinates of point T' = (-6, 0)
Coordinates of point O (-2, -5) → Coordinates of point O' = (2, 5)
Coordinates of point P (-2, 5) → Coordinates of point P' = (2, -5).
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Which expressions are equivalent to (5g+3h+4)\cdot2(5g+3h+4)⋅2left parenthesis, 5, g, plus, 3, h, plus, 4, right parenthesis, dot, 2 ?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
(5g+3h)\cdot8(5g+3h)⋅8left parenthesis, 5, g, plus, 3, h, right parenthesis, dot, 8
(Choice B)
B
(5g+3h)\cdot6(5g+3h)⋅6left parenthesis, 5, g, plus, 3, h, right parenthesis, dot, 6
(Choice C)
C
None of the above
Answers
Answer:
20043
Step-by-step explanation:
1+1=2
Answer:
c none of the above
i put this in on my own assignment for an answer and got it right
have a fangtastic day <3
Step-by-step explanation:
The average monthly income of three persons is rs. 3,600. If the income of the first is 1/5 of the combined income of the other two then his monthly income is
Answers
The monthly income of the first person is $600.
Given that, the average monthly income of three persons is RS 3,600.
The income of the first is 1/5 of the combined income of the other two.
Here, Let income of the first be A, let income of the second be B and let Income of the third be C.
A+B+C=3600 -----(i)
Income for the first person = 1/5(B+C) -----(ii)
Substitute equation (ii) in equation (i), we get
(B+C)/5 +B+C =3600
B+C+5B+5C=3600×5
6B+6C=18000
6(B+C)=18000
B+C=3000 ------(iii)
Substitute (iii) in equation (i), we get
A=$600
Therefore, the monthly income of the first person is $600.
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Choose an equivalent expression for two thirds to the fourth power times two thirds raised to the third power comma all raised to the second power.
A. four ninths raised to the fourteenth power
B. four ninths raised to the twenty fourth power
C. two thirds raised to the fourteenth power
D. two thirds raised to the twenty fourth power
Answers
Answer:
C. two-thirds raised to the fourteenth
Step-by-step explanation:
Help plz very much needed. will mark brainly
Answers
Answer:
16860
Step-by-step explanation:
16.86 × 10³
= 16.86 × 1000 ( move decimal point 3 places to the right )
16860
Answer:
Help plz very much needed. will mark brainly
Step-by-step explanation:
18. Multiply, then check your work by switching factors.
a. 693 x 83
b. 910 x 45
c. 38 x 84
d. 409 x 89
Answers
The requried, Multiplies(with switching factors.) area given below,
a.
693 x 83 = 57489
83 x 693 = 57489
The answer is 57489.
b.
910 x 45 = 40950
45 x 910 = 40950
The answer is 40950.
c.
38 x 84 = 3192
84 x 38 = 3192
The answer is 3192.
d.
409 x 89 = 36401
89 x 409 = 36401
The answer is 36401.
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A car is traveling at a rate of 108 kilometers per hour. What is the cars rate in meters per second? How many meters will the car travel in 20 seconds?
Answers
Answer:
\(\frac{30meters}{second}\)
600meters
Step-by-step explanation:
Use conversion factors that represent 1. You can cross cancel wods just like numbers.
\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)
\(\frac{108000meters}{3600seconds}\)
\(\frac{30meters}{second}\)
\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)
600 meters
Helping in the name of Jesus.
The July bank statement sent by the bank to ABC company shows a balance of cash on deposit at July 31 of Br.4,964.47 Assume that on July 31, assume the on July 31, ABCs ledger shows a bank balance of Br. 4 173. 83. 1. A deposit of Br 410. 90 made after banking hours and doesnt appear in the bank statement2. A check drawn for Br. 79 had been erroneously charged by the bank Br.973. For checks issued in July have not yet been paid by the bank (outstanding checks). : Theses checks are;- Check No date amount 801 June 15 ---Br.100,00 888 July 24 ----Br. 10.25 890 July 27--- Br. 294.50 891 July 30 ---Br. 205.004. A check written for birr 210 had been incorrectly charged by the bank as birr 120 5. Proceeds from collection of a interest bearing note receivable from David. ABC Company had left this note with the banks collection department. The face amount of the note was birr 500 6. Br. 24.75 interest earned on average account balance during July7. A check for Br. 10 returned with the statement had been recorded in the check register as Br. 100. The check was for the payment of an obligation to Davis Equipment Company for the purchase of office supplies on account 8. Br. 5,00 fee charged by bank for handling collection of note receivable 9. Br. 50.25 check from customer John deposited by ABC company charged bank as Non sufficient fund (NSF) 10. Br. 12.70 service charged by bank for the month of July. 11. Check number 875 was issued July 20 in the amount of Br 85 but was erroneously recorded in the cash payment Journal as Br 58 for payment of telephone expense prepare bank reconcilation and journal entry
Answers
The bank reconciliation shows an adjusted bank balance of Br.5,301.42 and an adjusted ledger balance of Br.4,173.83.
