Answer:
The circle's centre is at the position (3, 5), and it has a radius of 2
Step-by-step explanation:
First let's put it in a useful format by completing the squares:
x² + y² - 6x - 10y + 30 = 0
x² - 6x + y² - 10y = -30
x² - 6x + 9 + y² - 10y + 25 = -30 + 9 + 25
(x - 3)² + (y - 5)² = 4
This tells us that the centre position is (3, 5) and the radius is √4, or 2
ANSWER
The length of the diagonal is 5 ft
EXPLANATION
The diagram of the rug with the diagonal is:
The diagonal and the sides form a right triangle, so we can use the Pythagorean theorem to find x, the length of the diagonal:
![\begin{gathered} x^2=3^2+4^2 \\ x=\sqrt[]{9+16} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%3D3%5E2%2B4%5E2%20%5C%5C%20x%3D%5Csqrt%5B%5D%7B9%2B16%7D%20%5C%5C%20x%3D%5Csqrt%5B%5D%7B25%7D%20%5C%5C%20x%3D5%20%5Cend%7Bgathered%7D)
Answer: No and yes and no and yes??? ;-;
Step-by-step explanation:
Answer:
-512
Step-by-step explanation:
Rules of exponents come in hand here.
Multiplication rule: a^m x a^n = a^ m+n
Division rule: a^m / a^n = a^m-n
Negative exponent: a^-m = 1/a^m; 1a^-m =a^m
So it would be (-3)^7+5 / (-3)^-2; (-3)^12 / (-3)^-2; (-3)^12 x (-3)^2; (-3)^14
The answer is (-3)^14. If you multiply it out it is 4,782,969.
