2. If a line segment joins the midpoints of two sides of a triangle, then, its length is equal to one - half the length of the third side. Given: Triangle LME C and G are midpoints of LM and EM, respectively Prove: CG =-LE 2 M

Q: prove theorem: if a square is inscribed into a right triangle in such a way that one side of the…

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Q: Provide a proof of the statement given below the figure. You may submit your proof in any format…

A: ABCD is a kite with  AB≅ AD          and  CB≅ CD We need to prove that : ∠B≅∠D

Q: (a) Solve the linear congruence 26x = 1 modulo 33

A: Solution

Q: Use a) and b) to find A-1

A: Let's find inverse of A from given results a and b.

Q: Prove: Let a > 0 and b > 0 then either a > 0 and b > 0 or a < 0 and b < 0. where a…

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Q: Give a direct proof of the theorem: “if x and y are odd integers, then x + y is even.”  DISCRETE…

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Q: Justify the equations in either by deriving them from formulas.

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Q: Prove or disprove the statement: For all x E R, |x + 1| + |x – 1| > 2.

A:

Q: A B 30 find be

A: In △ABC, b = 30∠A = 30°AB = BC = x (assume) To evaluate: The value of x

Q: 5.)Write the aua mented matrix for the syshem X, +2X,-X, tXc =l =マ+ t bulo

A: We have to solve given problem:

Q: Prove that |ab|= |a | |b| for any numbers a and b.

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Q: D. Let A and B be sets. Prove that (A × B) ^ (B × A) = Ø if and only if AnB = Ø. (Use any…

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Q: (2) Show that for any integers a,b we always have a? – 4b # 2. -

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Q: If a = 2a - a² and b =1-(1-a), show that a = b for all natural numbers n. Assume that a, is a fixed…

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Q: If R is the set of all real numbers, what do the cartesian products R × Rand R × R × R represent?

A: Cartesian product R × R represents all the coordinates in R2  For example (1,2) , (5,6) coordinates…

Q: show the steps to get the answer to both of these questions

A: Given below solution Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Find k such that, 2 det 4 li0 -8 -5] -1 -7 = 510 k 0 .

A: Given det2-8-54-1-710k0 =510 we have to find k

Q: Does A − (B − C) = (A − B) ∪ C hold for all sets A, B, and C? Prove or give a counterexample for…

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Q: H 28. For all integers a, b, and c, if a b and a/c, then al(b + c).

A:

Q: 2. For all sets X, Y and Z, determine whether each of the statement is true or false. If it is true,…

A: (a) False. We know that if a set A has cardinality n , then it's power set P(A) has cardinality 2n…

Q: Prove by Contradiction: There are no integers x and y such that = 4y+2.

A: We have to prove the statement "There are no integers x and y such that x2=4y+2" by contradiction.…

Q: How many different size of infinity are there? How does it relate to one-to-one correspondence?

A: There are actually many different sizes or levels of infinity; some infinite sets are vastly larger…

Q: Determine the value of k that satisfies the following identity (x is a variable). +k = In(x + ab?)…

A: Given equation is: lna+xb2+k=lnx+ab2 To evaluate value of k k=ln(x+ab2)-lna+xb2…

Q: From fundamental property relations, proof the following equation is valid. %D | T.

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Q: . Consider the statement: Let A, B ∈ Z. If 6|A and 10|B, then 4|(A2 + B2). (a) Prove the statement.…

A: 5. Consider the statement: Let A, B ∈ Z. If 6|A and 10|B, then 4|(A^2 + B^2). (a) Prove the…

Q: For all real numbers x and y, x+y = x + y Disprove the following statements or prove it.

A: For all real numbers x and y, x+y=x+y.

Q: Each of the following is incorrect. Explain why or give a counterexample. 1. There are 60 zero…

A: Use the formula of zero divisors in Zm and the properties of Euler's Phi function as in next step.

Q: Matrix with rank A= 4 het A be a 5x6 ind cim Row A, dim Col A, dim Nul A, din Bow AT, dim Cal AT,…

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Q: Prove the following statement in three different ways, using a direct proof, a contrapositive proof…

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Q: Prove the following set identities: (a) (AUB) nC = (ANC) U (BNC); (b) (AUB)-C=(A-C) U (B-C); (c)…

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Q: If a|b, then a|(bc). Direct proof.

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Q: Let m and n be integers. Two integers m and n are said to be consecutive if m - n = 1. Consider the…

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Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.