To prepare the bank reconciliation and journal entry for ABC Company based on the given information, we need to compare the transactions recorded in ABC's ledger with the transactions shown in the bank statement. Here's the bank reconciliation:
1. Bank Statement Balance:
Cash on deposit at July 31: Br.4,964.47
2. Adjusted Bank Balance:
Bank Statement Balance: Br.4,964.47
3. Deposit not on the statement: + Br.410.90
(Adjusted Bank Balance: Br.5,375.37)
Erroneously charged check: + Br.79
(Adjusted Bank Balance: Br.5,454.37)
Outstanding checks:
Check 801: - Br.100.00
Check 888: - Br.10.25
Check 890: - Br.294.50
Check 891: - Br.205.00
(Adjusted Bank Balance: Br.4,844.62)
4. Incorrectly charged check: + Br.90
(Adjusted Bank Balance: Br.4,934.62)
5. Collection of interest-bearing note: + Br.500
(Adjusted Bank Balance: Br.5,434.62)
6. Interest earned: + Br.24.75
(Adjusted Bank Balance: Br.5,459.37)
7. Incorrectly recorded check: - Br.90
(Adjusted Bank Balance: Br.5,369.37)
8. Collection fee: - Br.5.00
(Adjusted Bank Balance: Br.5,364.37)
9. NSF check: - Br.50.25
(Adjusted Bank Balance: Br.5,314.12)
10. Service charge: - Br.12.70
(Adjusted Bank Balance: Br.5,301.42)
Adjusted Ledger Balance:
Bank Balance in ABC's Ledger: Br.4,173.83
Reconciled Bank Balance: Br.5,301.42
Reconciled Ledger Balance: Br.4,173.83
Journal Entry:
To record the bank reconciliation, we make the following journal entry:
Debit: Cash (Ledger Balance adjustment) - Br.5,301.42
Credit: Cash (Bank Statement Balance adjustment) - Br.4,964.47
Credit: Miscellaneous Income/Expense - Br.336.95 (the difference between the two balances)
This journal entry ensures that the ledger balance matches the reconciled bank balance by adjusting for the discrepancies identified during the reconciliation process.
The journal entry reflects the necessary adjustments to reconcile the two balances, with a debit to Cash (Ledger Balance adjustment), a credit to Cash (Bank Statement Balance adjustment), and a credit to Miscellaneous Income/Expense to account for the difference.
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How to add fraction 3/7+ 3/9=
Answers
\( \large \sf \pink{Answer: }\)
\( \large \purple{ \boxed{ \frac{16}{21}}}\)
\( \large \sf \pink{Explanation:}\)
\( \sf \large{ \frac{3}{7} + \frac{3}{9}}\)
\( \sf \large{ \frac{3}{7} + \frac{1 \times 3}{3 \times 3}}\)
\( \sf \large{ \frac{3}{7} + \frac{1}{3}} \)
\( \sf \large\frac{3 \times 3}{21} + \frac{1 \times 7}{21}\)
\( \sf \large{ \frac{9}{21} + \frac{7}{21}}\)
\( \sf \large{ \frac{(9 + 7)}{21}}\)
\( \sf \large \purple{ = \frac{16}{21}}\)
RESOLVER LOS SIGUIENTES SISTEMAS DE ECUACIONES APLICANDO EL METODO DE SUSTITUCION
2x +3y = 2
-6x + 12y = 1
Answers
Answer:
x = 1/2; y = 1/3
Step-by-step explanation:
2x + 3y = 2 Eq. 1
-6x + 12y = 1 Eq. 2
Eq. 1
2x + 3y = 2
2x = -3y + 2
x = -3/2 y + 1
Eq. 2
-6x + 12y = 1
De Eq. 1 sabemos que x = -3/2 y + 1
-6x + 12y = 1
-6(-3/2 y + 1) + 12y = 1
9y - 6 + 12y = 1
21y - 6 = 1
21y = 7
y = 7/21
y = 1/3
Eq. 1
2x + 3y = 2
2x + 3(1/3) = 2
2x + 1 = 2
2x = 1
x = 1/2
Respuesta: x = 1/2; y = 1/3
Please help me with this
Answers
Answer:
Equation: (3+x) +x= 49
Lynette's age: 23
Josh's age: 26