K, is planar . K3,10 is not planar . K23 is not planar -. K7 is planar

Q: Do the points (1, 0,−1), (0, 2, 3), (−2, 1, 1), and (4, 2, 3) lie in the same plane? Justify your…

A: To check: If the points (1, 0,−1), (0, 2, 3), (−2, 1, 1), and (4, 2, 3) lie in the same plane and…

Q: Find the length of the diagonals of rectangle WXYZ 

A: Solution The objective is to find the lengths of the diagonals of rectangle. By Rectangle Diagonals…

Q: Hiw.S Let Asitij-zk, B=-i-kandc=zituj-zk finds A-(2B-c) 4-2AX3B saCAXB).c 6- Ax(Bxc)

A: Given that: A=i+j-2kB=-i-kC=2i+4j-2k NOTE: As per our answering guidelines, we can only answer 1…

Q: (1,6) and perpendicular to 2x+7y=1

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Q: Translate quadrilateral BDFH using the rule (x, y) (x+ 6, y- 10) and label the image D B

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Q: #X-N, (M. E) where QX)-2X +3X;-2X,x, Find M.

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Q: If web₁x-b₂y-b3z, w= where b₁,b2, b3 are constants and b² + b² + b = 1. Show that 8² w 8² w 8² w əx²…

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Q: The corners for a fence are located at A (11,3), B (3,-11), C (-13,-9), and D (-5,9). What is the…

A: Any point on the cartesian coordinate system is represented by the ordered pair: x,y. Start from the…

Q: Show that A(-4, 2), B(1, 4), C(3, -1), and D(-2, -3) are vertices of a square.

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Q: 8. In Mr. Pelletier's classroom, 4 friends are seated at the points A,B,C, and D. Casey and Connor…

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Q: Q1/ Are the following points collinear? 1- A(-3,-7), B(0,-2), C(6, 8) 2- A (9,2), B(3,8), C(-5,-4)

A: Here we need to find whether these points are collinear or not the points are , then

Q: Centerville is the headquarters of Greedy Cablevision Inc. The cable company is about to expand…

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Q: Which of the following ordered pairs satisfy the 7x+8y0? а. (1,-5) b. (5,-1) . с. (1,1) • d. (0,0)

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Q: Find the area of the parallelogram with vertices: P(0,0,0), Q(-4,-5,4), R(-4,-3,6), S(-8,-8,10). 0

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Q: G F 5. The kite has vertices D(0, u), G(-w, 0), and F(0, -2u). What are the coordinates of E? (0, w)…

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Q: Which of the expressions below is not written as the difference of two squares? O A (4x² – 36)…

A: Four expression are : (1) 4x2-3636-4y2 (2) 81-x281-x2 (3) a6b4c2+1a6b4c2-1 (4) 4x6-16y84x6+16y8 We…

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.