Problem 1 The equation &r+ 12r +4x-1 = 0 has roots a, B. Y. Show that the equation with roots 2a + 1, 2B+1, 2y + I is y-y-1 = 0. The sum (2a + 1)" + (2B +1)"+ (2y + 1)" is denoted by S. Find the values of S, and S, -2"

Q: The equation (x-2)(x-4)%3D0 has. negative roots. а. 3 O b. None of these O c. 1 O d. 2

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Q: 5- 4=0

A: 4. xy'+1+xy=e-x Divide by x both side  y'+1+xxy=e-xx Given deferential equation is of the form…

Q: This problem requires that you show all work. There are two solutions to the equation æi – 256 = 0.…

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Q: Question 9 (b) Show that the equation (a) 1.5x – 7x+8.5= 0 has no real roots. (b) 9x +30x+ 25 = 0…

A: Answer and explanation is given below...

Q: Find the value/s of k in the given equation in order to have two distinct imaginary roots: 2x2 + 4x…

A: 2x2+4x-k=0 Given : the equation has two distinct imaginary root  When the roots are imaginary then…

Q: Problem #2 Consider the equation f(x) = -26 + 85x - 91x2+ 44x- 8x*+ x°. Use bisection to determine…

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Q: Problem 3 Given non-zero integers a, b and c, let a and B be the solutions of the general quadratic…

A: Let p and q are two roots of a quadratic equation ax2+bx+c=0 Then  Sum of the roots, p+q= - b/a…

Q: Question 8: If – 9 is a root of the 3 7 equation 2 7 6 2 = 0 = 0, then the other two roots are

A: Introduction :

Q: Question 4 Solve the equation. -15y + 75y = -y + 125 O y = 25 Oy = 5 O y - 5 and y =-5

A: Let's solve your equation…

Q: Problem 1.6 Prove that there are no solutions in integers x and y to the equation 2x² + 5y² = 14.

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Q: Problem 1: (a) Show that if z is a fifth root of unity (meaning a solution to z° = 1) then 23 = 2.…

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Q: A student was solving the following problem. 81**2 -273 Step 1: (3*)*- = (3')* Step 2: 3**2 = 3 %3D…

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Q: Problem 7 Using the method of undetermined coefficients, find a particular solution yp of the…

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Q: Problem 6 Find the solution(s) to each equation. 1. x2 – 6x + 8 = 0 2. x2 – 6x + 9 = 0 3. x2 – 6x +…

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Q: PROBLEMS 2.5 1. Which of the following Diophantine equations cannot be solved? (a) 6x + 51y = 22.…

A: By finding GCD and using extended Euclidean algorithm you can solve the problems as follows :

Q: Question 3 3.1 Solve simultaneously for x and y xy = 9 and 25x - 2y-3 = 0 %3D 3.2 3.2.1 Solve for p…

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Q: Problem 1. Consider the non-linear equation x³ + 2x = 1. (a) Find an interval that covers one root…

A: Intermediate value theorem: This theorem states that for a continuous function f there exists…

Q: K 12. Problem 54. Find a number such that if 7 is added to it and the sum multiplied by the root of…

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Q: If 7, r, and r, are the roots of equation x-2x+3=0, then findErr,. إختر أحد الخيارات: -2 a O .b O…

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Q: The second-order equation Yk+2 Yk+1 – k²yk = 0 (3.159) can be written in the following factored…

A: Given difference equation is  yk+2-yk+1-k2yk=0                               (i) The factored form…

Q: Question No.5 Find the particular solution of 9 - 12+ 4y = 3x- 1 given that when x-0, y=0 and

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Q: Which of the following most nearly gives the value of [A]¯1 for the following equations? x +y - z =…

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Q: Question 4 Using the method of undetermined coefficients, find the particular solution y, for the…

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Q: Question 1. Show that in S7, the equation x² = (1234) has no solutions.

