A whole number a is odd if and only if there is a whole number k such that a=2k+1. Use this representation of an odd number to prove that the square of any odd natural number leaves a remainder of 1 when divided by 4

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A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

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A: Follow the procedure given below.

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A: Answering the wrong part only. Given query is to find the time when object reaches the ground.

Q: Use Cramer’s Rule to solve the system x + y = 2 y + z = 2 x + z = 2

A: Use Cramer’s Rule to solve the systemx + y = 2y + z = 2x + z = 2

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Q: 1. If a is a natural number and both 3|a and 2|a, then 12|a.

A: 'a' is a natural number and both 3|a and 2|a, then 12|a

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A: Let's find.

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Q: Worksheet No. 5: Word Problems Involving Linear Inequality Direction: Solve the following word…

A: Total money= 1000 Php  Cost for pizza= 700 Php  Remaining balance= (1000-700)= 300 Php

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Q: So the system by elimination. 5-2x+2y=1a (5x-34=-24

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Q: Use 100 -4 -9 010 1 3 001-6-5

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Q: 10 Show that the function -x+px-g is negative for all real values of x provided that q is greater…

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Q: D. Two 23. How to determine the number of turning points of a given function? A. Same as degree B.…

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Q: Question 8 If E = 2ax + ay - 3az, F = ay - az, and G = 3ax + 5ay + 7az, determine, E - 2F + G. А)…

A: Given that E=2ax+ay-3az,  F= ay-az    and  G=3ax+5ay+7az. We have to determine E-2F+G

Q: 3i10124i51 Evaluate, 5253.1301° -1 1 i -i

A: Let's find.

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Q: Verify that 2, is an eigenvalue of A and that x, is a corresponding eigenvector. 11 = 6, x1 = (1, o,…

A: Thr solution is given in the next step.

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Q: 5. Solve: 4xy2(3x³y – 5xy) = 0, Let y = 2 %3D

A: A detailed solution is given below

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Q: 10. Solve the triangle. B 34.40 C: 4.20 b= 29.50.

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Q: a. Show algebraically that f(x) =2 x| - 9 is an even function. b. Solve the equation algebraically…

A: a) Even Function: A function is even if, f-x=fx for all x.   Given, fx=2x-9 f-x=2-x-9 f(-x)=2|x|-9,…

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Q: Write the equation of the trigonometric graph. try y = x)+ COS 3 5T 37 -1 2 -2 -3 -4 -5 四2

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A: This is a problem related to compound interest. Based on the general formula of compound interest we…

Q: I Simplify each of the following expression. 1. 8! 2. 10! 4. 4!+5!

A: Given :8!10!4!+5!

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Q: Graph-x2-4x + 5. What are the coordinates of the x-intercepts, y-intercept, and th vertex?

A: Axis interception points of -x2-4x+5:  X Intercepts: -5, 0, 1, 0, Y Intercepts: 0, 5Vertex of…