A 43-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece, and the third piece is three inches more than seven times the length of the first piece. Find the lengths of the pieces.

Tod does not have any cookies. david gives jeff 8 cookies. then he splits half of the cookies he has left with tod. david let’s c represent the number of cookies that he starts with. he finds the number of cookies that tod has is 1/2 the difference of c and 8. write an expression to represent the number of cookies that tod has.

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?

A3-dimensional figure has a square base and 4 lateral faces that meet at a point. explain the difference between the cross sections when a slice is made perpendicular to the base through the vertex, and when a slice is made perpendicular to the base and not through the vertex