Let x, y € Z. Prove that if 2 | (x² - y2) then 4 | (x² - y²)

Q: Let u = (2,6, 4) and 7 = (-1, -2, - 7). Compute the following: ū. v = vu - ||||²

A: Since you have asked a question with multiple parts in a single request we would be answering only…

Q: 2. Let f(x) = x - 5 and g(x) = x² +3x. a) Find (f + g)(x) b) Find (f – g)(x) c) Find (f g)(x) d)…

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Q: Determine integers x and y such that (а) gcd(51, 288) — 51х + 288у (b) gcd(357, 629) = 357x + 629y

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Q: 13. Find the intersection of [x, y, z)=[-8,-3,-5]+[1,2,-1] and [x. v.]=[1.9,4]+s[2,1,7].

A: We can find the intersection of the curve .

Q: Let a0, a1, a2, a3, a4 be constant real numbers such thata0/5 + a1/4 + a2/3 + a3/2 + a4 = 0.Show…

A: Consider−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−f(x)=5a0​x5​+4a1​x4​+3a2​x3​+2a3​x2​+a4​x.with  input from…

Q: Let →u=⟨6,−4,−6⟩ and →v=⟨−5,−3,−6⟩. Compute the following:

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Q: Let Q(x, y) be the statement "x + y = x – y." If the domain for both variables consists of all…

A: Given that Q(x, y) be the statement                         x + y = x -y .

Q: Let a, b, c and d be distinct real numbers. Show that the equation (x – b) (x – c)(x - d) + (x –…

A: Rolle's theorem:-

Q: Prove that: (5a + 6b|a, b = Z} = Z

A: To prove that .Concepts used:Consider two sets  and . To prove that , we first need to show and…

Q: Suppose that the translation T is described by (?,?)→(?+2,?−1)(x,y)→(x+2,y−1). What translation…

A: We have to find the translation described in x,y→x+2,y-1.

Q: (1) If R and S are surjective, then so is S composed with R.  (2) If S composed with R is…

A: (1) we have givenR : A → B is surjective. Thus, for any r ∈ B, there exists a t ∈ A such that R(t) =…

Q: 9. Write each quadratic relation in standard form, then find the zeros. a) y = 2(x + 1)² - 50 b)…

A: Given :(a) y=2x+12-50(b)  y=-3x-12+48

Q: Show that <a, b | a5 = b2 = e, ba = a2b> is isomorphic to Z2.

A: To show that the group <a, b | a^5 = b^2 = e, ba = a^2b> is isomorphic to Z2, we need to…

Q: Show that is isomorphic to Z2.

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Q: 2. (6 marks) Let a, b, c € Z with a 0. Prove that if a X (a + 2b + 3c), then a Xb or a Xc.

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Q: Let U = N, A = {1, 3, 5}, B = {x : x² - 6x + 5 = 0}, and D = {x:x>5}. Find a. D' b. D-A c. P(A)

A: Note:-Since you asked multiple subparts,according to our policy we can solve only first three sub…

Q: Let x) 4 and gx)-x-3. Find the foilowing lock

A: To find the following expressions

Q: 4 3 Find all zeros of f(x) = x + 6x° + 9x² + 14x – 30. Ente Preview

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Q: Let u = Compute the following: ū• v = (1, −5, −1) and v = (-5,2,0). v.u ||ū|| ² - 3 (u.v) (-3ū) v =…

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Q: Suppose x,y and z are positive real numbers. Prove that x+z/y+z>xy if and only if x<y.

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Q: Give all of the zeros of P(x)=x^2+4 as a comma separated list.

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Q: Show that S = {x* + 1, xª + x, xª + a², xª + æ*, xª} spans PA.

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Q: 4. What is the value of d in f (x) = 2x3 – 7x + d such that x + 2 is a factor of f (x). a) 1 b) 2 c)…

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Q: Show that (a + b)x = ax + bx for all a, b E F and all x € F¹.

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