Answer:
Therefore the roots of equation 1 are 1,3 1/2,-i,+i
Step-by-step explanation:
in this question we have given
[tex]f(x) = 2x^5 - 9x^4 + 12x^3 - 12x^2 + 10x - 3 = 0[/tex].......1
we have to find the roots of this equation
put x=1 in equation 1
[tex]f(1)=2-9+12-12+10-3\\f(1)=0[/tex]
It means x=1 is root of equation 1
now put x=3 in equation 1
[tex]f(3)=2\times3^5-9\times3^4+12\times3^3-12\times3^2+10\times3-3\\f(3)=0[/tex]
therefore,x=3 is root of equation 1
Now put x=[tex]\frac{1}{2}[/tex] in equation 1
[tex]f(\frac{1}{2})=2\times (\frac{1}{2} )^5-9\times(\frac{1}{2})^4+12\times(\frac{1}{2})^3-12*(\frac{1}{2})^2+10\times \frac{1}{2}-3\\f(\frac{1}{2})=0[/tex]
It means x=[tex]\frac{1}{2}[/tex] is also root of equation 1
therefore equation one can be written as
[tex]f(x)=(x-1)(x-3)(2x-1)(x^2+1)[/tex]
therefore remaining 2 roots can be calculated by solving
[tex]x^2+1=0\\x=\sqrt(-1)\\x=i,-i[/tex]
Therefore the roots of equation 1 are 1,3 1/2,-i,+i
Sal currently has an account balance of $2,835.48. He opened the account five years ago with a deposit of $2310.72. If the interest compounds twice a year, what is the interest rate on the account?
What is the simplified form of the fifth root of x to the fourth power times the fifth root of x to the fourth power?
Answer:
The simplified form will be: [tex]x\sqrt[5]{x^3}[/tex]
Step-by-step explanation:
The given expression is: [tex]\sqrt[5]{x^4}*\sqrt[5]{x^4}[/tex]
Simplifying the above expression......
[tex]\sqrt[5]{x^4}*\sqrt[5]{x^4}\\ \\ =\sqrt[5]{x^4*x^4}\\ \\ =\sqrt[5]{x^4^+^4}\ [Exponents\ gets\ added\ while\ multiplication]\\ \\ =\sqrt[5]{x^8}\\ \\ =\sqrt[5]{x^5*x^3}\ [As\ 5+3=8] \\ \\ =\sqrt[5]{x^5}*\sqrt[5]{x^3}\\ \\ =x\sqrt[5]{x^3}[/tex]
So, the simplified form will be: [tex]x\sqrt[5]{x^3}[/tex]
The average annual rainfall in California is 0.564 of a meter per year. What is the value of the digit 4 in that number
What is the missing term in the factorization?
18x2−32=2(3x+?)(3x−4)
The running back for the bulldogsame football team carried the ball 9 times for a totall loss of 15 3/4 yards find the average change in field position on each run
investment historically have doubled every 9 years if you start with $2000 investment how much money would you have after 45 years
Answer: $64000
Step-by-step explanation:
The exponential equation for growth in function with growth factor 'b'in time 't' is given by :-
[tex]y=Ab^x[/tex] , where A is the initial value.
Given : The initial value : [tex]A=\$2000 [/tex]
Growth rate = [tex]b=2\text{ every 9 years} [/tex]
Time periods in 45 years :[tex]t=\dfrac{45}{9}=5[/tex]
Then , the exponential equation for growth for t=5 is given by :-
[tex]y=2000(2)^{5}=64000[/tex]
Hence, the money you would have after 45 years = $64000
PLEASE HELP!!!!!!!!!!!!!! AND THANK YOU :-) 15 POINTS A concession-stand manager buys bottles of water and soda to sell at a football game. The manager needs to buy a total of 4,500 drinks and have 25% more water than soda. Let w be the number of bottles of water and let s be the number of bottles of soda. Create a system of equations for w in terms of s that the manager could use to find out how many bottles of water and soda to buy.
(?) = 4500 (?) (?)
W= (?) (?) (?)
Answer: [tex]w+s=4500[/tex]
[tex] w=1.25s[/tex]
Step-by-step explanation:
Let w be the number of bottles of water and let s be the number of bottles of soda.
Since , the manager needs to buy a total of 4,500 drinks.
Then , we have [tex]w+s=4500[/tex]
Also, the they have 25% more water than soda.
