Consider the equation where x1,x2,...,x9 € N. How many solutions are there if: a) b) c) Xi 9 for all 1 ≤ i ≤ 9? xi 32 for all 1 ≤ i ≤ 9 ? 1 ≥ 3, and xii (mod 7) for all 1 ≤ i ≤ 9? x1 + x₂ + .. + x = 73,

Q: How many integer solutions are there to the equation with x₁ > 1, 2 > 2, x3 > 2, x4 > 0 ? X1 + x₂ +…

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Q: Prove the equation is true if the absolute value of r is less than 1.

A: To prove the below equation

Q: can apply the definitions of even/oddness, absolute value to prove statements that involve cases.…

A: Answer — Exploring different cases and relation between x and 2                      a)…

Q: If æ is an irrational number, then it is the case that sup{q E Q : q< x} < x.

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Q: 20. Prove: Let x and y be real numbers. If x is rational and y is irrational, then x + y is…

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Q: 2. Find p and q such that 7x+1 5 |5x-1|≤4 implies p ≤: <q

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Q: What is the solution to 9|x – 8| 12 c)x > –12 or x < 8 d)–4 < x < 8

A: To solve the given inequality.

Q: Let f ={ (-6,4),(-5,3),(4,-6),(3,-5),(1,5),(2,6),(-3,5),(-8,2),(6,4)}  g=…

A: It is known that f-gx=f(x)-g(x) and f·gx=f(x)·g(x). The sets are provided as:…

Q: 7) |m - 10| ≤ 19 什 -10 + -5 0 5 + 10 15 + 20 25 30 8) n-4 <5 -3 -2 -1 0 1 + 2 3 4 5 6 7 8 9 10 11

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Q: Solve for the following: A) |x−4|≥−5 B) |2x+9|≤3 C) 4|x+8|+4>114|x+8|+4>11

A: Given: Solve for the following:  A) |x−4|≥−5  B) |2x+9|≤3  C) 4|x+8|+4&gt;11

Q: 10. Let x be a real number. Prove that at least one of the numbers /2 – x or /2 +x is irrational.

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Q: a) If x < 8, then x − 3 ? 5. (b) If x ≤ 8, then 3x ? 24. (c) If x ≥ 3, then −3x ? −9. (d) If x <…

A: When the inequality is multiplied by a negative number, the sign of inequality changes.

Q: For any numbers a andb and an even natural number n, show that the equation x" + ax + b = 0, x in R,…

A: Here, to prove this result we have to use Rolles theorem.

Q: Provide answers in interval notation. 18) x2 – 5x s -4 x2_5x

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: X. a. y> ]x + 4|- 4 b. y> ]x - 4| + 4 c. y< |x + 4|-4 d. y< |x- 4| + 4

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Q: Prove that −3 ≤ x ≤ 2 implies that |x² + x − 6| ≤ 6|x − 2|.

A: We have to prove thatWe know that

Q: How many solutions are there to the equation x1 + x2 + x3 + x4 + x5 + x6 = 25 in which each xi is a…

A: As per the question we are given a linear equation in 6 variables as : x1 + x2 + x3 + x4 + x5 + x6 =…

Q: a) Prove that |x| ≤ 2 implies that |x² − 4| ≤ 4|x − 21.

A: To prove the given statement, let's break it down into a few steps: Starting with the assumption…

Q: Let m be 40 and let n be 9. What are the integers q and r such that m = qn+r and 0 < r < n.?

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Q: 5) r + 5 ≤ 11 + + + + -1 0 1 2 3 4 5 6 7 8 9

A:

Q: Which number is NOT in the solution set of x + 5 > 10?7 A) 4 B) C) D) 12

A: Given : x+5&gt;10

Q: R= 24 -log (1--135 (2100) 135 Yog (1+ +122)

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Q: absolute value 1)  |3| 2)  |-3| 3) -|3| 4) -|-3|

A: Since you have posted many questions here, i can answer first 3 sub-parts Please repost the other…

Q: The interval notation for the set (xlx ≤4 or x>-2} is. [-2,4] A O (-2,4] BO R .CO DO [-2,4) EO…

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