Find the sum of the squares of the solutions of $x^2-13x+4=0$.
Answers
The sum of the squares of the solutions of the mentioned equation is 161.38.
The solution of the given quadratic equations can be calculated through factorization. So, rewriting the equation to factorize it.
x² - 13x + 4 = 0
Based on Dharacharya formula, stated as -
x = - b ± ✓b² - 4ac/ 2a, we get the roots -
x = 12.7 and 0.3
Now, the next formula to solve will be -
x = 12.7² + 0.3²
Taking the square of each number
x = 161.29 + 0.09
Performing addition on Right Hand Side of the equation
x = 161.38
Thus, the required answer is161.38.
Learn more about quadratic equation -
https://brainly.com/question/1214333
#SPJ4
Related Questions
even though emilio writes neatly and legibly, it takes him a very long time to write a few sentences. which strategy may help emilio to write more fluently?
Answers
One strategy that may help Emilio write more fluently is practicing speed writing or shorthand techniques.
Practicing speed writing or shorthand techniques can help Emilio increase his writing speed without sacrificing legibility. Speed writing involves using abbreviations, symbols, and shortcuts to represent words or phrases, allowing for faster transcription of thoughts onto paper.
Shorthand systems, such as Gregg shorthand or Pitman shorthand, provide structured methods for condensing words and phrases into simplified symbols.
By learning and practicing speed writing or shorthand techniques, Emilio can improve his writing efficiency and reduce the time it takes to write a few sentences. This strategy allows him to maintain neatness while increasing his writing speed, enabling him to express his thoughts more fluently.
With regular practice and familiarity, Emilio will become more comfortable with the shorthand system and experience a significant improvement in his writing speed and fluency.
To know more about shorthand, refer here:
https://brainly.com/question/31301365
#SPJ11
how many nonnegative integers can be written of the form a7 * 3^7 a2 * 3^6 where ai {1, 0, -1} amc
Answers
The non negative integers can be written of the form is 3281.
Given:
a7 * 3^7 a2 * 3^6 where ai {1, 0, -1}.
ai = 7,6,5,4,3,2,1,0
Total = 8
= \(3^{8}\) = 6561
= 6561 - 1 /2
= 6560/2
= 3280 is negative integers
Non negative or positive integers = 6561 - 3280 = 3281
Therefore the non negative integers can be written of the form is 3281.
Learn more about the non negative integers here:
https://brainly.com/question/16155009
#SPJ4
find hte volume of revolution when the area enclosed by y= root x, y=0, and x=9 is revolved about the line x=9
Answers
The volume of revolution is 81π/2 cubic units.
To find the volume of revolution, we can use the method of cylindrical shells.
The axis of rotation is x=9, so we need to express the function in terms of x-9. We have y=sqrt(x), so x=y^2. Therefore, x-9 = y^2 - 9.
The limits of integration are 0 and 3 (since y=sqrt(9-x) when x=6, and y=0 when x=9).
The height of each cylindrical shell is the difference between the right and left boundaries, which is 9 - (y^2 - 9) = 18 - y^2.
The radius of each cylindrical shell is simply y.
The volume of each shell is given by:
dV = 2πy(18 - y^2) dy
Integrating from 0 to 3:
V = ∫[0,3] 2πy(18 - y^2) dy
= 2π ∫[0,3] (18y - y^3) dy
= 2π [(9y^2 - (1/4)y^4)]_[0,3]
= 2π (81/4)
= 81π/2
For more such questions on volume:
https://brainly.com/question/6204273
#SPJ11
Point Q(4,-7) after a rotation of 90
degrees counterclockwise about the
origin.
Answers
Which of the following number sequences is the correct output for this "for" loop and "Range" function?
for number in range(99, -1, -11):
99 88 77 66 55 44 33 22 11
99 88 77 66 55 44 33 22 11 0 -11
99 88 77 66 55 44 33 22 11 0
90 80 70 60 50 40 30 20 10 0
Which statement is true regarding a "Fatal" logic error in Python?
In script mode - Python displays a traceback for the error and produces incorrect results
In interactive mode - Python displays a traceback, then terminates the script
In script mode - Python displays a traceback, then terminates the script
In interactive mode - Python terminates the current snippet and does not allow the next input
What is the correct statement regarding Python Indention?
