Algebra Answers

What is the next term in the geometric sequence -270, 90, -30?

Choose the answer you think is most appropriate among the given options.Six scientists A, B, C, D, E, and F are to present a paper each at a one-day conference,Three of them will present their papers in the morning session before the lunch break whereas the other three will be presented in the afternoon session. The lectures have to be scheduled in such a way that they comply with the following restrictions:B's should present his paper immediately before C's presentation; their presentations cannot be separated by the lunch break.D must be either the first or the last scientist to present his paper.45. In case C is to be the fifth scientist to present his paper, then B must be.
Answers
Choose an answer
First
Second
Third
Fourth
Sixth

At the movie theatre, child admission is $6.00 and adult admission is $9.40 . On Saturday, 147 tickets were sold for a total sales of $1198.20. How many adult tickets were sold that day?

Which of the following statements are true? Please justify the answers.
1. a≥b⇔-a≤-b is an absolute inequality.
2. If A=φ,B={1,2},C={-1,-2}, then A×B×C has 4 elements.
3. The argument of 1+√(3)i is π/3.
4. A linear equation over R can have at most one root in C\R.
5. |x₁-x₂|=|x₁|-|x₂|∀x₁,x₂∈R

Which of the following statements are true? Please justify the answers.
1. For any two sets A and B, A∩Bᶜ=A\B.
2. The matrix [1 1 is singular.
0 0]
3. The contrapositive of '∃ y∈Z such that P(y) is true' is '∃ x∈Z such that P(x) is true'.
4. The system 2x-3y=1 and 6y-4x+2=0 has a unique solution.
5. If x, y∈C such that x²=y and y²=x, then x=y=1.

To prove that 2ⁿ>1+n√(2ⁿ⁻¹)∀n>2, using:
Cauchy-Schwarz Inequality;
Weierstrass Inequalities;
Tchebychev's Inequalities.

3 major projects P₁, P₂, P₃, are being funded by 3 voluntary agencies V₁, V₂, V₃. V₁, V₂, V₃, are willing to pay Rs. 8,000/-, Rs. 4,000/- and Rs. 2, 000/-, respectively per person on the project P₁; Rs. 4,000/-, Rs. 3,000/- and Rs. 4, 000/- respectively per person on P₂; and Rs. 3,000/-, Rs. 5,000/-, Rs. 8,000/- respectively on the project P₃. Further, the amount that V₁, V₂, V₃, have kept aside for paying people on these projects is Rs. 2,17,000/-, Rs. 1,42,000/- and Rs. 1,32,000/- respectively. How many people should each project employ so that the total money available is utilised?

Consider the equation E ≡ 5x-2y=3.
Write down equations E₁, E₂, E₃, respectively so that
1.) E and E₁ are inconsistent;
2.) E and E₂ have a unique solution;
3.) E and E₃ have infinitely many solutions.

To apply Cramer's rule to solve the following system of equations:
2x₁+x₂+x₃=4
x₁-x₂+2x₃=2
3x₁-2x₂-x₃=0

To solve the linear system:
x+2y=4, 3x-y=2 .......(1)
by substitution.
If 4x+y=c, ax+by=3 is a system having the same solution set as (1), find a,b,c.