Prove that if AS B, then A x CCB C.

Q: In AFGH, FH is extended through point H to point I, mZFGH = (x – 2)°, mZGHI= (4x – 5)°, and m/HFG=…

A: Given data: The measure of the angle FGH is m∠FGH=(x-2)°. The measure of the angle GHI is…

Q: In real-number multiplication, if uv = uw and u # 0, we can cancel u and conclude that v = w. Does…

A: To explain: either v=w or give counter example.

Q: et A = PDP 1 and P and D as shown belo 1 2 1 0 P = 3 5 0 2

A:

Q: 2. Find the measure of AB if C is the midpoint of AB AC= 6x- 20, and CB = 4x -2. %3D

A: Here we are given measurement of two parts of a line . With the help of mid point , we will…

Q: If t(x)=0.08e^xx^2 and a=5, what is t′(a) to the nearest tenth?

A:

Q: II, Write TRUE if the statement is true and False if it is false. For items 3 to 6, JUSTIFY by…

A:

Q: ax? +b?y +c°z?) a'x+ b°y+c°z xyz abc X y Z. if - prove that b %3D 3. a

A:

Q: A is symmetric

A: In this question, we have to check the matrix A is symmetric or not.

Q: Given: B is the midpoint of AC Prove: AB- BC

A: Given that:                       9. B is the mid point of AC.10. AD is the angle bisector of ∠BAC.

Q: If a > 0 and b < 0 which of the following must be true?

A: We have to choose the correct answer from the given option according to the given condition

Q: If $ = 2xy?z + x²y, evaluate $ dr where C 3 from

A: Given, ϕ=2xy2z+x2y, We have to evaluate ∫Cϕdr where C(a) C is the curve x=t, y=t2, z=t3 from t=0 to…

Q: Let A, BC X. Is Bd(A) C Bd(B)?

A: We want to check for A, B ⊂ X Is Bd(A) ⊂ Bd(B) true or false.

Q: Prove that la + b + c| < ]a] + ]b| + |c[

A: Prove that,    a+b+c≤a+b+c

Q: B = and C: .Prove that A = B² =C? = 1. 3. Given A = %3D

A: Given: A=0110, B=0-ii0, C=100-1 We know that for a 2×2 matrixP=abcd, P2 is given by…

Q: Prove: If (where b + 0 and d + 0), then C + d d a + b

A: Consider the given information, If ab=cd then show that a+bb=c+dd. First we consider ab=cd.

Q: prove the ged (atb,a?+b³) =16Y2 assuming that gcd (a,b) =1 •

A: It is given that gcd(a,b)=1

Q: B = { t,f,-3 is compact. IS %3D

A: See the attachment

Q: Starting with C = A + B, show that C × C = 0 leads to A × B = −B × A.

A: Given: C=A+Bif C×C=0, then A×B=-B×A

Q: atisfies the given conditions = 30.3°, B = 38.6°

A:

Q: Give a paragraph proof for the following problem. GIVEN: AB > CD and BC > DE PROVE: AC > CE A C D E

A: Given,  AB &gt; CD ................ (1) BC &gt; DE ................ (2)

Q: Which statement proves that ry? a b. 1/2 3/4 5/6 7/8 y 9/10 11/12 13/14 15/16 O 22 is supplementary…

A:

Q: If z = xye», x = u · 3“, and y = u · v², find dz when u ди 2 and v = 5.

A:

Q: Find the degree of Q(V2, V5) over Q.

A:

Q: Let floo) = 0e 5 and gloo) = 2a19 Detemine Cgof) (x) 2079. %3D %3D

A: Topic:- function

Q: 4. If A is a 4x4matrix and det A=2 , then det(34)is equal to (a) (b) 162 (c) 48

A: Given query is to find the det(3A) when matrix A is a 4 × 4 matrix.

Q: or (F)alse. Determine whether the following is (T)rue %3D Do,(ZABC)=ZA'B'C', then mZA'B'C' = 2…

A: answer the following

Q: Given: ZE= ZH ZHFG = LEGF Prove: AEGF= AHFG G

A:

Q: .Prove that la + b + c| < |a] + |b| + ]c]

A:

Q: .In AWXY, if ZX = ZY , WX = 9x – 11, XY = 4x + 1, and WY = 7x- 3, find x and the each side. measure…

A: Given that &lt;X = &lt;Y , so the opposite sides of them are equal.  WX=WY Or, 9x-11=7x-3 Or,…

Q: Show thet the fens- 14 ベ+ ナ (A+1)(2p+1) (P+1) (241)(38+) (uluse convedges if 8a and divesgus if Bsd…

A: We will use the following results to solve the given problem : Result 1 : ( Ratio Test )  Suppose…

Q: Is the following statement true or flase? Select one: True False 5 [ 2 (xy) dydx = chỉ xdx xdy) 0 0

A: To check whether the statement is true or not. Given information; The statement is ∫05∫02xydy…

Q: of af 42. Assume that w = (х, у) — ху, and (х, у) ду dw dw Find and at ds

A:

Q: If A %3D аx + За, and B %3D 5ax + 2а, — баz, find @AB- АВ

A: ANGLE BETWEEN TWO VECTOR

Q: В. In circle E, AB CD. A C В E 7. If mZCED=105, what is m AB? 105 8. If mZBAE= 3x- 40 and mZDCE =…

A:

Q: If C = {x:x² + 11x + 30 = 0, x ∈ N}, then C is a/an ?

A:

Q: Use the diagram shown. В C 主 G 丰 Which is a needed step to prove that AABF EAEDG

A:

Q: Given: WH – Z bisector W H Y MZOWH=mZ by reason

A: Topic = Triangle

Q: Suppose AART = ADEB. a. AEBD = ? b. AT = ? c. m ZR =

A: Given: ∆ART≅∆DEB To determine: a) ∆EBD≅? b) AT≅? c) m∠R =?

Q: Find (t), given 7(t) = (- 2 In(5t), - 5/5t, – et). %3D F'(t) =

A: Explanation of the solution is given below...

Q: Show that if A and B are similar, then AT and BT are similar.

A: Let A and B are similar matrices. By definition of the similar matrices.  The matric A and B are…

Q: Iff = xi + yj + zk, F| =r,and i =, then show that grad -)

A: r = (x2 + y2 + z2) 1/2 . Then, we have to calculate the grad( 1/r ).

Q: Show that A ∩ B = A ∩ C need not imply B = C.

A: Let, A= {1,2,3} , B= {2,3,4} and C= {2,3,5}

Q: 2. If A and B are mutually exclusive, P(A) = 0.3 , and P(B) =0.47, find %3D (а) Р(А); (b) Р(В'); (с)…

A:

Q: The translation of ABCD to A'B'C'D' is given by (x+[?lyD- IC A D C'. 1. -7 -6 -5 4 -2 -1 0 3 -1 A'…

A: According to the diagram, we have

Q: In the figure alongside, D is mid-point of BC. If 2CG = AC and BA//DE, prove that 3DF = FG. %3D

A: Consider the given triangle. Given that D is the mid point of BC. Hence, BD=DC. Also, the lines…

Q: = , where C is W 19

A:

Q: If A-B=0, implies that A*=B" %3D 0 صواب ylgn İhi O

A: Given A⇀-B→ = 0

Q: B) Prove that (A + B) +(C + D) = (A+B) (C+D) %3D

A:

Q: EF C and 0 are subsets of Y, then %3D

A: Solution for 6: Given C and D are the subset of Y. We have to show f-1(C)-f-(D)=f-1(C-D)

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.