Since 25%=0.25
Then, [tex]w=s+0.25s=s(1.25)[/tex]
[tex]\Rightarrow\ w=1.25s[/tex]
Hence, the system of equations for w in terms of s that the manager could use to find out how many bottles of water and soda to buy.
[tex]w+s=4500[/tex]
[tex] w=1.25s[/tex]
Points J, K, L, and M are midpoints of the sides of the rectangle EFGH. Prove that quadrilateral JKLM is a rhombus by finding the lengths of the sides. The diagram is not drawn to scale.
Quadrilateral JKLM is a rhombus because its sides are all equal in length. By using the midpoints of the rectangle EFGH, we find that JK and LM are both 2a in length, and KL and MJ are both 2b in length, confirming that all four sides are equal.
To prove that quadrilateral JKLM is a rhombus, we find the lengths of its sides.
Since J, K, L, and M are midpoints of the sides of rectangle EFGH, the segments connecting them will be parallel to the sides of EFGH and half the length.
We can use the coordinates of F(-a,b), G(a,b), H(a,-b), and E(-a,-b) to find the lengths:
JK is parallel to EH and GH, so its length is half of EH and GH, and since E and G are on the same vertical line, the length of JK is a - (-a) = 2a.
KL is parallel to EG and FH, so its length is also half of EG and FH, and since E and F are on the same horizontal line, the length of KL is b - (-b) = 2b.
LM is parallel to EH and GH, hence its length is the same as JK which is 2a.
MJ is parallel to EG and FH, hence its length is the same as KL which is 2b.
Given that JK = LM and KL = MJ, and all are equal to 2a or 2b, quadrilateral JKLM has all sides of equal length. Therefore, it is a rhombus.
The probable question may be:
Points J, K, L, and M are midpoints of the sides of the rectangle EFGH. Prove that quadrilateral JKLM is a rhombus by finding the lengths of the sides. The diagram is not drawn to scale.
F(-a,b)
G(a,b)
H(a,-b)
E(-a,-b)
J(-a,0)
K(0,b)
L(a,0)
M(0,-b)
Jaime had $37 in his bank account on Sunday. The table shows his account activity for the next four days. What was the balance in Jaime’s account after his deposit on Thursday?
Jaime’s Bank Acc.
______________________
| Day | Deposit | withdrawal |
| Mon| $17.42 | none |
| Tues| None | -$12.60 |
| Wed| None | -$9.62 |
| Thur| $62.29 | none |
———————————————
A) $57.48
B) $59.65
C) $94.49
D) $138.93
(I would really appreciate
it if someone will help me)
Answer:
Option C. $94.49
Step-by-step explanation:
Jaime had a balance in his bank account on Sunday = $37
The table shows his account activity for the next four days.
From the given table we add all the deposits to his balance and then subtract all the withdrawals.
Balance on Sunday + Deposits
= 37.00 + 17.42 + 62.29 = $ 116.71
Now we subtract all the withdrawals
= 116.71 - (12.60 + 9.62)
= 116.71 - 22.22 = $94.49
The balance would be $94.49 in Jaime's account after his deposit on Thursday.
Kathryn goes out lunch with Mia and Fran. each girl orders the $7 lunch speical. Kathryn agrees to pay the bill. How much will she have to psu?
Planes Q and R are parallel. Lines a and b are shown on planes Q and R, respectively.
Which statement is true about lines a and b?
They are parallel lines.They are perpendicular lines.They are skew lines.They will intersect.The point (-7, -24) is on the terminal ray of angle θ which is in standard position. A student found the six trigonometric values for angle θ. The student’s answers are shown
The student wrongly calculated the value of [tex]\rm tan\theta[/tex], [tex]\rm sin\theta[/tex], [tex]\rm cosec\theta[/tex], and [tex]\rm cot\theta[/tex] and this can be determined by using the Pythagorean theorem and trigonometric functions.
GIven :
The point (-7, -24) is on the terminal ray of angle θ which is in standard position.
To determine the trigonometric function first determine the value of the hypotenuse and to determine the value of the hypotenuse, the Pythagorean theorem can be used.
[tex]\rm H^2 = P^2 + B^2[/tex]
where H is the hypotenuse, B is the base, and P is the perpendicular.
Now, substitute the value of known terms in the above equation.
