Use the triangle inequality to establish the following inequalities: (b) ||c| – |d|| < |c – d| IPl + |이 > \p - 기 () (Note: these can be proven by cases, but they can also be deduced from the triangle inequality by choosing c or d cleverly. )

Q: What is the triangle inequality? How is it proved? Why is the inequality |a+b| |a|+|b|, where a and…

A: What is the triangle inequality? How is it proved? Why is the inequality |a+b| |a|+|b|, where a and…

Q: 7x+6≤7(x-4) 2.) x-2y≥4     2x-y≥-2 Also, make a short essay on the observation about the graphs.

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Q: ne solution to the inequality x" 5x“ + 2x + 8 201IS: | a) -2 s xs 1 or x< 4 b) 1 < x < 2 or x s -4

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Q: 3. Find and plot the solution to the following inequality on a number line: a) -x2 + 2x > 0 4 - 2г…

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Q: write the inequality with the following boundary lines A) x+3y=3 B) y=x-2

A: Given equations We need to write the inequality of the given graph using the provided equation Use…

Q: above below b. the line would be dashed with shading below c. the line would be solid with shading…

A: We have to choose correct options for given Questions.

Q: - Whenever one has an inequality, an interesting problem is to characterize the cases of equality.…

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Q: 1. Sketch the solution to the inequality y < -2(x-1)²-4.

A: The given inequality is .The aim is to sketch the solution set of the given inequality.

Q: (1) that the reverse triangle inequality holds for all real numbers. (HINT: Write a as a - b+ b.…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: 3. Write an inequality that best represents the graph. (0, 0) y ¿x - 3 А. х — | В. | С. У 2х — 3 O A…

A: Equation

Q: 3. a) Graph the inequality given. y < -x+1 3 -2 ST b) What was the student's error?

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Q: B. Prove that the ordered pair (5,5) is a solution of the linear inequality y2 2x-5. hint:…

A: y≥2x-55≥2(5)-55≥10-55≥5 True

Q: Q3. Solve he 1X+41>2 yollowing ineqralitisom2. . Ix -1|s /2x+3/ m/onli 4 1x-31 d. X+3 e. x-8x+7<o 2.

A: Please post questions with multiple subparts separately.a) x+4≥2We know that,If x≥a, a&gt;0then,…

Q: 2. Explain how a test point can be used to determine the solution to an inequality.

A: In mathematics, a test point is a specific value chosen from the solution set of an inequality to…

Q: Solve the following inequalities: a.) -6x(x+1)2(3-x)&gt;0 b.) 5/(2x-7)&gt;1

A: To solve the below inequalities:

Q: -7 -6 -5 10 1 2 3. 4. 5 6 7 Pick the correct inequality. A) x-6 B) x2-6 D) x<-6

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Q: Use the graph of f(x). f(x) 5 x² + 5 x+1 to solve the ineq

A: Introduction: The circumstance of an illegal and/ or uneven distribution of openings and coffers…

Q: Prove that for x&gt;0 the inequality 1+2lnx≤x2 is true.

A: Inequality given in the question is: Consider the function; f(x) = 1+2ln(x)-x2 Let us find critical…

Q: 12. Solve the following inequality by using a table/diagram. Write the solution set in interval…

A: Solve the following inequality by using a table/diagram

Q: (6B) 2. x5 5 a. -10-8 -2 0 2 4 6 8 10 b. + -10 -8 6 4 2 0 2. 8 10 с. + 8 10 -10 8 2. 4 6 -10 -8 -6 4…

A: (6B) The inequality represents the values less than 5 including 5.

Q: dont understand how A ⋅ B ≤ |A ⋅ B|, when the dotproduct can't be less than zero, so the absolute…

A: We have to prove  A ⋅ B ≤ |A ⋅ B|We know

Q: Triangle Inequality

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Q: Derive Hoeffding's inequality by applying McDiarmid's inequality.

A: Let  be independent random variables, and let  be a function that satisfiesfor all  where . Then for…

Q: Solve the inequality 2X 7 X + X<3

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Q: 1. What is the possible(s) value of x in the inequality 2x ≥ 10 ?  A. x = 5 B. x > 5 C. x ≥ 5 D. x ≤…

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Q: 1. Solve the following inequalities using an algebraic method, show all work. х2+2х-3 a) 2x3 – 7x2 –…

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