Please answer fast I'll rate 1. Use direct proof to prove the following:(a) If a is odd, then 2² is odd.(b) Let x and y be positive numbers. If r ≤y then √ √y(c) If z and y are positive real numbers then 2√xy ≤ x + y(d) If n € N, then 1+ (-1)" (2n-1) is a multiple of 42. Prove the following by counter example:(a) Vn € Z if n is odd. then n² +n is even.(b) The difference of any two rational numbers is rational.(c) The average of any two rational numbers is rational.

Answered: Image /qna-images/answer/8fea0a7e-1090-4239-9fae-48f38c2c9f64.jpg

Ifr is odd, then 2² is odd. If Let z and y be positive numbers. If x ≤y then √√√ and y are positive real numbers then 2√ry ≤a+y N, then 1+ (-1)" (2n-1) is a multiple of 4 I If n the following by counter example: ne Z if n is odd. then n² +n is even.

Ifr is odd, then 2² is odd. If Let z and y be positive numbers. If x ≤y then √√√ and y are positive real numbers then 2√ry ≤a+y N, then 1+ (-1)" (2n-1) is a multiple of 4 I If n the following by counter example: ne Z if n is odd. then n² +n is even.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.3: Quadratic Equations

Problem 82E

See similar textbooks

Related questions

Q: 68. A jeep and a pickup truck enter a highway running east-west at the same exit heading in opposite…

A: Let speed of jeep = j speed of pick up = p j = p - 7 Jeep entered 30 minutes before Time…

Q: The behavior of objects falling near Earth's surface depends on the mass of Earth. On Mars, a much…

Q: Assume that A is a matrix with three rows. Find the matrix B such that BA gives the matrix resulting…

A: NOTE: Refresh your page if you can't see any equations. . the 3*3 elementary matrix is given by

Q: The functions f and g are defined as f(x) = 5x +3 and g(x)=1-10x. f a) Find the domain of f, g, f+g,…

Q: 64. A moving company charges a flat rate of $150, and an additional $5 for each box. If a taxi…

Q: Rewrite using a single positive exponen 4 4 -2 7

Q: The sum of the squares of the eigenvalues of the following matrix [4] OA. 12 OB. 36 OC. 2 O D. 3 OE.…

Q: The following table shows the average yearly tuition and required fees, in dollars, charged by…

Q: An object is thrown upward at a speed of 79 feet per second by a machine from a height of 18 feet…

Q: Let b = (2, 1, 3). Find the point p on the plane 3x − y + 2z = 2 that is closest to b.

A: Letx1,y1,z1 be point p on the plane that is closest to b

Q: Determine if the set S = 0 4 3 6 is linearly independent.

Q: a) g'(x) = b) g(1) = c) g(5) =

Q: If data are evenly spaced, we need only calculate differences to see whether the data are linear.…

Q: The data in the table below are not linear, but if we omit the first point, the remaining data are…

Q: 2. f(x): x+1 x²-6x+5

Q: Subtracting Fra value of each express 5. (7)/(2)-(4)/(3)

Q: A machine is now worth $144,400 and will be depreciated linearly over a 5-year period, at which time…

A: We can solve this as follows:

Q: Part II-Graph the function, be sure to pass through x and y intercepts where possible. 4. f(x)==…

A: 4). The given function is: fx=3x-105 Graph the function.

Q: The difference of two numbers is 6. Their sum is 14. What is the bigger number?

A: NOTE: Refresh your page if you can't see any equations. . x=bigger number y=smaller number and the…

Q: Manuel is taking out an amortized loan for $28,000 to buy a new car and is deciding between the…

Q: 40-m=11

A: Given 40-m= 11

Q: Use properties of logarithms to expand the logarithmic expression as much as possible. Where…

A: A detailed solution is given below.

