Given:
The equation of a circle is
A tangent line l to the circle touches the circle at point P(12,5).
To find:
The gradient of the line l.
Solution:
Slope formula: If a line passes through two points, then the slope of the line is
Endpoints of the radius are O(0,0) and P(12,5). So, the slope of radius is
We know that, the radius of a circle is always perpendicular to the tangent at the point of tangency.
Product of slopes of two perpendicular lines is always -1.
Let the slope of tangent line l is m. Then, the product of slopes of line l and radius is -1.
Therefore, the gradient or slope of the tangent line l is 
.
Answer: 7,-7
Step-by-step explanation: 7 squared is 7 times 7 which equals 49
-7 times -7 is also 49 bc the negatives cancel each other out
Answer:
- C) (x − 3)2 = 25
- C) Factor out 4 from 4x2 + 40x.
Step-by-step explanation:
1. Adding the square of half the x-coefficient to both sides of the equation will "complete the square." That square is 9, so the result on the right is 16+9 = 25. Only selection C matches.
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2. To complete the square, you want to be able to put the quadratic into the form a(x -h)^2 = -k. For the purpose, it is most convenient to first factor "a" from the given quadratic. Then you can determine "-h" to be half the x-coefficient inside the parentheses.
Here, that looks like ...
4(x² +10x) = 80 . . . . . . . . . . step 1: factor out 4
4(x² +10x +25) = 180 . . . . . add 25 inside parentheses and the same number (4·25) on the right side of the equation
4(x +5)² = 180 . . . . . . . . . . . written as a square
Answer:
C
Step-by-step explanation:
look up rules of multiplying radicals.
You can multiply the radicands (the number inside the square root) then take the square root of the new number.
3*21 = 63
Factor 63 into 3*3*7
Pull out 3^2 from inside the square root
leaves you with 3sqrt7 or answer C