Indenting a code suite is optional in Python
Indentation of code suite can be replaced with Java like braces and parenthesis
Incorrect indentation will result in an "IndentationError"
There are no best practices in regard to the Indentation in Python
Answers
The correct statement regarding Python indentation is that incorrect indentation will result in an "IndentationError."
The correct output for the given "for" loop and "range" function is:
99 88 77 66 55 44 33 22 11 0 -11
Regarding the statement about a "Fatal" logic error in Python, the correct answer is:
In script mode - Python displays a traceback, then terminates the script.
When a fatal logic error occurs in Python during script execution, Python will display a traceback message that provides information about the error, such as the line where it occurred, and then terminates the script. This traceback message helps in debugging the code and identifying the cause of the error.
In interactive mode, if a fatal logic error occurs, Python will also display a traceback message but will not terminate the entire session. Instead, it will allow you to continue entering new commands or snippets of code.
Regarding Python indentation, the correct statement is:
Incorrect indentation will result in an "IndentationError."
Python relies on indentation to define the grouping and structure of code blocks. It uses consistent indentation to determine which lines of code belong to a particular block, such as loops or conditional statements. If the indentation is incorrect or inconsistent, Python will raise an "IndentationError" and the code will not run successfully.
Learn more about Python
https://brainly.com/question/26497128
#SPJ11
The blue dot is at what value on the number line?
Answers
what’s equivalent to six to the negative power of two
Answers
The expression which is equivalent to; six to the negative power of two as given in the task content is; 1 / 36.
Which expression is equivalent to six to the negative power of two?It follows from the task content that the expression which is equivalent to six to the negative power of two is to be determined.
Since the given word phrase can be expressed as; 6^-²; it follows from the laws of indices that we have;
= (1 / 6)²
= 1² / 6²
= 1/36.
Ultimately, the equivalent expression is; 1 / 36.
Read more on equivalent expressions;
https://brainly.com/question/28944114
#SPJ1
Kylie starts with $145 in her piggy bank. Each month she adds $20.
Which recursive function rule models the total amount in Kylie’s piggy bank at the end of each month?
A. an=20⋅an−1 and a1=145
B. an=20+an−1 and a1=145
C. an=145⋅an−1 and a1=20
D. an=145+an−1 and a1=20
Answers
The recursive function model which correctly represents the total in Kylie's Piggy bank after each month is; Choice B; a (n) = 20 + a_(n−1) and a (1) = 145.
Which answer choice correctly represents Kylie's balance after each month?According to the task content; it follows that the recursive function rule which correctly represents Kylie's situation bis to be determined.
Kylie's starts with $145 in her piggy bank; therefore, it can be inferred that; a (1) = 145.
Also, each month, she adds $20.
On this note, since recursive function rules indicate the common difference between each successive term; it follows that the answer choice which correctly represents the recursive model is;
Choice B; a (n) = 20 + a_(n−1) and a (1) = 145.
Read more on recursive function rule;
https://brainly.com/question/25697253
#SPJ1
given the function f(x)=x 2, find the net signed area between f(x) and the x-axis over the interval [−9,5]. do not include any units in your answer.
Answers
Therefore, the net signed area between f(x)=x^2 and the x-axis over the interval [-9,5] is 338/3.
To find the net signed area between f(x)=x^2 and the x-axis over the interval [-9,5], we need to break the interval into two parts since the function changes sign at x=0. First, we need to find the area under the curve from x=-9 to x=0. Using integration, we get the area to be (-1/3)(0-(-9))^3 = 243/3 = 81. This area is negative since the function is below the x-axis. Next, we need to find the area under the curve from x=0 to x=5. Using integration again, we get the area to be (1/3)(5-0)^3 = 125/3. This area is positive since the function is above the x-axis. To find the net signed area, we simply add the two areas together: 81 + 125/3 = 338/3.
