84
(7x - 1)(6x + 5)
2x(x + 4)(x - 25)
16x2 - 49 = 42x2 - 72 = (4x)2 - 72 = (4x - 7)(4x + 7)
X=16 (i failed Algebra so it's probably wrong :D )
84 divided by 2 = 42 to check Ur answer you can multiply 42x2.
The one which says it is "6x".If that is not one of the statements, then you'll have to re-ask the question INCLUDING the statements so that your question NO LONGER CONTAINS INSUFFICIENT INFORMATION for it to be answered.
To find the answer, one does 4x4 to get your 4 squared. Then times that by 2. Then times that 4 times. It should look like this: (42x2)4 (16x2)4 (32)4 32x32x32x32 1,048,576
84 is composite because it factors are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28,42, 84
Kari's pulse rate is 84 beats per minute (21 beats in 15 seconds). In 30 seconds, there would be 42 beats (84 beats per minute * 30 seconds / 60 seconds).
If you fold a piece of paper in half, it doubles in thickness. Therefore, if you fold a piece of paper 42 times, it would be 2^42 layers thick, which is an incredibly large number and practically impossible to achieve in reality due to physical limitations.
There are many possible factorisations of 84 e.g. 42x2, 21x4, 2x3x14, etc. The prime factorisation of 84 is 2^2 x 3 x 7.
Okay, so you simply plug the equation of the line into the equation of the circle.(The reason you do this is because whenever they intersect, their x and y values are equal)I'll give an example.Say, for instance, you want to know if y=x+1 (the line) intersects with x2+y2=4 (the circle)Plug in the x+1 for the y in the circle.So you now have:x2+(x+1)2=4(Make sure that you include the parenthesis!)x2+(x+1)(x+1)=4x2+x2+2x+1=42x2+2x+1=42x2+2x-3=0Then you will use part of the quadratic formula, which is:x=(-b±√(b2-4ac))/2aFor this problem, you're interested in what the value under the radical sign is.(b2-4ac)Plug in the numbers22-(4)(2)(-3)4-(-24)4+2428When you plug in the numbers for b2-4ac (known as the discriminant)If the final result is:Greater than 0 - you have 2 intersection pointsEqual to 0 - you have 1 intersection pointLess than 0 - they do not intersectSo, for your original question, if the discriminant ends up being equal to or greater than 0, then the line and the circle intersect.I hope that made sense.