[tex]\rm H^2 = 7^2+24^2[/tex]
[tex]\rm H^2=49+576[/tex]
[tex]\rm H^2 = 625[/tex]
H = 25
Now, the values of the trigonometric functions are as follows:
[tex]\rm cos\theta=\dfrac{-7}{25}[/tex]
[tex]\rm sin\theta=\dfrac{-24}{25}[/tex]
[tex]\rm tan\theta=\dfrac{24}{7}[/tex]
[tex]\rm cosec\theta=\dfrac{25}{-24}[/tex]
[tex]\rm sec\theta=\dfrac{25}{-7}[/tex]
[tex]\rm cot\theta=\dfrac{7}{24}[/tex]
The student wrongly calculated the value of [tex]\rm tan\theta[/tex], [tex]\rm sin\theta[/tex], [tex]\rm cosec\theta[/tex], and [tex]\rm cot\theta[/tex].
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To find the six trigonometric values for angle θ (-7, -24) on the terminal ray, we can use sine, cosine, tangent, cosecant, secant, and cotangent ratios.
Explanation:The given point (-7, -24) lies on the terminal ray of an angle in standard position, denoted by θ. To find the six trigonometric values for angle θ, we can use the values of the coordinates of the point. The coordinate (-7) represents the x-value (adjacent side) and the coordinate (-24) represents the y-value (opposite side).
We can use the trigonometric ratios: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot), to find the values.
Here, sinθ = y/r = (-24)/7.6, cosθ = x/r = (-7)/7.6, tanθ = y/x = (-24)/(-7), cscθ = 1/sinθ, secθ = 1/cosθ, and cotθ = 1/tanθ. By substituting the respective values, we can find all six trigonometric values.
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Two angles form a complementary pair (sum is 90 degrees) one angle is 3x - 10 and the other angle is x + 8. Write an equation and solve for each angle.
Could somebody help? Thank you :)
The length of a rectangle is four times its width. if the area of the rectangle is 400 yd2 , find its perimeter.
Find the value of angle c?? Please help
Suppose that a compensation professional would like to calculate the median salary. he orders four salaries as follows: $20,000, $22,000, $24,000, $26,000. what is the median salary for this data set?
The median salary for the given data set of four salaries ($20,000, $22,000, $24,000, and $26,000) is calculated by averaging the two middle values ($22,000 and $24,000), resulting in a median of $23,000
To calculate the median salary from an ordered data set, you first need to determine if the number of data points is even or odd. In this scenario, there are four data points: $20,000, $22,000, $24,000, and $26,000. As the number of data values is even, the median is the average of the two middle values.
Steps to Calculate Median Salary
Arrange the salaries in ascending or descending order. This step is already completed, as the salaries are presented in order: $20,000, $22,000, $24,000, $26,000.Find the two middle salaries since the number of data points is even. In the given data set, the two middle salaries are $22,000 and $24,000.Calculate the average of these two middle salaries. Add $22,000 and $24,000 to get $46,000, then divide by 2 to obtain $23,000. This value is the median salary for the data set.Therefore, the median salary for this data set is $23,000
Five less than twice what negative number squared is 157?
Using algebraic equation, the negative number that is squared is: -9.
What is an Algebraic Equation?An algebraic equation can be used to find an unknown value, by making the unknown value the variable.
Let the negative number that would be squared be represented by the variable, x. Thus, we have -x². Therefore:
2x² - 5 = 157
2x² = 157 + 5
2x² = 162
x² = 162/2
x² = 81
x = √81
x = -9
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Using the given information, which lines, if any, can you conclude are parallel? Justify your conclusion with a theorem or postulate.
Which expression represents the phrase, "one third the sum of 12 and a number"?
13(12)+x
13x+12
13+12+x
13(12+x)
Teo makes a necklace of x wooden beads at .50 each and 6 glass beads at 1.25 each. The average cost of the beads in the necklace is .75. What is an equation that will model this solution?
Which inequality best represents that ice cream at −5°C is cooler than ice cream at 4°C?
−4°C > 5°C
4°C < −5°C
−5°C < 4°C
−5°C > 4°C
Answer:
IS D
Step-by-step explanation:
w = 13, x = 9, y = 1.9, z = 0.5 x + 20 – 1
A. 28
B. 19
C. 30
D. 32
The value the given expression x + 20 – 1 is, the solution is A. 28.
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
w = 13, x = 9, y = 1.9, z = 0.5
x + 20 – 1
Since X Is 9 ,
You're Problem Would Now Be
= 9 + 20 - 1
Then You Subtract 20
And 1 Which Will Give You 19
Then , You're Left With 9 + 19
Which Is 28.
Hence, the solution is A. 28.
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If it takes 5 machines 5 minutes to make 5 widgets, how long would it take 100 machines to make 100 widgets?
