Step Statement Reason ABCD is a parallelogram AF FD Given ZFDA LEBC ZFAD E ZFDA In a triangle, angles opposite of congruent sides are congruent AD BC Opposite sides of a parallelogram are parallel ZFAD ZECB Parallel lines cut by a transversal form congruent alternate interior angles Type of Statement BE EC In a triangle, sides opposite of congruent angles are congruent

Q: Prove that Va - Vb is irrational number if 'a' and 'b’ are prime number?

A: Given To prove that a-b is irrational number if a and b are prime number.

Q: 483 4 (-3+2 (3-6)), 3 {11-3 (2+3)]

A:

Q: 1. Simplify the following expressions: a) (x– 1)(x+ 2) b) (х- 10) - (х — 2) c) 4(x – 1)(x+ 1) + 2(x…

A: topic - simplification

Q: ai a2 az 5. If b₁ b2 b3 C1 C2 C3 = 4, find a1 a2 bi b2 ܪ ܪ C₁ C2 4a3 - 2a2 4b3-2b2 203 - 02

A:

Q: Q) The Sum of three numbers is 6 If we multiply the third numbers by 2 and add the first number to…

A:

Q: 1 2 5. 2 . 5 +1. Va) da Find + C

A: Given: I=∫-5·x6+1x-2x6+1·xdx We know that; The Sum rule; ∫fx±gxdx=∫fxdx±∫gxdx The Power rule;…

Q: How many 10 digit real even number can be created (It cannot start with a 0) with 5 zeroes and 5…

A: Basic concepts of making combination are used. Information given, As we have only two choices of…

Q: (a) 1,2, ..., 16, i.e. such that the sum of all numbers in each row, each column and each diagonal…

A:

Q: If student 10 is not selected, then student 5 should be selected how can I represent this constrain…

A: Given If student 10 is not selected, then student 5 should be selected

Q: True or False and Why. {{1}, {42}} = {1, 42} U{{1}, {42}} = {1, 42} U{1, {1,42}} = = is What? Why?

A:

Q: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

A: Assume that there are 10 girls and 12 boys in the neighborhood club, and a team of 7 is to be…

Q: The sum of the squares of the first 5 fibonacci terms, check and prove

A: Fibonnaci Sequence is: 1,1,2,3,5,8,13,21,34,55,89,... (That is, each term of the sequence is the sum…

Q: 2. A student did not study for Philosophy quiz which consists of 10 true or false questions. If the…

A: Introduction: It is required to find all possible number of answers that can be given to the true or…

Q: In part 2) why is it K+1and K + 2 and so on(addition) instead of K1,K2,K3... (multiplication).

A: As you asked that why we use  instead of

Q: Which of the followings are false? I. General term of {2,3,2,3,...} is an =;+(-)". . General term of…

A: The details solution is given bellow.

Q: How many three-digit numbers are possible under each condition? (a) The leading digit cannot be zero…

A: We know that 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits in the number system.

Q: 1 금sin-1를 +C True False

A: We have to check

Q: In a health examination of the 72 faculties at Brac University, the numbers of faculty with blood…

A: The term probability is defined as the chance of occurrence of an event. The probability value…

Q: Find the values of z2n = 5- i, n will be taken from the set (2, 3, 4, 5} while w is the argument…

A: In the given question we have to find the value of z2n=5-i,n∈{2,3,4,5}.in the given we use the…

Q: Question 15) -9(7x + 4) + 2(7x + 4)

A:

Q: Which of the following is the graph of (y-2)² = −4(x - 2)² 12 5 n 24 X + 3 24 CV 9 T ny 7 T O & 7 6…

A: (y-2)2 = -4(x-2) compare with equation   (y-k)2 = – 4a(x-h) so we get   k = 2 h = 2 a = -1

Q: (-3z? – 4z + 7) - (2z2 + 2z – 1) - (2z - 3z + 7) = -3z? +z - 1 O True False

A:

Q: 7. 2,7. 7 5 5 5 x?.- x² + x2 (5 – + 1 +1) 고은 + x2•1

A: Given,

Q: At the end of a course the final grade is decided with the help of an oral examination. There are a…

A: (a) To maximize the chances of drawing an easy subject, the best position to choose is the fifth…

Q: Write the truth-functional form (TFF) for each sentence. Use P, Q, R, etc. as replacement letters.…

A: Since you have posted a multi sub part question according to guidelines I will solve first three…

Q: Question 9 (Show your solutions) In how many ways can 6 books be arranged on a shelf if: a.) any…

A: Here total 6 books arranged in shelf

Q: If A= { 1,2,3} and B= { 4,5,6} then , n(AxB) is equal to

A: We are given the set A and B and we need to find the number of elements in the Cartesian product…

Q: I need to do a table proof and I don't know what theorems and postulate to use for this. Will I…

A: Similar triangle property

Q: What is (4, 11) n (8, 12]? What is (4, 11) U (8, 12]?

A:

Q: (a) Given the word "CORPORATION", determine the number of i) three letters can be formed, if each…

A: The word CORPORATION has 8 unique letters (C,O,R,P A,T,I,N)

Q: Let a be a real number and f(x, y) = 2ax²y + 8xy³. Let v = 3i – j and let Vf(x, y) denote the…

A: use the formula for gradient of a function.

Q: What is (5, 7) N (6, 8]? What is (5, 7) U (6, 8]?

A: Solution: The given sets are

Q: 1 If A = -5 | -4 -7 then det (A). is Select an answer Thus, A-1 and det (A-1) = ||

A: if A =  abcd then | A | = ad - bc  A-1 = adjAA-1

Q: The solution for 'part b' is actually the same as 'part a' !!

A:

Q: Using strong PMI, show that every natural number is a sum of powers of 2. For example, 11 = 23 +2¹…

A: Using strong PMI, we have to show show that every natural number is a sum of powers of 2.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.