Q: Find a matrix A such that A 1 ГОТ A = 13 5 A 4

Q: Question 6 of 17 A county has constructed a conical building to store sand. The cone has a height of…

Q: 3. Is the picture being reflected in the y-axis or x-axis? F(4,1) G (2,2) X (3,3)

A: Question no. 3,Given, The figure is shown below : To find : Is the picture…

Q: A 100kg bag contains peanuts and almonds Peanuts are priced at $2 per kg and almonds are priced at…

Q: x-1 20. f(x)= x²-1 --6-5 -1 2 Xx Domain: Vertical Asymptote:_ Horizontal Asymptote:_ Oblique…

Q: Use Mathematical Induction to prove that n³ - 7n + 3 1. is a multiple of 4 for all positive…

Q: Describe the end behavior of each polynomial. (a) y=x³6x² + 5x - 15 End behavior: y y → (b) y = -5x…

Q: For the function f(x)=x²-8, construct and simplify the difference quotient f(x +h)-f(x) h

A: The given function fx=x2-8. We have to find the difference quotient fx+h-fxh.

Q: The chart to the right shows a country's annual egg production. Model the data in the chart with a…

Q: Find the size of the matrix. Identify a square, column, or row matrix. Give the additive inverse of…

Q: The charge to rent a trailer is $15 for up to 2 hours plus $7 per additional hour or portion of an…

Q: Which of the following is the definition of FC OVx(x EG → x = F) OVx(xEFA x G) OVx(x E F → x G)…

Q: 6. Evaluate the following limits: (a) 18 lim lim ¹-1. z+2i (b)(2 pts.) lim lim -3:² (c) pts) lim Co…

A: NOTE: Refresh your page if you can't see any equations. . multiply and divide by i

Q: MULTIPLE CHOICE The function y = 5x + 40 represents the weight (in pounds) of a container containing…

Q: A salesman drives from Ajax to Barrington, a distance of 114miles, at a steady speed. He increase la…

A: The given data is: The distance between Ajax to Barrington is d1=114 miles the distance between…

Q: (b) f(x) = f-¹(x) -52+9 -6x1 9+x 6x-5

Q: Nadia deposits $125 at the end of every three months into an account that earns 2.93% compounded…

A: NOTE: Refresh your page if you can't see any equations. . here we have PMT=125 n=4 for quarterly…

Q: - C6-37) (627) > CG+37) -4×CG+37) (6-3√7)(6+3√7) -24-12√7 6x6-3v7x3v7

Q: Recall that the following notation P(S) stands for "the power set of S". The sets A and B are…

Q: Find the smallest integer x for which (x4 + 4x)/(x + 2) is O(xx). 01 02

Q: Use synthetic division and the Remainder Theorem to evaluate P(c). P(x) = 3x² + 14x + 3, C = -3…

A: Given:- P(x) =3x2+14x+3

Q: find four consecutive integers whose sum is 406

A: This is question of algebra here we have to find 4 term whose sum is 406 further calculation is…

Q: Find the equilibrium quantity and equilibrium price for the commodity whose supply and demand…

Q: Y=x-14; y=-4x+16 solve system by substitution check your solution for at least two questions

Q: Graph and analyze the function f(x) = 2(x-1)^2. A.) Use the graph provided below to graph f(x).…

A: We will find the required.

Q: Question 8 y = 4 3 2- 1 -4 -3 -2 -1 -1 -2 -3 -4 my < Complete an equation for the function graphed…

A: Given query is to find the equation of the function.

Q: For the piecewise function, find the values g( – 6), g(1), and g(8). x+6, for x ≤ 1 3-x, for x> 1…

Q: Given the functions: f(x) = −5x g(x) = 3x + 7 h(x) = 18x² + 33x – 21 Determine each of the…

Question

Please answer fast I'll rate

1. Use direct proof to prove the following:
(a) If a is odd, then 2² is odd.
(b) Let x and y be positive numbers. If r ≤y then √ √y
(c) If z and y are positive real numbers then 2√xy ≤ x + y
(d) If n € N, then 1+ (-1)" (2n-1) is a multiple of 4
2. Prove the following by counter example:
(a) Vn € Z if n is odd. then n² +n is even.
(b) The difference of any two rational numbers is rational.
(c) The average of any two rational numbers is rational.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here