Tim made a down payment of $1,000. He pays $450 for 36 months. What is the total amount he pays for the car?
Answer:
$ 17,200
Step-by-step explanation:
Given,
The amount of down payment = $ 10000,
Also, monthly payment = $ 450,
Number of months = 36,
So, the total payment ( except down payment ) = number of months × monthly payment
= 36 × 450
= $ 16200,
Hence, the total amount paid for the car = down payment + total payment
= $ 1,000 + $ 16,200
= $ 17,200
Find the turn of sonnet 73. what is its logical relationship to what comes before
Final answer:
The volta in Sonnet 73 is a shift that occurs between lines eight and nine, serving to transition from metaphors of aging to considering their impact on love. This turn is common in sonnets, marking a change in argument or tone.
Explanation:
Finding the Volta in Sonnet 73
The volta, or the turn, in a sonnet marks a shift in thought or argument and is crucial to understanding the poem's structure and meaning. In Sonnet 73, the volta can be identified between lines eight and nine, where the poet moves from reflecting on the images that convey the passage of time and coming to terms with mortality, to directly addressing the beloved and discussing the importance of this realization for their relationship. The logical relationship between the octet (the first eight lines) and the following sestet (the last six lines) in Sonnet 73 is that the octet sets up a series of metaphors about aging and the passage of time, which the sestet then responds to by contemplating the impact of these realizations on love and connection.
The Petrarchan sonnet typically follows a structure with an octave that presents a problem that is resolved or responded to in the following sestet. Although the rhyme scheme might vary, the purpose of the volta remains the same across different sonnets: it signifies a pivot or shift in the argument or mood of the poem.
The reference to Shakespearian and Petrarchan sonnet styles in the question helps us understand that the student likely confuses the structure. Sonnet 73 is a Shakespearian sonnet that consists of three quatrains and a concluding couplet, with the volta being a conceptual rather than structural shift in Shakespeare's sonnets, typically occurring at the start of the third quatrain or the couplet.
The radius of a large sphere is 8 times the radius of a small sphere. the surface area of the large sphere is how many times the surface area of the small sphere?
The large sphere is 64 times the surface area of the small sphere.
What is a sphere?A sphere is a geometrical object that is a three-dimensional analogue to a two-dimensional circle. A sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the centre of the sphere, and r is the sphere's radius.
Given that, the radius of a large sphere is 8 times the radius of a small sphere.
Let the radius of a small sphere be x, then the radius of a large sphere is 8x.
We know that, the surface area of a sphere is 4πr².
Here, surface area of a small sphere = 4πx²
The surface area of a large sphere = 4π(8x)²
= 256πx²
Now, 256πx²/4πx² =64
Therefore, the large sphere is 64 times the surface area of the small sphere.
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is 0.12112111211112 a rational number ?
Answer: The given number is NOT rational.
Step-by-step explanation: We are given to check whether the number 0.12112111211112 . . . a rational number or not.
We know that
if the digits after the decimal in a number are either repeating or terminating, then the number is rational.
The given number is
[tex]x=0.12112111211112 . . .[/tex]
We can see that the digits after the decimal are neither repeating nor terminating.
Therefore, the given number is NOT rational.
Building a is 160160 feet shorter than building
b. the total height of the two buildings is 14801480 feet. find the height of each building
2.1e-10 in standard form?
The value of 2.1e-10 = 0.00000000021
What is exponents?An exponent refers to the number of times a number is multiplied by itself.
Here e is used when the number is too large and small for the calculator.
We know 'e' represent exponents
2.1e-10, represents [tex]2.1* 10^{-10}[/tex]
= 2.1 x [tex]\frac{1}{10^{10}}[/tex]
= 2.1 x [tex]\frac{1}{10000000000}[/tex]
= 0.00000000021
Hence, 2.1e-10 = 0.00000000021
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For the linear equation, x + y - 1 = 0, determine a corresponding value of y for the x-value of -6.
x + y-1 = 0
if x = 6
replace x with 6 to get
6 +y-1 =0
subtract 6 from each side
y-1 =-6
add 1 to each side
y = -5
Scott earns $25 an hour at his job as a landscaper. His boss Danny gives him $10 per day for lunch. Scott works thirty hours per week (He works Monday thru Friday, for six hours each day). An expression for determining how much Scott gets paid per week might be written as follows:
25 h + 10 d
Identify each part of this expression and explain what it represents, and which numbers should be substituted for which variables in order to calculate how much Scott earns per week. Do you think this is the best expression to use for this application? Why or why not?