Are there any real numbers that are both rational and irrational? Are there any real numbers that are neither? Explain your reasoning.

Q: Is there a real number whose square is-I

A: Square of any real number should be positive.

Q: Find all numbers that must be excluded from the domain of the rational expression : (x + 5) / (x2 -…

A: The denominator can never be equal to 0

Q: On the real number line, label the points with coordinates 0, - 2, 2, - 1.5,3/2, 1/3, and 2/3

A: Real numbers numbers are numbers on which arithmetic operations can be performed and can be…

Q: Define the Consequence for Root Finding?

A:

Q: Let S = {(x, y) : x and y rational numbers}. a. What is the interior of S? Justify your answer by…

A: A point x is said to be an interior point of S if there exists a neighborhood N(x) of x such that…

Q: Describe the kinds of numbers that have rational fifth roots.

A: For a number that that have rational fifth root ,must be rational itself. Let A/B be the number that…

Q: Is there a real number whose square is –1? a. Is there a real number x such that _? such that x =…

A: In general, there does not exist any such real number whose square is a negative real number. Hence,…

Q: What are the real numbers?

A: We need to find the definition of real numbers. First let us define what are real numbers and then…

Q: Computers can store integers exactly but not real numbers in general. Instead, they approximate them…

A: (e) floating point numbers We have to find out the reason that why real numbers cannot be stored in…

Q: How do you find the domain of a rational function? do you just set the numerator to zero and solve?…

A: Domain of a rational function f(x) is the set of all the points of x for which f(x) is defined, that…

Q: What is the variables in this statement; the cube root of any negative real numbers is negative

A:

Q: Which figures can be precisely defined by using only undefined terms?

A: The figures are  1. Circle 2. Parellel line 3. Line segment

Q: Is this statement true or false? Prove each true statement directly from the definitions and give a…

A: Given: Given statement is The quotient of any two rational number is rational number.

Q: Is any real number exactly 1 less than its cube?

A: Is any real number exactly 1 less than its cube?

Q: Express your answer in interval notation  |3x-10| 2

A: Note Expression is not written in proper form. Therefore i am taking |3x-10|<2

Q: The interval [7, 13] is described by Ix - 101 < 3.

A: Given: x-10<3 we know that if x-a<b then -b<x-a<b

Q: The value of an item (h) is greater than or equal to $55. Which represents this statement?

A:

Q: The sum of any two rational numbers is rational work this poblem out with step and why.

A: Let A and B are two rational numbers such that A=pq, q≠0 and B=rs, s≠0 Find the value of A+B

Q: perform the indicated operations involving rational numbers. Be sure to express your answers in…

A: Given:              14+56 Simplify: 14+56 Take LCM of 4 and 6 LCM of 4 and 6 is 12

Q: Define/Explain what a Fact and a Truth is in terms of mathematics.

A: Lets briefly define what is the difference between fact and truth.

Q: What is meant by the absolute value of a number?

A: To explain the absolute value of a number.

Q: Express your answer in interval notation 9|x-1|+4 < 22

A:

Q: Among those positive real numbers x and y whose sum is 50, find these numbers that makes their…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find all numbers for which the rational expression is undefined.

A: The rational expression is undefined when the denominator of the rational expression becomes equal…

Q: every two rational numbers there is an irrational number.

A: We have to prove the given statement that is '"between every two rational numbers there is an…

Q: perform the indicated operations involving rational numbers. Be sure to express your answers in…

A: Given: 23-78+14 To determine: The simplified form of the given expression.

Q: Is there a positive real number “closest” to 0?

A: Suppose there is a positive real number closest to 0. Let it be a. Now the distance from 0 to a is…

Q: Is the number 0.5 above the interval (0.52,0.63) ?

A: we have to find the point 0.5 lies above the interval 0.52, 0.63or not

Q: In interval notation, (- ∞, -1] represents the set of real numbers_______ -1.

A:

Q: nslate this statement into its symbolic form: "For every rational number here exists a real number y…

A:

Q: The product of an irrational number and an irrational number is irrational. Always Sometimes Never

A: Given statement: Irational number×Irational number=Irational number

Q: What is the value of the discriminant whose root are real,rational,and equal?

A: Given: - The discriminant whose roots are real, rational, and equal. To find: - The value of the…

Q: perform the indicated operations involving rational numbers. Be sure to express your answers in…

A:

Q: How can I explain using (x0+ ε, x0-ε)? Explain why it is true that, if x0 is in (a,b), then there…

A:

Q: Can a real number be both rational and irrational? Explain your answer?

A: Consider the given information as Can a real number be both rational and irrational

Q: what is the absolute value for a number that is positive

A:

Q: The perimeter of a square must be greater that 52 inches but less than 84 inches. Find the range of…

A: The perimeter of a square must be greater that 52 inches but less than 84 inches. Find the range of…

Q: Translate this statement into its symbolic form: "For every rational number x, there exists a real…

A:

Q: how to tell whether the rational number is a reasonable approximation of the square root

A:

Q: perform the indicated operations involving rational numbers. Be sure to express your answers in…

A: Consider the given rational numbers: 35 + 16 Taking LHS of denominator 5 and 6 LHS = 5×6 = 30 35 +…

Q: Find two concecutive odd integers such that when the smaller is added to twice the larger, the…

A:

Q: Why do we say that absolute value number cannot be negative

A: Explanation of the answer is as follows

Q: perform the indicated operations involving rational numbers. Be sure to express your answers in…

A: We have to perform the indicated operations involving rational numbers: 79-16 Rewriting the…

Q: The set of real numbers for which a rational expression is defined is the__________ of the…

A: Given:Rational expression

Q: Show that the product of a non-zero rational and an irrational is irrational.

A: A number 'a' is said to be rational if 'a' can be written as,pq where p, q≠0 are integers. And, a…

Q: Is the sum of two irrational numbers always an irrationalnumber?

A:

Q: 1. Joseph wants to find the side length of a square that has an area of 150 feet. Should his answer…

A:

Q: perform the indicated operations involving rational numbers. Be sure to express your answers in…

A: Subtraction or Addition between rational numbers can be done by taking their L.C.M(lest common…

Q: perform the indicated operations involving rational numbers. Express final answers in reduced form.…

A: 3-8×-612

Q: A machinist must produce a circular metal brace that is within 0.001 inches of the correct diameter…

A: According to question,Given data,Diameter = 6.5 inches,Let Diameter of the circular metal brace = x,

Statements and Logic

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