Algebra Answers

A bag contains 15 green 18 yellow and 16 orange balls one ball is randomly selected to the nearest percent what is the probability of the event

at roosevelt high school there are six more students on the newspaper staff than on the boys? varsity tennis team and a total of 42 students in these two clubs. how many students work on the newspaper, and how many are on the boys tennis team if none of the students are involved in both organization

One integer is seven less than another integer. The product of these two integers is 228. What are the two intergers?

The sum of the squares of two consecutive is 1201. What are the integers?

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

Write the converse of the statement:
‘If p and q are the only roots of a polynomial f over C , then 2 deg f = .’

Give a direct proof, as well as a proof by contradiction, of the following statement:
‘ B A ∩ B ⊆ A ∪ for any two sets A and B

Find the polynomial equation over R of lowest degree which is satisfied by 1− i
and 3 + .i2

Use De Moivre’s theorem to show that cos3θ = 4cos θ − 3cosθ
3
.

Let A = { x ∈Z x is a multiple of 5} and B = { x∈Z x is a divisor of 20}.
Represent B,A and A &cap B c, where &cap means the intersection of sets and B c means the complement of the set B,
by the listing method and in a Venn diagram.