13: Factor out, relative to the integers 2 1) 3 y - 8 y - 3 4) 6 x ? + 48 x 72 2) 4x2 - 20x + 25 3) 9 x 2 - 4 5) 4u ³v - uv 3 6) 8x' - 125

Q: 7 8. The sum of two consecutive even integers is of their product. Find these integers. 24

A: Topic- basic maths

Q: Find a general integer solution of the equation 198x + 288y + 512z = gcd(198,288,512)

A:

Q: How many independent variables are there in a 10 x 2 x 6 x 2 factorial design?

A: Independent variables in 10×2×6×2.

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A:

Q: The sum of any two integers of the from 4k+ is always: a) prime b) zero c) Even

A:

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Q: 1) Use the chain rulc to find the deriva five of fcx) = 4(-3x6+7x5)7 You do not necd to expand…

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Q: 1. Find the 5roots of z1 = -V3+iv3. %3D

A: (As per bartleby guidelines, for multiple questions asked, only the first question will be solved.…

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A: We have to check whether there exist n such that if n is divided by 5 then remainder is 2. Let if n…

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A: Pigeonhole Principle- If n items are assigned to m containers, and m<n,then at least one…

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Q: Show by mathematical l Induction y 4n-2 3. +17 can be divided by +22 possitive integers 16 far all

A: To prove the given statement by using mathematical induction.

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A:

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A: Solution: let suppose the board is a 3 × 7 rectangle.

Q: 16. As a generalized interpolation problem, find the quadratic polynomial q(x) for which q(0) = -1,…

A: let the polynomial q(x)=ax2+bx+c q'(x)=2ax+b since q(0)=-1(given) a(0)+b(0)+c=-1⇒c=-1

Q: 18. (a) Show that of all the rectangles with a given area, the one with smallest perimeter is a…

A: Here is the solution

Q: What is the greatest common factor of 5x^75x75, x, start superscript, 7, end superscript,…

A: The given polynomials are: 5x7 ,   30x4 ,   10x3

Q: How many integer solutions are there to x1+ x2 + x3 = 0  with Xi >= -5 ?

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Q: Show that there are infinitely many examples of two consecutive positive integers that cannot be…

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Q: How many integer solutions to x1 + x2 + x3 + x4 = 32 are there for which x1≥6, x2 ≥5, x3 ≥3 and x4…

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Q: Prove: The product of 2 numbers is equal to the product of their least common multiple and their…

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Q: Are the rest of division of Euclidean method to give the GCD(351,231): o 351, 231, 120, 111, 9, 0 o…

A: GCD = Greatest common division

Q: if two even integers are multiflied, then the product is also even

A: Ans. True

Q: 15. Find the general solution of dr bcosedr + rsinode

A: General solution of differential equation

Q: Show that 2 + V5 is irrational number

A: To prove that 2+53 is irrational number. (It is evident that 2 is irrational, but here providing its…

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Q: What two positive real numbers whose product is 11 & have the smallest possible​ sum?

A:

Q: Choose two distinct integers, x and y, between 0 and 9. Derive the number of 9- digit integers that…

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Q: What two positive real numbers whose product is 50 have the smallest possible sum?

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Q: Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width,…

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Q: 6. Determine. 2r - 3x 4x SET A.

A: I have stated the used formula in the solution

Q: 7. How many integer solutions are there to 2r, + 2tz + 2rz + Xg +X5 = 9 with x; 2 0? (Hint: break…

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A: Let us determine whether the statement is TRUE or FALSE in the next step.

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Q: 2. Find two nonnegative numbers whose sum is 2022 and whose sum of squares is as large as possible

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Q: List the sides of AFGH in order from least to greates if mZF=(5x+6)°, mZG=(12x-4)°, and m…

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Q: How many integer solutions are there to 1 +X2+X3+X4+Xs=31 with

A: Given, x1+x2+x3+x4+x5=31 Number of Solutions when xi≥0 and xi>0.

Q: 2 4-x2 x2 +4 1 2x

A:

Q: the acdjainbaf square of As of 2.

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A: Before we begin proving the statement, we shall understand the shapes. An L-shaped three-square tile…