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Q: Problem A.4 Find all solutions of the following equation: 0 1 1 2 1 2 3 4 20 20 -4

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Q: Question 17 Solve the following equation. If the solution is extraneous, please say so. V3n 4. %3D -

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Q: Question 13 Solve: 7m + 11 – 5m – 2 = 2m – 9 - O m = 7 O m3D =D3 O Infinitely Many Solutions O No…

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Q: Find an equation whose roots are the 3 times the reciprocal of the roots of 6x-4x +3x-4 0. 6y' -4y?…

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Q: If a, B,y are the roots of x+4x+1 = 0 then the equationm whose roots are B+y'y+a'a +3

A: The given equation is x3+4x+1=0. The given roots are α, β, γ. Observe the following.…

Q: QUESTION 3 Use the Quadratic formula to find TWO solutions to 2x2+4x – 11=0. Select them from the…

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Q: PROBLEM NO. 11 Given: x-64-0 Find the secondary root. A) 1 + 1.732/ B)-1 + 1.732j C) 1-1.732j…

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Q: Problem No.4 show that A3 - 2A? - 9A = 0 but A? - 2A - 9I# 0 2 1 3 A= 1 -1 2 1 2 1 If

A: To show that A³ - 2A² -9A =0 but A² - 2A - 9A € 0

Q: Problem 7. When you solve the equation -3z + 2z = 0, how many roots are greater than D three roots…

A: To find the roots

Q: 1. Solve the exact equation: (20 points) (3y² + 2x }kx + (4y² + 6xyk$y =0 - 6xy kty = 0

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Q: Problem 2 a) Given the second order equation y" + 2ay + (a2 +b)y=0, %3D where a andb are real…

A: As per our guidelines I am solving only 1st for second kindly resubmit the question mentioning that…

Q: Problem 1. Consider the non-linear equation x + 2x = 1. (a) Find an interval that covers one root of…

A: The given non-linear equation is  x3+2x=1 (a) To find the interval which covers the root of the…

Q: If p, q e {1, 2, 3, 4}, the number of equations of the form px? + qx + 1 = 0 having real roots is

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Q: 1. Use the graph of y = VI to estimate the solution(s) to the following equations YA -150 -120 -90…

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Q: 3.9 Suppose z = x/2y/4 and y = 2x. Find x and y in terms of z

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Q: Question 6 The roots of the equation 2x2 + 7x - 3 = 0 are A - and -3 -7+ V73 B and 3 7 + V73 D 4

A: Given: 2x3+7x-3 = 0 To find: The roots of the equation.

Q: PROBLEM NO. 11 Given: x-64=0 Find the secondary root. A) 1 + 1.732j B) -1 + 1.732j C) 1 - 1.732j D)…

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Q: Question 1 5 pts Solve using Elimination. SHOW ALL WORK! (no work= no credit) x - 2y+4z = 6 x+y+13z=…

A: Since you have posted more than one question  we have solved the first question for you.  For…

Q: QUESTION 15 Solve for y. 7y -2= 2 V+9 V +9

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Q: Question 11 A quadratic equation x²-4x+4-0 is defined with an initial guess of 2 and 2.5. Find the…

A: The given quadratic equation is x2-4x+4=0 with an initial guess of 2 and 2.5. The formula for the…

Q: Problem 1 Identify all values of z that make the equation true or write "no solution". 2. 2r+1 3. -…

A: We are solving the first question of all subparts. Kindly repost the other question inthe next…

Q: Given m2 - 8m + 15 = 0 then the roots of the equation %3D | O m = -5 (or) m= 3. O None of these m…

A: Given quadratic equation is: m2-8m+15=0 Roots of any quadratic equation of the form ax2+bx+c=0; a≠0…

Q: 3 The roots of the equation x -4x+ 9 = 0 ar 1) 2+1/5 2)2t/5 3) 2+1/13 4) 2t 13

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Q: Question 13 of 15 Solve for y. 24 = 2y + 4y Simplify your answer as much as possible.

A: Given:- 24=2y+4y To find:- Solve given equation for y

Q: If the auxiliary roots of a certain HLDE with constant coefficients are 2, -3, and -3, then the…

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.