Let a and b be positive integers. If ax + by = c has an integer solution (x, y), it is necessarily true that ax – by = -4c has am integer solution? Justify vour response.

Q: If a, b, c are integer powers of 2, prove that equation a³ + 64 = c does not have solution,…

A: Step:-1 Statement:-  Given Statement is  a3 +b4 =c5 ----(1) Counter Example:-  Take a=28,  b=26  and…

Q: Solve the equations for x . ax +2x =a x = if a ≠ −2.

A:

Q: + k-a a 거+a a-k

A: Given:   ya=-xk-a+1 To Prove: y=aa-kx+a

Q: If P(z) = z3 + qz – 52 and z =-2 – 3i is one of the solutions of P(z), which of the following is…

A:

Q: If A = (; A-: )-..R. e M2x 2(R), find A" for any positive integer n.

A:

Q: [20] Find the general solutions of 4y" – y = 8et/2 2+ et/2

A:

Q: Let (c1, c2) be a solution of the 2 × 2 system a11x1 + a12x2 = 0 a21x1 + a22x2 = 0 Show that for any…

A:

Q: How many non-negative integer solutions are there to the equation xi + x2 + x3 = 13, if we insist…

A:

Q: How many non-negative integer solutions are there to the equation 21 + x2+ x3 + x4 + æ5 = insist…

A:

Q: How many nonnegative integer solutions are there to the equation Xị + x2 + x3 + x4 + x5 = 40 if we…

A:

Q: a) For what value of k does the equation e2x = ksqrt(x) have exactly one solution?

A: Note: According to Bartleby guidelines; for more than one question asked, only the first one is to…

Q: The set of of solution of x2 - 5x+ 6 0 in Z12 is (a ).{2,3,4} d){2,3,6,11} (b) {2,3} (c) {.2,3,6}

A: Hence option (b) is correct.

Q: How many non-negative integer solutions are there of the equation: x + y + z + w = 15, such that…

A:

Q: The value of x such that 8x + 4, 6x – 2, 2x+7 will be consecutive terms in an AP is

A:

Q: If x, y and z are real numbers and x*y°z0 > 0, which of the following must be positive?

A: Given  x8y9z10>0

Q: Prove that there are no integer solutions to the equation x² = 4y + 3

A: To prove that there are no integer solutions to the equation…

Q: B. Verify if the given values of x are solutions to the equations/ ined 1. 7x + 2 = 9 2. 3x-5 4 srps…

A: 1. 7x+2=92. 3x-5=43. x+8<64. -4x≥15. 3x+1≥7

Q: Given that Xx²=16 Solve for x

A: The given that xx^2 = 16

Q: Verify that x = C1et + C2 is a solution to x′′ − x′ = 0.

A: To Verify that x = C1et + C2 is a solution to x′′ − x′ = 0.

Q: For which values of a does ax = 1 have a solution in Z5?

A:

Q: For any numbers a andb and an even natural number n, show that the equation x" + ax + b = 0, x in R,…

A: Here, to prove this result we have to use Rolles theorem.

Q: Only solve z for both a) & b) on the attached.

A: To compare two proportions, a hypothesis test can be conducted. If there are ,  are the number of…

Q: How many non-negative integer solutions are there to the equation x1 + x2 + x3 = 13, if we insist…

A:

Q: 2 Solve for "x", In(x – 2) = -1 = -1

A: Take both side as the exponential

Q: How many solutions are there to the equation: x1 + x2 + x3 = 19 where 1. x1, x2, x3 are all…

A: As per Bartleby guideline for more than one question asked only first is to be answered please…

Q: Solve the IVP: X' = AX, where -() xw - () 3 -3 1 A = 2 -1 0 1 -1 1 and 7 X(0) 4 3

A:

Q: If a, b, c are integer powers of 2, prove that equation a³ + 64 = c does not have solution,…

A: Given,a,b,c are integers of the form 2k, k∈Na3+b4=c5

Q: Determine the number of integer solutions to the equation below: X1 + x2 + x3 + X4 + x5 = V subject…

A:

Q: Eliminate the arbitrary constant in x^3 - 3yx^2 = c. *

A:

Q: Suppose Ax b has a solution. Explain why the solution is unique precisely when Ax = 0 has only the…

A: To show:   The statement Ax=0 has only the trivial solution.

Q: The product of 2x3 + 3x? +1 and 2x2 + 4 in zs (x]/ is: O None O 5x^2+ 5x +1 O 4x+1 x^2+2

A:

Q: Which of the following is NOT a solution of 35 + 15x = 18r8? O x- V5 O x-1 O x- -V5 O x- 3

A:

Q: If P(2) = z³ – 3z² + qz + 100 and z = 4 + 2i is one of the solutions of P(z), which of the following…

A:

Q: How many integer solutions are there to the equation x+y+z=10 if x, y, and z are all bigger than -2?

A: Given, x+y+z=10 x,y,z>-2

Q: how many integer solutions are there to the equation  X + y + z = 10 for which  a. x,y and z + 10…

A: The positive integers are all the numbers that are greater than 0. The negative integers are the…

Q: How many non-negative integer solutions are there of the equation: x + y + z + w = 15, such that w=5…

A: If we have an equation of the form x⩾a then the variable x can take up any value greater than or…

Q: For which values of a and m does ax = 1 have a solutionin Z m?

A: To find for which values of a and m does ax=1 have a solution in Zm. Zm=0,1,2,....,m-1 when a=0,…

Q: 3 Find the general solution of x = Ax, where A

A: we need to find all eigenvalues and eigenvectors for the coefficient matrix

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

A: Two different proofs are given for the given problem as follows :

Q: The value of x such that 8x+4, 6x-2, 2x +7 will be consecutive terms in an AP is

A: If a, b, c are consecutive terms in an AP then 2b= a + c

Q: Show that if A is singular and Ax = b, b = 0, has one solution, then it has infinitely many.

A: Given: A is singular and Ax = b, b = 0

Q: Find the number of integer solutions of X +x, +x, = 10 subject to the conditions given. a. 저20,%…

A: Integer solution

Q: and (A) (B) = x, = 2x, = 3x, Show that if 8. N N (AB) _ (BC) _ (AC) 1 = y, then the value of neither…

A:

Q: Solve the zeroes of the following: Copy before answe 12:07 .ll? A cdn.kutasoftware.com 1) 3p - 2p-5…

A:

Q: How many non-negative integer solutions are there of the equation: x + y + z + w = 15, such that w =…

A: We need to find the number of non-negative integer solutions are there of the equation: x + y + z +…

Q: How many solutions are there to the equation x1 + x2 + x3 + x4 = 17 where all the x are nonnegative…

A: C320=1140

Q: For which values of a does ax = 1 have a solution inZ6?

A: Z5=0,1,2,3,4,5ax=1If a=0, then 0x=1⇒ No solution.If a=1, then 1x=1⇒One solution,x=1

Q: Which of the following is the solution set of In(5x – 7) < In(2x + 8) (5, 00) (-00, 5] (-00, 5) [5,…

A:

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.