Express the following statement using O-notation: 12.a5 (3x + 4) < 36 |a*| for all real numbers x > 2. x + 2

Q: Determine whether the following equality is true or false. 2-x2 D -1 x where D = {(x,y)| xr² + y²…

A: ∫∫Df(x,y) dA = ∫x1x2∫y1y2 f(x,y) dy dx.

Q: Do not use a calculator in this question. V8 V7- V5 (a) Express in the form va+vb, where a and b are…

A: (a) We will express 87-5 in the form a+b, where a and b are integers

Q: Write the following in interval notation. The set of all real numbers greater than or equal to 4 and…

A: The set of all real numbers greater than or equal to 4 and less than 8

Q: Show by contraposition that for any real number x if - 5 < x< 4 then x2+x – 20 < 0

A: For the solution follow the next step.

Q: Show that √2 + √3 is irrational.

A:

Q: TRUE OR FALSE  x and y are POSITIVE integers.

A:

Q: Express the following statement using O-notation: 12.5 (3x + 4) 2. x + 2

A: Given, x5≤12x53x+4x+2≤36x5 Comparing the given expression by, Axn≤fx≤Bxn

Q: Declare x as an integer From all x from -5 to 2 Print 9x -7

A:

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: Express the following statement using N-notation.: 12 (3x + 4) for all real numbers x > 2. x + 2

A: Consider the given statement.

Q: Express the following statement using O-notation: |125 (3x + 4) 2. x + 2

A:

Q: show that (ex1 )^x2 = e^(x1 x2) = (ex2)^(x1 ) for any numbers x1 and x2.

A: In order to prove the equations:

Q: Let, a, = 3, a2= 4 and for n2 3, a,= 2an-1+ an-2, express a, in terms of n. %3D

A: we have the nth term of A.P is given by  an=a+n-1d here,  a=3, d=4-3=1an=3+n-11=2+n we get,…

Q: A student has scores of 78, 77.25, and 81.75 on his first three tests. He needs an average of at…

A:

Q: Prove by CONTRAPOSITIVE if x is an odd integer, then x²+3x+5 is odd

A: Explanation of the answer is as follows

Q: Show by contraposition that for any real number x if -5 <x<4 then x2+x- 20 <0

A:

Q: A rectangular room is shown. 3x + 6 3x + 6, 4x minus 1, x, door, x, 4x minus 1 4x - 1 4x-1 Door TX…

A: It is given that,         We have to find the width of the door.

Q: Let a be a real number. Prove by contrapositive that if a+ 7x = 90, then a < 4.

A:

Q: Q- Prove the following identities. (a):- 1-0- AV

A:

Q: It is possible to rewrite the expression 4. 2 In(x) – In(ax) as In(kx) where k is a constant.…

A:

Q: Determine whether the statement is true or false. 1 dr In (8) x2 -

A:

Q: Rewrite the equation in Ax +By= C form. Use integers for A, B, and C. 1 y=x+2

A: From the given problem: y=15x+2....1

Q: Use proof by contraposition to show if r + y 2 2 where r and y are real numbers then r> 1 or y > 1.

A: A contraposition method is used to prove a conditional statement. Let A and B be any two statements.…

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

A:

Q: Use the quotient rule to show the following: If n is a negative integer, and g(x) = x" then g' (x) =…

A: Solving by Quotient rule we can get

Q: HxER x2- 9х — 36 >0 х>12 or x < —3

A:

Q: Express the set of real numbers between but not including 2and 7 as follows.(a) In set-builder…

A:

Q: For each positive integer n, show that и(п)и(n + 1)u(п + 2)u(n + 3) — 0

A: To prove : μ(n) μ(n+1) μ(n+2) μ(n+3) = 0  for each positive integer n.

Q: Express the following statement using O-notation: 12.x5 (3x + 4) 2. x + 2

A:

Q: Write the following in numerical form : The product of two consecutive positive integers is at least…

A: To Write the given statement in numerical form.

Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2 +n², express an in terms of n.

A: a1=3, a2=4 n≥3; an=2an-1+an-2+n2 First from the given, the given values shows that the terms are in…

Q: Let a be a positive real number. Evaluate So Va? – x²dx.

A:

Q: For each nonnegative integer n, let Un = (n, -n]. Find U3

A:

Q: It is possible to rewrite the expression 2 In(x) – In(ax) as In(kx) where k is a constant. Perform…

A: The given expression is: 2 ln(x)-ln(ax)

Q: Find all positive integers n for which n1º +1 is divisible by 10.

A:

Q: 2x-1 2

A: Given expression is   2x-114-x2

Q: Use a direct proof to show that the product of two odd numbers is odd.

A:

Q: Express the following using factorials: 10 x 9 x 8 x 7

A: Meaning of factorial of a natural number : Suppose n is a natural number then meaning of n! is…

Q: Show that 5 – V7 is an algebraic number.

A:

Q: Consider the statement: 3 a| I. Express this statement usíng O-notation.

A: The given inequality is 3x2≤3x2+17x+5≤25x2 for all real numbers x&gt;1.  Let fx=3x2+17x+5 and gx=x2,…

Q: Let P (x) be the statement "x = x²." If the domain consists of the integers, give True/False…

A:

Q: Express +he number as a raho of integers 0.135 10.1353535

A: Given expression can be expressed as series shown on board.

Q: Let x be a real number. Prove by contrapositive that if x' + 7x = 90, then x < 4.

A:

Q: In P2, find all real numbers a such that x - ax +1-a? is in the span of x -2x+1, x-1,and3x -2x-1. Oa…

A:

Q: Fill in each blank so that the resulting statenment is true. 3x-42-216x= (x-14x-72)=_(x+4)(x_U…

A: Solution-

Q: The operation * is defined over the set of real numbers "R" by a * b = a + b + 1/2ab. What is 6 * (2…

A: Given that the relation defined on real number R as a*b=a+b+12abTo find 6*(2*5)?

Q: Use a direct proof to show that if x is a real number such that (x – 1)? = 0, then x³ –1 = 0.

A: