2. The vertices of a triangle are A (3,2), B (7,2), and C (3, 5) (a) Verify that triangle ABC is a right triangle. Show your work! (b) Which side among AB, BC, AC is the hypotenuse? (c) Find the distance between the midpoint of the hypotenuse and the vertex which is facing hypotenuse. Draw a picture! 3. Graph the following relations (Note that Z is the set of all integers and R represents the set of all real numbers): (a) {(r,y),yR, |2 + y] < 1} 13 15 (b) {(x, y)|,y Z, -V10 y10 4

Q: e following sets of points is collinear 2. L(-5,13), M(-10,10), N(-20,4)

A: Here we have to prove that each of the following sets of points is collinear.  L(-5,13); M(-10,10),…

Q: Which of the following graphs represents y = e +2? a) O y= f(z) b) O y= f(z), 5 5- 3 2- -3 -2 -1 1 2…

A: To graph the equation y=ex+2, To find the points to plot, give values of x, and find respective…

Q: 3. Find the distance between the two points given on this graph. 61 -5 4 1 2 3 4 5 6 7 8 9 10 11 12…

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Q: 10.5 Prove that the following inequalities hold for all points x, y e R" : d* (x, y) S d(x, y) < n…

A:

Q: 2. Show that the graphs are not planar: 2.c. 2.b. 2.a. S 6o

A: Given problem is related with graph theory. In this problem, we have to show that  given three…

Q: Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

A: There are 3 elements in A And there are 2 elements in B

Q: Come up with an open interval A and closed interval B such that A U B = (0,4) and A (upside down U…

A:

Q: 2. Let A = {r|x is older than 25}, B = {y|y_is older than 50}, C = {z |z is between 20 and 30}. Draw…

A: The question is related to sets. The solution is explained below.

Q: Give a geometric description of the following sets of points. x2 + y2 - 14y + z2 ≤ -13

A: Consider the given equation: Here the objective is to give the geometric description of the given…

Q: 1 In the relation . If R, =1 and %3D R R R, R,%3D3, find R.

A:

Q: 4. Consider the relation R = {(-3, –3), (-3, –5), (-5, –7), (–7, –3), (–7, –7)} on the set А 3D {-1,…

A: We have to  (a) To Draw Directed Graph.  (b) To find R2=RoR.

Q: (b) Show that the set A = {(x, y) E R² : y > 0} is not complete.

A: Given: The given set ,

Q: 7. What is the significance of writing the domains in the following ways, what will be different…

A: To write the difference between both the ways od writing domain

Q: Graph the image of ALMN after a reflection across the line y = x. 10 9. 14 2. -10 -8 -4 -2 101 2 4.…

A: The rule for a reflection across the line y =x is x,y→y,x.

Q: 2 1-Find the geometric location of the relation z – 3 -ži = v2. 3

A:

Q: Show that the relation R defined in the set A of all polygons as R = {(P1, P2) :P1 and P2 have same…

A: Given, relation R defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have same number…

Q: 1.2 Consider the following subintervals of the real line: A = [2,5], B = (0,4). %3D (a) Express the…

A:

Q: Identify and sketch the graph of the following SURFACES. 2 = √9-y²

A: We have z=9-y2 Since z is square root of 9-y2 so z is positive always. We can write z=9-y2 as:…

Q: This is the graph of -2x + 4y 2 -4. O True O False

A: In -2x+4y≥-4Let -2x+4y=-4Let x=0 then4y=-4y=-44y=-1,If y=0 , then-2x=-4x=-4-2x=2Therefore line is…

Q: Select any of the following points that are on the graph of y = 3-2 %3D O (1, 6) O(-1, 1.5) O (3,…

A: Given: the graph of y=3·2x

Q: Give a geometric description of the following sets of points. x2 + y2 - 14y + z2 ≤-13

A:

Q: The arrow diagram below represents a relation. 1 2 3 Figure 1: An arrow diagram shous three…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 3. Write down the neighborhood of {X, y3} in the graph given below. X2 yi X6 y2 y6 y3 V5 y4 X5 X4

A: Solution :-

Q: Consider the relations given below: xRy:x loves y xRy:x2y iii. xRy:x is in the same classroom with y…

A: If x = y and y = x then we can say that relation is symmetric relation.

