Aperçu des questions

1. 1. If a pentagon P with vertices at (– 2, – 4), (– 4, 1), (–1, 4), (2, 4), and (3, 0) is reflected across the line y = x to get a new pentagon, P’, then one of the vertices of P’ is
2. 2. The length of a rectangle is twice its width. Given the length of the diagonal is $5\sqrt{5}$, find the area of the rectangle.
3. 3. A positive integer n is called “powerful” if, for every prime factor p of n, p^2 is also a factor of n. An example of a powerful number is
4. 4. At breakfast, lunch, and dinner, Joe randomly chooses with equal probabilities either an apple, an orange, or a banana to eat. On a given day, what is the probability that Joe will eat at least two different kinds of fruit?
5. 5. Suppose $f(x)$ is a function that has this property: For all real numbers $a$ and $b$ such that $a<b$, the portion of the graph of $y=f(x)$ between $x=a$ and $x=b$ lies below the line segment whose endpoints are $(a,f(a))$ and $(b,f(b))$. (A function with this property is called strictly convex.) Given that $f(x)$ passes through $(-2,5)$ and $(2,9)$, what is the range of all possible values for $f(1)$? Express your answer in interval notation.

… et 35 autres questions.

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