Answer:
- solution: (1/(1+m), m/(1+m))
- no solution for m = -1 (lines are parallel)
Step-by-step explanation:
Two distinct lines will always have a point of intersection, provided they are not parallel. That is, the system of equations {x +y = 1, y = mx} will have a unique solution as long as m ≠ -1.
The solution to the system can be found by substitution:
x +mx = 1
x(1 +m) = 1 . . . . factor out x
x = 1/(1+m) . . . . . divide by the coefficient of x; we must have m ≠ -1
y = m/(1+m) . . . . find the y-coordinate of the solution
The point of intersection is (1/(1+m), m/(1+m)).
__
The above solution is undefined when the denominator is zero: m = -1. There is no solution for m = -1.
Given:
A number is q, multiply it by 2 and add 5.
You get the same answer as when you minus 2 from q.
To find:
The value of q.
Solution:
The algebraic representation of the statement "a number is q, multiply it by 2 and add 5" is
Multiply q by 2 = 2q
Multiply q by 2 and then add 5 : 2q + 5
So, the first result is 2q+5.
When you minus 2 from q = q-2
So, the second result is q-2.
According to the question, both results are equal. Equate both results to get the value of q.
Isolate variable terms.
Therefore, the value of q is -7.
Answer:
The angle Rick must kick the ball to score is an angle between the lines BX and BZY which is less than or equal to 32°
Step-by-step explanation:
The given measures of the of the angle formed by the tangent to the given circle at X and the secant passing through the circle at Z and Y are;
The direction Rick must kick the ball to score is therefore, between the lines BX and BXY
The angle between the lines BX and BXY = ∠XBZ = ∠XBY
The goal is an angle between 
Let 'θ' represent the angle Rick must kick the ball to score
Therefore the angle Rick must kick the ball to score is an angle less than or equal to ∠XBZ = ∠XBY
By the Angle Outside the Circle Theorem, we have;
The angle formed outside the circle = (1/2) × The difference of the arcs intercepted by the tangent and the secant
We get;
∠XBZ = (1/2) × (122° - 58°) = 32°
The angle Rick must kick the ball to score, θ = ∠XBZ ≤ 32°
Two thirds is equal to 66.666666 etc. percent so 64 is pretty close to 66 so I would consider it right.
Answer: God
Step-by-step explanation: LORD HAVE MERCY
