7.) the equation of the circle is
(x - 3)^2 + (y - 4)^2 = 25
If you substitute the point in you get
(6-3)^2 + (8-4)^2 = 25
3^2 + 4^2 = 25
9 + 16 = 25
25 = 25
Both sides of the equation are the same so it proves it lies on the circle
8.) you add the x coordinates together and divide by 2
7 + 4 = 11
11/2 = 5.5
You use +7 because you need to find the midpoint.
You then add 5.5 to - 7 or - 5.5 from 4
-7 + 5.5 = - 1.5
You do the same for y coordinates
6+5 = 11
11/2 = 5.5
6-5.5 = 0.5
So the coordinates of Rachel's house are
(-1.5, 0.5)
Part A: First, list multiples for each number. The multiples of 5 are: 5, 10, 15, 20, 25 30, 35, 40, 45, 50, 55, 60, etc. The multiples of 12 are: 12, 24, 36,48, 60, etc. The least common multiple is the first common multiple between the two, in this case being 60. The LCM of 5 and 12 is 60.
Part B: SImilar to above, list all factors for each number. 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. 81: 1, 3, 9, 27, and 81. The greatest common factor is the highest common number, 9 in this case. The GCF of 72 and 81 is 9.
Part C: To rewrite, we need to take out the 9 by dividing. 72/9 is 8. 81/9 is 9. Therefore, we would get 9(8+9), to equal 153. Your answer here is 9( 8 + 9 ). Hope this helped!
Check the picture below, so the parabola looks more or less like that.
now, the vertex is half-way between the focus point and the directrix, so that puts it where you see it in the picture, and the horizontal parabola is opening to the left-hand-side, meaning that the distance "P" is negative.
![\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\supset}\qquad \stackrel{"p"~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Ctextit%7Bhorizontal%20parabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%204p%28x-%20h%29%3D%28y-%20k%29%5E2%20%5Cqquad%20%5Cbegin%7Bcases%7D%20%5Cstackrel%7Bvertex%7D%7B%28h%2Ck%29%7D%5Cqquad%20%5Cstackrel%7Bfocus~point%7D%7B%28h%2Bp%2Ck%29%7D%5Cqquad%20%5Cstackrel%7Bdirectrix%7D%7Bx%3Dh-p%7D%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%5C%5C%5C%5C%20%5Cstackrel%7B%22p%22~is~negative%7D%7Bop%20ens~%5Csupset%7D%5Cqquad%20%5Cstackrel%7B%22p%22~is~positive%7D%7Bop%20ens~%5Csubset%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\begin{cases} h=-7\\ k=-2\\ p=-4 \end{cases}\implies 4(-4)[x-(-7)]~~ = ~~[y-(-2)]^2 \\\\\\ -16(x+7)=(y+2)^2\implies x+7=-\cfrac{(y+2)^2}{16}\implies x=-\cfrac{1}{16}(y+2)^2-7](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%20h%3D-7%5C%5C%20k%3D-2%5C%5C%20p%3D-4%20%5Cend%7Bcases%7D%5Cimplies%204%28-4%29%5Bx-%28-7%29%5D~~%20%3D%20~~%5By-%28-2%29%5D%5E2%20%5C%5C%5C%5C%5C%5C%20-16%28x%2B7%29%3D%28y%2B2%29%5E2%5Cimplies%20x%2B7%3D-%5Ccfrac%7B%28y%2B2%29%5E2%7D%7B16%7D%5Cimplies%20x%3D-%5Ccfrac%7B1%7D%7B16%7D%28y%2B2%29%5E2-7)
Answer:
1.7 units
Explanation:
The length of an arc is calculated using the formula below:
Substitute the given values of θ and r:
The length of the arc is 1.7 units.
Answer:
8.50
Step-by-step explanation:
Find the unit rate.
51/6 = 8.5
