th 6) Let t, be the k" triangular number. Prove that t, + 4 k + 10 is k k also triangular.

Q: 7) Prove that for every natural number n, the cartesian product of n copies of IN is countables

A: To prove that the cartesian product of n copies of the set of natural numbers, IN, is countable for…

Q: The area of the triangle with vertices V141 P (1, 5, 2), Q (0, 0, 0), R (3, 5, 1) is

A: Here, PQ = <-1, -5, -2> and QR = <3, 5, 1>. Now,         -1-5-2×351=-5· 1--2· 5-2· 3--1·…

Q: sing direct proof, prove the following statements: 1. Prove: If x2-4=0, then x = 2 or x = -2. 2. If…

A: follow next step

Q: a.Given an integer a, then a² + 4a + 5 is odd if and only if a is even. b. There exists a positive…

A: Since you have posted multiple subpart questions, we will solve the first three questions for you.…

Q: Find the oidered pair that is a member of both -2x+3y=19 and 2x+5y=53 or indicate if it does not…

A: We need to find ordered pair that is member of both given lines.

Q: 1. (2ab)3 Ob) 2ab3 Oa) 8a3b3 O d) 6ab O ) 6a b3 Simplify:(x*Xx?) 2. O b) x6 O a) x5 O d) x1.5 O C) X

A:

Q: #5 Let x, y, z be nonnegative real numbers such that y + z> 2. Prove that (x + y + z) >4x + 4yz.

A:

Q: 14 Find the range of values of x for which:(x- 3)(x + 4)(x + 6) < 0. .

A: The given inequality is, x-3x+4x+6≤0 To find the range of the values of x. Since the given values is…