Assume that a circular pizza is being cut into pieces. If there are C cuts and I points of intersection of pairs of cuts, how many pieces of pizzas (P) are there? Suppose that cuts can only intersect inside the pizza and that at most two cuts intersect at the same point inside the pizza. For example, there are 10 pieces of pizza when there are 4 cuts intersecting in 5 points.

Q: Prove that quadrilateral PLUS with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle.

A: 1) Opposite sides are equal , 2) The diagonals of a rectangle are equal.  Distance formula of point…

Q: Q2: The plane is divided into a finite number of regions by drawing infinite straight lines in an…

A: Let n denote number of lines drawn on plane. We will prove the result with the help of mathematical…

Q: Of all rectangles with given area, A, which has the shortest diagonals? A rectangle with area A has…

A: Dimention are : A×A

Q: Prove that quadrilateral PLUS with the vertices P(2,1), L(6,3), U(5,5), and S(1,3) is a rectangle.…

A:

Q: 2. If there are seven distinct points on a plane with no three are collinear, how many different…

A: A polygon requires at least 3 points (and 3 sides). Since no 3 points are collinear, that means you…

Q: Show that if n > R(6,6) and we partition the edges of the complete to 4 pieces then one of the…

A: According to the given information, it is required to show that:

Q: If all perpendicular bisectors of all three segments of the following triangle are drawn, where will…

A: We know that, The circumcenter of a triangle is the point of intersection of the perpendicular…

Q: 5. Suppose AABC is a triangle and l is a line such that none of the vertices A, B, or C lies on l.…

A: Find your answer below

Q: How many triangles can be formed from 11 distinct points on the plane, no three points of which are…

A:

Q: Prove a quadrilateral with vertices G(1,1), H(5,3), I(4,5) and J(0,3) is a rectangle

A:

Q: Write TRUE if the given situation illustrates combination, otherwise FALSE. 1. Forming a committee…

A: Permutations are those arrangements where order is important, while combinations are those…

Q: Prove: In the five-point geometry, each point has exactly four lines on it.

A:

Q: It is possible for two intersecting lines to be noncoplanar.

A: It is possible for two intersecting lines to be noncoplanar.

Q: In AQRS, mZQ = 11° and mZR = 40°. Which list has the sides of AQRS in order from shortest to…

A:

Q: A cube has four diagonals. Show that no two of them are perpendicular.

A: Given: A cube has four diagonals.

Q: The segment addition postulate only works when the segments in question are collinear. O True O…

A: Let's find.

Q: If three corners of a parallelogram are (1, 1), (4, 2), and (1, 3), what are all three of the…

A: Three corners P{1,1} ,Q{4,2} ,R{1,3} are given so three possible fourth corners are  A{4,4} B{4,0}…

Q: What are the coordinates of the point on the directed line segment from (4, 3) to (9, 8) that…

A: Our Aim is to find the coordinates of the point on the directed line segmentfrom (4,3) to (9,8) that…

Q: Without lifting your pencil from start to finish, draw 4 line segments through all 8 dots. The…

A:

Q: Given n ≥ 3 circles on the plane, satisfying . Each two circles intersect at exactly 2 points; . No…

A:

Q: IFA and B have 6 and 9 elements each, what is the minimum number of elements Aunion B?*

A:

Q: 1) How many triangles can be drawn on a plane using 8 non-collinear points?

A:

Q: What are the coordinates of the point on the directed line segment from (4, 3) to (9,8) that…

A:

Q: If m straight cuts are to be made right across a huge circular pizza (with no three cuts…

A: 1. There are m straight cuts.  2. The pizza is divided into 121 parts, not necessarily equal.    3.…

Q: Given n ≥ 3 circles on the plane, satisfying • Each two circles intersect at exactly 2 points; . No…

A: Given: for n≥3 circles on the plane, every two circles intersect at exactly two points and No three…

Q: Prove without using the concept of duality: In the four-line geometry, there exists a pair of points…

A:

Q: 2. Show that if two sides of a cyclic quadrilateral are parallel, then the other two sides are of…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 7. The diagonals of Parallelogram ABCD intersect at point X, the mAX is 152.

A:

Q: 3. Given a line and a plane in three dimensional space, what are all the possible ways they can…

A: The Answer is given below in a picture(handwritten) format.

Q: What are the coordinates of the point on the directed line segment from ( 1,9) to (3,-7) that…

A:

Q: If line DB is the perpendicular bisector of AC, list all the congruent segments

A:

Q: In ANOP, mZN = 110° and mZO = 38°. Which list has the sides of ANOP in order from longest to…

A: Given that, m∠N=110°, m∠O=38° in ∆NOP

Q: quadrilateral is cyclic if and only if a pair of its opposite angles are supplementary. True or…

A: A convex quadrilateral polygon in a plane is cyclic if, and only if, its opposite angles are…

Q: 27. How many triangles collinear points? can 'be drawn on a plane using 8 non-

A:

Q: In ASTU, mZS = 14° and mZT = 50°. Which list has the sides of ASTU in order from shortest to…

A:

Q: Find all points where fex)= |21x-131 fails be be differenbiadle

A: Given:- f(x) = |21x-13| To find:- All points where function non differentiable

Q: What point divides the directed line segment AB into a 2:3 4. ratio? 3- -2- 456 89 10 11 12 13 14 15…

A:

Q: Find the number of sides of a convex polygon if the measures of its interior angles have a sum of…

A:

Q: Draw three shapes that are symmetric. Draw at least one line of symmetry through each shape to prove…

A: The symmetric shape's are given below

Q: Create a partition that would be the same as the one provided. Directed Line Segment RQ is…

A: Given data is : RQ¯ is partitioned by point P into ratio of 4:5

Q: Let Q be the quadrilateral with vertices (-2,3), (1,4), (3,0), and (-1,–3). Find the area of Q

A: Consider a quadrilateral Q with vertices  A−2,3,B1,4,C3,0 and D−1,−3

Q: In AUVW, UW is extended through point W to point X, MZVWX = (7x + 10)°, mZWUV MZUVW = (2x + 17)°.…

A:

Q: Since a line segment is defined by two distinct points, therefore the total number of line segments…

A:

Q: Based on triangulation of polygons, prove that copies of a regular n- gon can tile the plane only…

A:

Q: The point on the directed line segment from (2,0) to (14,12) that divides the segment in the ratio…

A:

Q: Assume there are 3 ways to get from point A to B and 5 ways to get from B to C. How many possible…

A: Given Assume there are 3 ways to get from point A to B and 5 ways to get from B to C.

Q: Find two values of k such that the points (-3, 4), (0, k), and (k, 10) arecollinear.

A: To Find: Two values of k such that the points -3,4, 0,k and k,10 are collinear. Concept: Slope…