Create similar right triangles by changing the scale factor of the right triangle. When the scale factor is 1, what is the ratio of the side length of the side opposite ∠A and the length of the hypotenuse? Change the scale factor to 3. What is the ratio of the side length of the side opposite ∠A to the length of the hypotenuse? What is the ratio of the side length of the side opposite any 30° angle and the length of the hypotenuse?

Jenisey has $24 to spend on seven pencils. after buying them she had $10. how much did each pencil cost.?

The length of a rectangle is x times the square root of 100. the width is one-half y more than three-halves x. given that the area of the rectangle is 125 cm2, which equation could represent the rectangle in terms of x and y? a) 5xy − 15x = 125 b) 5xy + 15x = 125 c) 15x2 − 5xy = 125 d) 15x2 + 5xy = 125

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?