To know more about area visit:
https://brainly.com/question/1631786
#SPJ11
The function A(b) relates the area of a trapezoid with a given height of 14 and one base length of 5 with the length of its other base. It takes as input the other base value, and returns as output the area of the trapezoid. A(b)=14xb+5/2 Which equation below represents the inverse function B(a), which takes the trapezoid's area as input and returns as output the length of the other base? A. B(a)+a/7+5 B. B(a)=a/5-7 C. B(a)=a/7-5 D. B(a)=a/5+7
Answers
Answer:
\(b(a) =\frac{a}{7} -5\)
Step-by-step explanation:
Given
\(A(b) = 14 * \frac{b + 5}{2}\)
Required
Determine the inverse function b(a)
Write A(b) as a
\(a = 14 * \frac{b + 5}{2}\)
Swap a and b
\(b = 14 * \frac{a + 5}{2}\)
\(b = 7(a + 5)\)
Divide both sides by 7
\(a + 5 = \frac{b}{7}\)
Maka a the subject
\(a =\frac{b}{7} -5\)
Swap a and b again
\(b =\frac{a}{7} -5\)
Hence:
\(b(a) =\frac{a}{7} -5\)
You are interested in doing a content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers. your unit of analysis is:_______.
Answers
To do content analysis on the characteristics people seek in a partner by examining the personals section of three newspapers the unit of analysis will be objective of the section.
Given that we are interested in doing content analysis on the characteristis people seek in a partner by examining the personals section of three newspaper.
Content analysis is basically a research tool used to determine the presence of certain words, themes,or concepts within some given qualitative data. Using content analysis, a researchers can quantify and analye the presence meanings and relationships of such certain words, themes and concepts.
When we are required to do content analysis by examining the personals section of three newspapers, its units can be objective of section. Some part is related to matrimonials, some are for rent,etc.and some are for commercial advertisements.
Hence the unit of analysis is objective of the section.
Learn more about content analysis at https://brainly.com/question/890849
#SPJ4
Shifting into first gear generally increases the engine speed (rpm) while decreasing the
tractor speed (mph). What would be the effect of this change?
A. Both area rate and flow rate would increase.
B. Area rate would increase, and flow rate would decrease.
C. Area rate would decrease, and flow rate would increase.
D. Both area rate and flow rate would decrease.
Answers
The effect of this change should be option D. Both area rate and flow rate would decrease.
Information regarding speed:In the case when the first gear is shifted so it increased the engine speed. While on the other hand, it reduced the tractor speed. Due to this, the area rate and the flow rate should be decreased.Learn more about the speed here: https://brainly.com/question/24772838
HELP DO NOT KNOW HOW TO DO THIS!!!!!!!
Answers
Answer:
x = 8
Step-by-step explanation:
( 6x + 1 ) + 90 + ( 5x + 1 ) = 180
6x + 1 + 90 + 5x + 1 = 180
11x = 88
x = 8
What is the slope of the line that passes through the points -15,-1 and -5,5
Answers
Ticket to a play cot $4 in advance and $5 at the door. The theater club preident want to raie at leat $400 from the ticket ale. If the club ell 40 ticket in advance, what i the leat number of ticket the club need to ell at the door to reach the preident’ goal?
Answers
the number of tickets sold in advance to the number of tickets needed to be sold at the door is 88 .The club needs to sell at least 160 tickets at the door to reach their goal of $400.
1. Calculate the total amount of money raised from the tickets sold in advance: 40 tickets x $4 = $160
2. Subtract the total amount from the goal of $400: $400 - $160 = $240
3. Calculate the number of tickets needed to be sold at the door to reach the goal: $240 / $5 = 48 tickets
4. Add the number of tickets sold in advance to the number of tickets needed to be sold at the door: 40 + 48 = 88
Therefore, the club needs to sell at least 88 tickets at the door to reach their goal of $400.
Learn more about number here
https://brainly.com/question/10547079
#SPJ4
evaluate the expression for z = -3
-15 -6z = ?
Answers
Answer:
3
Step-by-step explanation:
-15+18=3
:)
Answer:
z=3
Step-by-step explanation:
-15-6(-3)
-15+18
3
B
Th
Note: Figure is not drawn to scale.
If h= 17 units and r= 7 units, then what is the approximate volume of the cone shown above?
168 cubic units
OA.
