Answer:
(x+3)² + (y+4)²=25
Step-by-step explanation:
The question is on equation of a circle
The distance formula is given by;
√(x-h)²+ (y-k)²=r
The standard equation of circle is given as ;
(x-h)²+ (y-k)²=r²
The equation of this circle with center (-3, -4) and radius 5 will be;
(x--3)² + (y--4)²=5²
(x+3)² + (y+4)²=25
Answer should be 0.9 or .9
I could help you, but how many paper clips were there? divide 7.20 by whatever number it is...
Answer:
Hi there!
The correct answer is: (x+8)² = 73
Step-by-step explanation:
First you want to modify the equation: x² + 16x - 6 = 3 into x² + 16x = 9 by adding 6 on both sides.
Then you analyze the new equation, if you can see, 16x is positive which means two positive numbers have to be added up to equal a positive. Which eliminates the choices that have (x-8)²
And now you are left with two choices:
(x+8)² =73 and (x+8)² = -55
Now remember, when you factor out (x+8)² it equals to x² + 16x + 64
next let's bring it back to the very first equation: x² + 16x = 9
now which choice matches the result x² + 16x = 9. The answer will be (x+8)² = 73 because when you subtract 64 on both sides you get 9.
Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
