an is an even number, show that a2 = 0 (mod 4), and if an is an odd number, show that a2 = 1 (mod 4)? %3D

Q: If a number is an element of the set of real numbers, which of the following statements must also be…

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Q: Verify that 1; is an eigenvalue of A and that x; is a corresponding eigenvector. 7 A = d1 = 7, x1 =…

A: The given matrix is;  A= 7 0      0 -7.

Q: Given the arithmetic sequence: -16, -22, -28, -34, .. A) Find the formula for the nth term, an B)…

A: A detailed solution is given below

Q: The deer population in a certain area increases at a rate of 2.2% per year. There are 2,143 deer in…

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Q: Let B be the basis of P, consisting of the three Laguerre polynomials 1, 1-t, and 2- 4t + t, and let…

A: Find your answer below

Q: Can you show it the "'short" way without using Pascal's method?

A: Given expression is: x-12x-24 We try to simplify it first: x-12x-24=x-12x-14=x-1·24·x-14=16x-15

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A: We can solve this as follows:

Q: B, Determine if the following compound propositions is a TAUTOLOGY, CONTRADICTION, or CONTINGENCY 1.…

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Q: Solve the following Initial Value Problem using Laplace transform: y" – 15y + 14y= e" -10t y(0) = 1,…

A: We are given that;y''-15y'+14y =e-10t; y(0)=y'(0)=1Taking laplace transforms on both the sides;s2…

Q: Given the system of equations: axtby+cz =1 extdy+fz=-2 9x+2y+-17z=0 and considering that the…

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Q: If BC =BD then c c D If AB= BA and A then A? B =BA -I is in lertible

A: True / False problem.

Q: Let f(x) = (8x^ - 3)² and g(x) = 8xª - 3. Given that f(x) = (h ° s)(x), find h(x). Enter the correct…

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Q: A student's statistics test is 18 questions and worth 30% of their overall grade. The student is…

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Q: Find a subset of the vectors v1=(1,−2,1,−1), v2=(0,1,2,−1), v3=(0,1,2,−1) and v4=(0,−1,−2,1)that…

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Q: 7. x2-x-42 = 0 %3D

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Q: The face value of a 97-day Treasury bill is $30,000. The interest rate is 2.96%. The purchaser buys…

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Q: The two triangles below are similar. Also, mz Y=30° and mzX=95° as shown below. Find mz C, m z D,…

A: topic - similar triangles

Q: Evaluate L{- }. (s² + 81) (8 – 8)

A: First I have made the partial fraction and then by taking inverse Laplace transform find its Laplace…

Q: x² - 9x + 14 = 0

A: Since you have asked question 1,

Q: The complex number z is defined by z = 3 -z+4-j where z is real. a) Find, in terms of z, the real…

A: I have appended the formula used in the solution part

Q: Each of the following functions a (f of-')(x) = x, find the inverse (i) f(r) = 1- x

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: I. Find the Laplace transform of each of the following functions and simplify the result. Apply the…

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Q: Solve A x A T matrix: A = -2  1  -1 3   -3   2

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Q: The graph of g(x) is obtained by applying the following transformations to the graph of f(z) in the…

A: Let the function be fx then some of graphical transformation rules will be defined as following 1)…

Q: 1. Classify each of the following relations as linear, quadratic, or exponential. a) b) c) d) e) f)…

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Q: Given the function g(x) = – 2x* + 7x" +x2 + r - There are at most x-intercepts, and based on the…

A: For a polynomial P(x) of degree 'n' 1. The maximum number of x-intercepts is given by 'n' 2. The…

Q: (3r-31)

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Q: %10% hemakes. Compounded Semiannualy; Assuming no payments, how much Will he owe in 5 years? い Dpp…

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Q: AE and DE intersect at E. 2. Given: AE Prove: * BE = = DE CE

A: Given, AE and DE intersect at E.

Q: Lesson 11 Practice Problems 1. Select all expressions that are equal to log, 8. A. logs 20 B. logs…

A: Solving the problem by finding the value.   NOTE :: As per our Expert guidelines we are supposed to…

Q: f(x)=x^4+3x^3-45x^2-175x  What is the factored form of the polynomial

A: We can factorise the  given polynomial by splitting the second and the third terms.

Q: Use the quadratic formula to solve the equation. (All solutions for the equation are real numbers.)…

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Q: Find a basis for the eigenspace corresponding to the eigenvalue. 1 -6 A = - 4 2 =9 6. ... A basis…

A: Matrix

Q: Find the equilibrium point of the demand and supply equations. Demand Supply p = 470 – 0.5x p = 338…

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Q: Below are two triangles with their side lengths shown. Answer the questions about each triangle. 16…

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Q: At a diner breakfast buffet, Diana counts 18 oranges, 5 bananas, 3 mangos, and 8 watermelon slices.…

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Q: Find the Arithmetic Series. 19, an = 309, 1 n 30

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Q: Calculate the simple interest rate. (Round your answer to one decimal place.) P = $1800, I =…

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Q: Consider the graph of the function f(x) = x*. Which change in the function rule will translate f (x)…

A: topic- transformationof a function

Q: Verify that A; is an eigenvalue of A and that x; is a corresponding eigenvector. 11 = 9, x1 = (1, 0)…

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Q: A. Construct the TRUTH TABLE for the following compound propositions p(~ p) 2. (pV q) — р (p ^ g)^ ~…

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Q: What happens to the function f (x) = x² when it becomes f'(x) = x² – 3? It moves 3 units to the…

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Q: Determine whether 2; is an eigenvalue of A with the corresponding eigenvector x;. 4 A = 0 - 5 (a) 11…

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Q: -1 with a =-1, b =8, c =12, and d =7. Find the d [3 b a Let A : and B 7 difference between the (1,2)…

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Q: I. Find the Laplace transform of each of the following functions and simplify the result. Apply the…

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Q: ections: Evaluate the derivatives of the following functions with respect to x and simplify the ults

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Q: y -5 -1 -1 3 1 2 11 Function 3 Function 4 y=-3x+ 5 The slope is - 5 and the y-intercept is - 4. rer…

A: 7

Q: Given the geometric sequence: -4, -2, -1, -1/2, .. A) Find the formula for the nth term, an B) Find…

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Q: Prove the following identities: sin? 0 - cos? 0 b) tan 0-1=- sin O cos0+ 0 cos²

A: We can prove the following as below.

Q: Given a6 4096 and ag 262144,

A: