If the answers are in the standard form of a line then it would be -x + (-3x) = -5y. This is because the standard form of a line is written as Ax + Bx = Cy
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:
width=11/2
length=8
Step-by-step explanation:
44=(2w-3) x w <em>area for a rectangle (44) = the length (2w-3) times the width (w)</em>
44=2w^2 - 3w <em>distribute</em>
2w^2-3w-44 = 0 <em>subtract 44 from both sides</em>
(w+4)(2w-11) <em>factor</em>
width=11/2
(11/2 x 2) - 3
length = 8
Answer:71
Step-by-step explanation:
range is the difference between the highest number and the smallest number in a group of data
Highest number=85
Smallest number=14
Range=highest number-smallest number
Range=85-14
Range=71
Step-by-step explanation:
n(U)= 150
n(F)=80
n(M)=70
n(MuN) complement= 30
