1. 5^-12<span> because a^m * a^n = a^m+n</span>
2. 10<span> because a^m / a^n = a^m-n</span>
3. -3 because ( a^n)^m = a^n*m
<span>4. (5^-6 * 5^2) / 5^-4 = 5^-4 / 5^-8 = 5^-4+8 = </span>5^4
<span>5. 5^8 / ( 5^-4)^-3 = 5^8 / 5^12 = 5^8-12 = </span>5^-4
1. To solve this exercise, you must use the "Intersecting chords theorem".
2. You have that:
AP=3.5 in
PC=6 in
DP=4 in
3. Then, by applying the "Intersecting chord theorem", you have:
(AP)(PC)=(BP)(DP)
4. When you substitute the values into (AP)(PC)=(BP)(DP), you obtain:
(3.5 in)(6 in)/BP(4 in)
5. Now, you must clear BP. Then:
(3.5 in)(6 in)/4 in=BP
21 in^2/4 in=BP
6. Therefore, the value of BP is:
BP=5.25 in
(-1,8) is the correct answer I’m pretty sure
Two rectangles can be similar, but that's not always guaranteed.
In fact, similar shapes have the same angles and correspondant sides in proportion.
All rectangles will always have four right angles, so we only have to worry about the sides.
Let be the sides of a rectangle, with . Let be the sides of a rectangle, with .
Then, the two rectangles are similar if and only if
So, for examples, a rectangle with dimensions 3 and 7 is similar to a rectangle with sides 6 and 14 (both sides have been doubled), but it's not similar to a rectangle with sides 6 and 21 (one side has been doubled, the other has been tripled).