OB. 277.67π cubic units
OC. 833m cubic units
OD. 674.33r cubic units
Answers
Answer:
277.67pi
Step-by-step explanation:
The formula of volume of a cone is V=π r^2 h/3
So, put the values in
V= PI 7 sqruared 17/3
3.14159*49*17/3
That is equal to
872.32
Then divide by pi and its 277.67Pi
find the variable y=[y1 y2] of the form y=Mx, where M is a matrix so that the differential equation x′=Ax, A=[4414] is diagonal for the variable y. use that this coefficient matrix A has eigenpairs λ1 = 6, v1 = [1 2], and λ2 = 2, v2 = [1 -2]
Answers
The matrix M that satisfies the given conditions is M = [3/2 -5/2; 3/2 5/2].
To find the variable y = [y1 y2] of the form y=Mx, where M is a matrix so that the differential equation x′=Ax, A=[4414] is diagonal for the variable y, given that this coefficient matrix A has eigenpairs λ1 = 6, v1 = [1 2], and λ2 = 2, v2 = [1 -2], we can use the following steps:
Step 1: Write the matrix A in terms of its eigenvectors and eigenvalues. The matrix A can be written as A = PD where D is a diagonal matrix with the eigenvalues on the diagonal and P is a matrix whose columns are the eigenvectors. Thus, we can find the matrices P and D as:
P = [v1 v2] = [1 1 2 -2]D = [λ1 0; 0 λ2] = [6 0; 0 2]
Step 2: Express y in terms of the eigenvectors. Since A and M have the same eigenvectors, we can express y in terms of the eigenvectors as y = Pz where z is a vector of constants. Therefore, we can find z.
Step 3: Express x in terms of the eigenvectors.
Since A is diagonal in the eigenvector basis, we can express x in terms of the eigenvectors as x = Pw where w is a vector of constants. Therefore, we can find w = x/P
Step 4: Express y in terms of x. We know that y = Mx. We can substitute the expressions for y and x in terms of the eigenvectors to get:
Mx = Py = PDz = P[Mz1 Mz2] = [6z1 2z2; 0 2z2]Thus, we can write M = PD = [1 1 2 -2][6 0; 0 2][1/4 1/4 -1/8 -1/8] = [3/2 -5/2; 3/2 5/2]
You can learn more about eigenvalues at: brainly.com/question/29749542
#SPJ11
What expression represents the volume of the prism, in cubic units? one-halfx3 one-halfx2 x 2x3 2x2 x
Answers
Volume of prism = \(\frac{1}{2x^{3} } + x^{2}\)
Given that:
The oblique prism below has an isosceles right triangle base and the length of the base is x
=> the area of the base: \(\frac{1}{2}\) × x × x = \(\frac{1}{2}\)
The vertical height of the prism is (x + 2)
=> The volume of the oblique prism is:
V = the base area * the vertical height
<=> V = \(\frac{1}{2}\) \(x^{2}\) (x + 2)
<=> V = \(\frac{1}{2x^{3} } + x^{2}\)
To learn more about volume of the prism from the given link
https://brainly.com/question/15892907
#SPJ4
Xy^-3
How do you solve this problem
Answers
Answer:
Unknown, Solve for x or y?
Step-by-step explanation:
You need to elaborate on your answer... sorry.
In the meantime, here is Microsoft Math Solver, With your equations:
https://mathsolver.microsoft.com/en/solve-problem/x-y%20%3D%20%203
You can use this tool next time :)
Have a great day,
Nate
What is the diameter of a circle with the equation (x 6)2 (y − 4)2 = 16?.
Answers
The diameter of the circle with the provided equation of circle which has radius 4 units is 2 units long.
What is the equation of circle?The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
\((x-h)^2+(y-k)^2=r^2\)
Here (h,k) is the center of the circle and (r) is the radius of the circle.
The equation given in the problem is
\((x+ 6)^2 +(y - 4)^2 = 16\)
Make it like equation of circle as,
\((x+ 6)^2 +(y - 4)^2 = (4)^2\)
Let's compare it with the equation of circle we get,
\(h=-6\\k=4\\r=4\)
Here, the radius of the circle is 4 units. As the radius of the circle is twice the diameter of the circle. Thus, the Diameter of the circle is,
\(d=\dfrac{4}{2}\\d=2\)
Hence, the diameter of the circle with the provided equation of circle which has radius 4 units is 2 units long.
