Use the drawing below as needed to answer the question. Three lines form 8 labeled angles. Line m and line n appear parallel. Line m is to the left of line n and both lines start at the bottom and go up and to the right. Line k starts to the left of both m and n and travels down and to the right intersecting m and then intersecting n. ∠1 is formed by the top side of k and the top side of m. ∠2 is formed by the bottom side of k and the top side of m. ∠3 is formed by the top side of k and the bottom side of m. ∠4 is formed by the bottom side of k and the bottom side of m. ∠5 is formed by the top side of k and the top side of n. ∠6 is formed by the bottom side of k and the top side of n. ∠7 is formed by the top side of k and the bottom side of n. ∠8 is formed by the bottom side of k and the bottom side of n. Given: m ∥ n transversal k m∠1 = (3x + y)° m∠2 = (2x + y)° m∠8 = (2x + 3y)°Find:x, y, and m∠8 in degrees

Q: Which set of line segments could create a right triangle? A - 24, 30, 35 B - 12, 18, 30 C - 18,…

A: If triangle right angled then  C2= a2+b2   c = longest side                      a =  second side…

Q: a. X= 5 6. How long is line segment MN in Figure 2? b. x = 1 figure 2. AY c. 9V7 d. 162 a. 18 b. 9…

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Q: Find the radius of the circle inscribed in a triangle formed by the lines 7x+24y-70-0, 21x-20y-70-0,…

A:

Q: Use linear pairs to find the sum of all the angles labeled in the triangle. Then use what you know…

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Q: Indicate whether each pair of angles would be congruent or supplementary. Lines p and q are…

A:

Q: Pac-Man can be formed by the intersection of the Unit Circle with the lines y = x (x ≥ 0) and y =…

A: Converting in polar coordinates x=r cosθ,  y=r sinθ Here radius "r" is 0≤r≤1, -π4≤θ≤π4

Q: If A(-2, 1), B(2, 3) and C(-2, -4) are three points, find the angle between BA and BC.

A: Given points are A(-2,1) , B(2,3) and C(-2,-4).We have to find the angle between the lines BA and…

Q: 1. If P, = (2,1), P2 = (-4,1) and P = (-4, –3) then state whether the triangle is right angle…

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Q: For numbers 8-10, consider parallelogram CARE. A E R

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Q: ZM and ZN are consecutive (same-side) interior angles forme by two parallel lines cut by a…

A: Same Side Interior Angles Theorem:- If two parallel lines are cut by a transversal, then the same…

Q: 6. Plot the following points on a coordinate plane: (-1, 1), (-1, -6), (4, Inv. 1 (5, 1) and (5,…

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Q: Find the third angle of a triangle if the sum and difference of the first and second ongle are 100…

A: Given:- The sum and difference of the first and second angle are 100 degrees and 20 degrees,…

Q: Indicate whether the statement is true or false. If ∠1 and ∠2 are vertical angles with m∠1 = 4x − 11…

A:

Q: Pac-Man can be formed by the intersection of the Unit Circle with the lines y = x (x ≥ 0) and y = -x…

A: It is given that - Pac-Man can be formed by the intersection of the Unit circle with the lines y=x…

Q: Choose the parallelogram that best matches the diagonals shown: 니.. 2.

A:

Q: 23. Find the radius of the circle inscribed in a triangle formed by the lines 7x+24y-70-0,…

A: To find- Find the radius of the circle inscribed in a triangle formed by the lines 7x + 24y - 70 =…

Q: State the representation that does not change the location of the given point. (4, 110°) A) (4,…

A: (4,110°)

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.