On her birthday Julie receives three $25 gift cards and two $75 gift cards for her favorite store. She decides to go shopping with the goal of ending her trip with a balance of at least $50 in gift cards. Which of these purchases will allow Julie to do so? (No sales tax is charged)
A
a coffee maker for $88, software for $34, and a jacket for $51
lotion for $27, a bathrobe for $39, a pair of slippers for $19, a set of towels for $49, and an alarm clock for $46
.
C
glasses for $67 and a comforter for $109
D
jeans for $45 a wallet for $56, and a pair of boots for $78

What is the vertex form of f(x) = x2 + 6x + 3

Find the length of the following tangent segments to the circles centered at o and o' whose radii are 5 and 3 respectively and the distance between o and o' is 12. what is the tangent segment of cd?

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."