Learn more about the equation of circle here;
https://brainly.com/question/1506955
Select the correct answer.
Which statement about this system of equations is true?
a. no solution
b. unique solution at (0,0)
c. unique solution at (0,3)
d. infinitely many solutions
Answers
No solution.
When 2 graphs are parallel, there are no solutions.
The scale on a map is 1 : 25000
How many kilometres on the ground is represented by 7 cm on the map?
Answers
Answer:
175000 km
Step-by-step explanation:
the 1:25000 essentially means that every centimeter represents 25000 kilometers. so the answer is 175000 by multiplying 7 and 25000
5.9 inches of snow in 15 hour
Answers
Answer:
I don't think you added your question here. Can you post your question again?
Given the velocity v = ds/dt and the initial position of a body moving along a coordinate line, find the body's position at time t. v = 9.8t + 9, s(0) = 17
Answers
We are given v = ds/dt, v = 9.8t + 9, s(0) = 17. We need to find the position of a body moving along a coordinate line at time t.
Using the formula of velocity, we can integrate it with respect to t to find the position of the body at any time t. The formula for velocity is:v = ds/dt... (1) Integrating equation (1) with respect to t, we get's = ∫vdt + C ...(2)
Here, C is the constant of integration, and it is found using the given initial position. Given, s(0) = 17Substitute s = 17 and t = 0 in equation (2).17 = ∫(9.8t + 9)dt + C [∵ s(0) = 17]17 = 4.9t² + 9t + C
Therefore, C = 17 - 4.9t² - 9tOn substituting the value of C in equation (2), we get:s = ∫vdt + 17 - 4.9t² - 9t ...(3)Now, we can substitute the given velocity, v = 9.8t + 9, in equation (3).s = ∫(9.8t + 9)dt + 17 - 4.9t² - 9ts = 4.9t² + 9t + 17 - 4.9t² - 9ts = 9t + 17
Hence, the position of the body at time t is 9t + 17 units.
Learn more about velocity here.
https://brainly.com/question/30559316
#SPJ11
please i need this anwser the teacher is gonna litterly murder me
Answers
Answer:
65 degrees
Step-by-step explanation:
Answer:
1. obtuse angle 105 degrees
2. acute angle 60 degrees
Step-by-step explanation:
Gabe wanted to put paneling on his living room wall. He knew the wall was 24 feet wide. Each sheet of paneling was 4 feet wide, and cost $12.49. How many sheets of paneling would he need?
Answers
Answer:
74.94
Step-by-step explanation:
As, we will see how many 4 feet panels will cover 24 feet wall
So, 24/4 = 6
So we need 6 panels
So, 6x 12.46 = 74.94
So no. of panels = 6
Total cost: $74.94
In a class of 25 students, 15 of them have a cat, 16 of them have a dog and 3 of them have neither. Find the probabillity that a student chosen at random has both
Answers
9/25
Step-by-step explanation:
students who have either cat or dog =25-3=22
students who have both= 15+16-22= 9
probabillity that a student chosen at random has both= 9/25
The quadratic function f (x) = 3 (x – 4)– 6 was translated 5 units left and and 4 units up. Determine the equation of the
transformed function.
O g(x) = 3 (– 1)? +4
O g(x) = 3 (2 – 9)? +2
O g() = 3 (x + 1)2 – 2
O g(x) = 3 (x – 9)2 – 2
Answers
Answer:
C. g(x) = 3(x + 1)² - 2Step-by-step explanation:
Given function:
f(x) = 3(x - 4)² - 6Translation 5 units left and 4 units up:
g(x) = f(x + 5) + 4Apply the rule to the given function:
g(x) = 3(x + 5 - 4)² - 6 + 4 = 3(x + 1)² - 2Correct choice is C
Translation of 5units left so change in x
y=3(x-4+5)²-6y=3(x+1)²-64units up so change in y.
y=3(x+1)²-6+4y=3(x+1)²-2Option C
Is this the correct answer?
Answers
Answer:
Yes!
Step-by-step explanatio: