The answer is A. To understand that, you need to put it in order by the x's and the y's to get x^2-6x + y^2-16y = -48. Now complete the square on both the x and the y terms to get (x^2-6x+9) +(y^2-16y+64) = -48+9+64. Rewriting that in vertex form on the left and doing the math on the right gives you
(x-3)^2 + (y-8)^2 = 25, which shows you a center of (3,8) and a radius of 5.
Answer:
Step-by-step explanation:
3a²*2a³ = (2*3)(a² *a³)= 
Answer:
Step-by-step explanation:
Given the simultaneous equation 2p - 3q = 4 and 3p + 2q = 9, to get the value of p and q we will use elimination method.
2p - 3q = 4 ...................... 1 * 3
3p + 2q = 9 ..................... 2 * 2
Multiplying equation 1 by 3 and 3 by 2:
6p - 9q = 12
6p + 4q = 18
Subtracting both equation
-9q-4q = 12-18
-13q = -6
q = -6/-13
q = 6/13
Substituting q = 6/13 into equation 2
2p - 3(6/13) = 4
2p - 18/13 = 4
2p = 4+18/13
2p = (52+18)/13
2p = 70/13
p = 70/26
p = 35/13
<em>Hence p = 35/13 and q = 6/13</em>
<em></em>
<em>b) </em>If if 223ₓ = 87 find x
Using the number base system and converting 223ₓ to base 2 will give us;
223ₓ = 2*x² + 2*x¹ + 3*x⁰
223ₓ = 2x²+2x+3
Substituting back into the equation, 2x²+2x+3 = 87
2x²+2x+3-87 = 0
2x²+2x-84 = 0
x²+x-42 = 0
On factorizing:
(x²+6x)-(7x-42) = 0
x(x+6)-7(x+6) = 0
(x+6)(x-7) = 0
x+6 = 0 and x-7 = 0
x = -6 and 7
<em>Hence the value of x is 7 (neglecting the negative value)</em>
351 because 293 multiplied by 3 = 879, and 1230 - 879 = 351
Hopefully, you remember that the hypotenuse in a right triangle<span> is the longest side, which is also directly across from the </span>90<span> degree angle. It turns out that in a </span>30-60-90 triangle<span>, you can find the measure of any of the three sides, simply by knowing the measure of at least one side in the </span>triangle<span>.</span>
