Answer:
Step-by-step explanation:
<u>Equation of a line</u>
A line can be represented by an equation of the form
Where x is the independent variable, m is the slope of the line, b is the y-intercept and y is the dependent variable.
We need to find the equation of the line passing through the point (7,2) and is perpendicular to the line y=5x-2.
Two lines with slopes m1 and m2 are perpendicular if:
The given line has a slope m1=5, thus the slope of our required line is:
The equation of the line now can be expressed as:
We need to find the value of b, which can be done by using the point (7,2):
Operating:
Multiplying by 5:
Operating:
Solving for b:
The equation of the line is:
Answer:
The length of the chord is 16 cm
Step-by-step explanation:
Mathematically, a line from the center of the circle to a chord divides the chord into 2 equal portions
From the first part of the question, we can get the radius of the circle
The radius form the hypotenuse, the two-portions of the chord (12/2 = 6 cm) and the distance from the center to the chord forms the other side of the triangle
Thus, by Pythagoras’ theorem; the square of the hypotenuse equals the sum of the squares of the two other sides
Thus,
r^2 = 8^2 + 6^2
r^2= 64 + 36
r^2 = 100
r = 10 cm
Now, we want to get a chord length which is 6 cm away from the circle center
let the half-portion that forms the right triangle be c
Using Pythagoras’ theorem;
10^2 = 6^2 + c^2
c^2 = 100-36
c^2 = 64
c = 8
The full
length of the chord is 2 * 8 = 16 cm
X+y=155. Y= -x+155
1.50x +4(-x+155)= 520
1.50x-4x+620=520
-2.5x =-100
X= 40. Y=110
Answer:
y = -|x|+2
Step-by-step explanation:
The graph represents y = |x| where the given graph opens upside down so it's negative and +2 translation towards the top
Answered by GAUTHMATH