Q: [The graphs are labeled (a), (b), (c), (d), (e), and (f).] (a) (b) -5-4-3-2–1-- (c) (d) (e) (f) 1. +…

A: As per our guidelines only 1 question can be solved, Hence Exercises 1-6 is answered below in the…

Q: come back to an equation for the parabela in standart form (Q 7 -10 -3 (-1-21 -5 -10 trmine the…

A:

Q: consider the relation R={(1,a),(1,b), (3,b),(3,d), (4,b)} form X={1,2,3,4} and Y={a,b,c,d}. Thus…

A: Consider the relation

Q: 5) Compute the number of ordered pairs (x,y) with x>0 and y>0 that satisfy x+(y)=5.3 and y+(x)=5.7

A: In this question we have to find the number of ordered pairs (x,y).

Q: - List the ordered pairs in the relation R from A = (0, 1, 2, 3, 4} to B = {0, 1, 2, 3}, where (a,b)…

A:

Q: 4.4.4 List the relation on N defined bv h(x, y) e N x N : x > y } 9 Scanned with CS CamScanner as a…

A: The relation given is already a subset of the Cartesian product N x N. It can be written as follows.

Q: 1. Suppose that we have the binary relations R1 C Ax B, R2 C B×C, and R3 C C x D. Then the relations…

A: Use the following definitions, to obtain the solution. Let A and B be any two sets. The binary…

Q: How different can two sets of R ^ 2 that have the same boundary be?

A:

Q: Give an alternative description of the sets specified below. 1. {x ∈ R : x^2 = 1}. 2. {x ∈ Z : x >…

A:

Q: What is the distance between the vertices of the graphs corresponding to y = 4(x - 2)2 + 1 and y =…

A:

Q: a Are ALL the following three pairs in the relation R: (4.2) (1,2) (5,1) b Is 4 a minimum element?…

A: R=4,21,2,5,1a. (1,2) is not the element of R because from Hass diagram 2 is related to 1    here…

Q: Prove that for the sets. B={4x+3|X€Z3 we have A =B

A:

Q: out of it. Let A {2, 3, 4} and B {2,6, 8} and let Rbe the "divides" relation from A to B: %3D CHECK…

A: We will first find A×B then R and then we will draw  the arrow diagram for R.

Q: A relation consists of the following points and the segments drawn between them. Find the domain and…

A:

Q: 7) Sketch in the xy-pkane the set of all of numbers (x,4) that salisfy all the following three 4x +…

A:

Q: If an expoential relation such as y=bx, if b > 0 and b ≠ 1, then the y intercept is at zero. Is this…

A: The given problem is to check whether the y intercept is at zero is true or false.

Q: Q2: Test the symmetries of the graphs about which axis. y = x²y = 1 x2 + 4y? = 1

A:

Q: Clearly sketch in R3 the graphs of (a) y = z, (b) x = – 4.

A:

Q: Use the graph of y = Cax to determine C and a. Ay 10- C=I 8- 4- 2- -10-8 -6 -4 10 -2- -4- -6- 10-…

A:

Q: Let S be the set defined as follows: S := {(x, y) | 2x + 3y ≥ 12} On the graph provided below,…

A:

Q: 3. Eliminate B and a from the relation x = Bcos(wt + a) in which w is a parameter not to be…

A:

Q: 7.1.6 For the relation R = {(x, y) : x < y} defined on N, what is R-1, and what is the intersection…

A: The detailed solution is as follows below:

Q: practice question 3

A: Hey, since there are multiple subparts posted, we will answer first question. If you want any…

Q: The Cartesian product of finite and nonempty sets can be illustrated by the intersections of a…

A: Given:  a=nA and b=nB To find: Explain why the number of intersection points in the crossing line…