Show for all t>0 it is possible to find an angle A such that cosA = (2t)/((t^2)+1)

The sum of the product of 4 and x and the product of 7 and y is 61. the sum of the product of 12 and x and the product of 21 and y is 61. what are the values of x and y?

Celeste wants to have her hair cut and permed and also go to lunch. she knows she will need $50. the perm cost twice as much as her haircut and she needs $5 for lunch. how much does the perm cost?

Raj encoded a secret phrase using matrix multiplication. using a = 1, b = 2, c = 3, and so on, he multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. the matrix representing the encoded text is . what is the secret phrase? determine the location of spaces after you decode the text. yummy is the corn the tomato is red the corn is yummy red is the tomato