how that the quality [x+y]=[x]+[y] is not valid for all real numbers x and y. please explain clearly.

Q: 2. What is the true value of x²-x-2

A: Given the equation, x2-x-2 This can be written as, x2-x-2x2-2x+x-2x(x-2)+(x-2)(x-2)(x+1)

Q: what would the interval notation be for (x^2+3x)/(x-2)

A: we have given,

Q: Prove that = Aatilag (Elog Xi) An. %3D

A:

Q: Express {x : 2 ≤ |x − 1| ≤ 6} as a union of two intervals.

A:

Q: Express the set of numbers x satisfying the given condition as an interval. |3x + 5| < 1

A: 3x+5<1

Q: Use the equation Σ x" for [x] < n=0 (Express numbers in exact form. Use symbol 6 1 - x4 Σ 1 1-x Σ…

A:

Q: Determine whether the statement is true or false for all x > 0, y > 0.

A: a.)logbxlogby = logbx-logbyThis is wrong statement.The correct statement is given by formula -…

Q: Determine whether each of these statements is true or false. Explain why. 0 ∈ ∅ ∅ ∈ {0} {0} ⊂ ∅ ∅ ⊂…

A: 1.   0 ∈ ∅ As ∅ is empty set so it can't contain any element. Hence 0 can belongs to ∅. Answer:…

Q: determine the union of XuY  express in interval notation X = {x | x > 14} and Y = {x | x ≤ 11}

A:

Q: Using the definition of infimum, prove that inf(-1, 3] = -1.

A:

Q: Prove the equality:

A:

Q: 2+x X-2

A: We have to evaluate the limit: limx→2-2+x We know  is representing for greatest integer function or…

Q: Describe all numbers x that are at a distance of 2 from the number 10. Express this using absolute…

A:

Q: Express the domain of f(x) = v20 – 7x using interval notation. Use oo for o. Domain of f(x) is…

A:

Q: Express the inequalities xs 3 and -1sx< 4 in interval notation.

A: x≤3 and -1≤x&lt;4 The first inequality means x values less then and equal to 3. For equal to sign…

Q: Why is (subtracting two positive numbers that are each less than 1), less than or equal to (1 minus…

A: Since r and s are both between 0 and 1  Then 1-r is positive and also 1+s is positive  Now , take…

Q: A recent study showed that 90% of all people have a commute time to work of 15 minutes or more. The…

A: Solution: Given information: Margin of error E= 0.06  The 90% confidence interval for the all people…

Q: Does ⌊ -x⌋ = -⌈x⌉ for all real x? Give reasons for your answer.

A:

Q: d) The set of real numbers, with addition defined by x + y %3D х - у

A:

Q: Use the Quotient Rule to differentiate K(x) = (2−x−√(x)) / (x+ 1)

A: K(x)=2-x-xx+1

Q: What value of x verifies that

A:

Q: Consider f(x) = (x - 1) / (x - 3). Use A = (-infinity, 3) union (3, infinity) as the domain. What is…

A: Let y = f(x). Then

Q: 2(x+1) +4|< 8. Please express your answer both on number line and also using interval notation. 69 F

A:

Q: The principle of Analytic continuation:

A:

Q: Describe all numbers x that are at a distance of 4 from the number 6. Express this using absolute…

A: Let us assume x∈R. The distance of x from 6 (positive or negative) is given by x-6. But it is given…

Q: The set of real numbers in interval notation is represented by

A: The set of real numbers in interval notation is represented by ℝ=-∞,∞.  Interval: An interval  a,b…

Q: The algebraic translation of "x is no more than 7" is

A: the algebraic translation of "x is no more than 7 " is ?

Q: A³ f2 = V³ fs 3

A:

Q: Describe all numbers x that are at a distance of 3 from the number 6. Express this using absolute…

A:

Q: Express the interval using two different representations. -8 -6 4. 6 10 12 -12 -10 (6) U or Interval…

A:

Q: Alice is in a 20-km running race. She always runs the first half at an average speed of 2 km/h…

A: Alice is in a 20-km running race.She always runs the first half at an average speed of 2km/h faster…

Q: How could the absolute value of -2 make it a twin of 6 when |-2| = 2? Show work

A: Given that absolute value of -2 is 2 . And we want to prove that the absolute value of -2 make it a…

Q: Express the interval using two different representations. -12 -10 -8 -6 -4 -2 2 4 6. 10 12 [ ] [, )…

A: Here we will find Interval Notation and Inequality Notation,

Q: What is the range of f(x)= x square rooted (use interval notation)

A:

Q: ) Use interval notation to describe the set of real numbers {x \x² + x – 2 2 0}.

A: Given: x|x2+x-2≥0. Here, x2+x-2≥0x+2x-1≥0x+2≥0 and x-1≥0   or x+2≤0 and x-1≤0 When x+2≥0 and…

Q: Evaluate x2 - 2x for the value of x satisfying 4(x + 2) + -16 = 3x - 5(4 - x).

A: 4x+2+-16=3x-54-x⇒4x+8-16=3x-20+5x⇒4x-8=8x-20⇒8x-4x=20-8⇒4x=12⇒x=3

Q: Vr(x < 0) V (x < 2x)

A:

Q: True or False The distance between two distinct points on the real number line is always greater…

A: Given: The distance between two distinct points on the real number line is always greater than zero.

Q: Explain the Intermediate Value Theorem using words and pictures.

A: Intermediate value theorem is an important theorem which tells us about the continuity of a function…

Q: am not understanding why it is (negative infinity, 4) U (4,Positive Infinity) Can you please…

A:

Q: What is x for 5(x+3) -x+1=x

A:

Q: (*;)-()0)

A:

Q: Express all real numbers greater than 6 and less than or equal to 7 in interval notation.

A:

Q: The algebraic translation of "x is no less than 7" is .

A: Given statement is "x is no less than 7:. To translate into algebraic form. Solution: Given that x…

Q: Express the set of numbers x satisfying the given condition as an interval. |x − 4| &lt; 2

A:

Q: Show that: αλ (a-1)²(a-2) Var(x)=-

A:

Q: Describe all the x-values at a distance of 11 or less from the number 4.

A: An inequality for for the x-values at a distance of 11 or less from the number 4 will be:…

Q: Use intermediate theorem to explain P [x] = x* – x' – 10 has a zero in [2, 3]

A: According to intermediate value theorem of a function f(x) is continuous on [a, b] and L is any…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.