5m-8=3m+8
(Plus the '8' to both sides)
5m=3m+16
(Subtract '3m' from both sides)
2m=16
(Divide by 2)
m=8
The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).
<h3>What is a circle?</h3>
It is a locus of a point drawn an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
Prove algebraically that the straight line with equation x = 2y + 5 is a tangent to the circle with equation x² + y² = 5.
x = 2y + 5 ...1
x² + y² = 5 ...2
If the intersection of the point of the circle and line is one. Then the line is tangent to the circle.
Then from equations 1 and 2, we have
(2y + 5)² + y² = 5
4y² + 25 + 20y + y² - 5 = 0
5y² + 20y + 20 = 0
5y² + 10y + 10y + 20 = 0
5y (y + 2) + 10(y + 2) = 0
(5y + 10)(y + 2) = 0
y = -2, -2
Then the value of y is unique then the value of x will be unique.
The value of x will be
x = 2(-2) + 5
x = -4 + 5
x = 1
The intersection point is only one. Then the equation of the line is tangent to the circle at point (1, -2).
More about the circle link is given below.
brainly.com/question/11833983
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Answer:
Step-by-step explanation:
Solutions, zeros, and roots of a polynomial are all the same exact thing and can be used interchangeably. When you factor a polynomial, you solve for x which are the solutions of the polynomial. Since, when you factor a polynomial, you do so by setting the polynomial equal to 0, by definition of x-intercept, you are finding the zeros (don't forget that x-intercepts exist where y is equal to 0). There's the correlation between zeros and solutions.
Since factoring and distributing "undo" each other (or are opposites), if you factor to find the zeros, you can distribute them back out to get back to the polynomial you started with. Each zero or solution is the x value when y = 0. For example, if a solution to a polynomial is x = 3, since that is a zero of the polynomial, we can set that statement equal to 0: x - 3 = 0. What we have then is a binomial factor of the polynomial in the form (x - 3). These binomial factors found from the solutions/zeros of the polynomial FOIL out to give you back the polynomial equation.
Answer: 169.56 or 170 units^3
Step-by-step explanation:
Volume of a cylinder
3.14(3)^2=28.26*6=169.56
