Prove that the set of integers is denumerable Prove that N x N is countable by defining a specific bijection from N x N to N. Prove that a countable union of countable sets is countable Prove that the interval (0, 1) has the same cardinality as the interval (a, b) where a < b

Q: What is the solution for solving for +y?

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Q: b by factory Solve -2 2p²² + p ²²-1 1 = 0 D

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Q: solve for x

A: Solve the equation for x as follows.

Q: Solve a, = 2an-1+ 3an-2 with ao= 1, a,= 6. %3D

A: Given an=2an-1+3an-2 with a0=1, a1=6 We will solve the given recurrence relation.

Q: Solve the equation  Y/5 +9=y/2 +18

A: Given equation =&gt;           Y/5 + 9 = Y/2 + 18    * Bring same terms on same side          Y/5  +…

Q: 4) Solve for x: 3x-24 16 - 3x-12 12 = 3

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Q: X - 2y = 3  3x = 6y + 9 solve by substition

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Q: x+y=3 2x-y=0 solve by substituion

A: Firstly, we find y in term of x from first equation

Q: if mZD = 5x - 39 and E mZA= 2x + 12.

A: Two similar triangles are there in the given diagram. So corresponding angles are equal.

Q: 2 cos (3xtZl) = VZ 0°EX Ę 360 2(05

A: 2cos3x+21=2

Q: Why do we make the equation =0 to begin with?

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Q: Solve x = " 3x X 3x y = 4y + 2z = 4 Y + 2y N = 22 = 2 2=

A: The given problem is to find the solution for the given linear equations.Given linear…

Q: 5) Solve: 2 1n(4 - 3x) + 1 = 7

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Q: 4х +1 Зx + 2х 1 3х +2 | 8 a.

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.