To give you a context on the problem, a tangent line is a line that intersects the parabola only at one single point. A parabola is a curve that forms an arc-shaped figure. A tangent line to a parabola is shown in the attached picture.
Now, we apply the concepts in calculus and analytical geometry. The first derivative of the equation is equal to the slope at the point of intersection. This slope must be equal to the slope of the tangent line.
y = x² - 5x + 7
dy/dx = slope = 2x -5
Since tangent lines must have the same slope with what they intersect with, we can determine the slope from the equation: y = 3x + c. This is already arranged in a slope-intercept form, where 3 is the slope and c is the y-intercept. So, we can equate the equation above to 3.
2x - 5 = 3
x = 4
Now, we substitute x=4 to the original equation of the parabola:
y = (4)² - 5(4) + 7
y = 3
Therefore, the point of intersection is at (4,3). Now, we use it to the equation of the tangent line to find c.
y = 3x + c
3 = 3(4) + c
c = -9
What is the slope of the line through (2,−2)(2,-2)(2,−2)left parenthesis, 2, comma, minus, 2, right parenthesis and (9,3)(9,3)(9
Musya8 [376]
The slope of line passing through (2,-2) and (9,3) is 5/7
Step-by-step explanation:
Given two points are:
(x1,y1) = (2,-2)
(x2,y2) = (9,3)
The slope is defined as the steepness of a line.
When two points are known, through which the line passes,
The slope is given by:

Putting the values

Hence,
The slope of line passing through (2,-2) and (9,3) is 5/7
Keywords: Slope, Equation of line
Learn more about slope at:
#LearnwithBrainly
It is easily observed that every coordinate was scaled up by a factor of 8.
(2×8=16, 3×8=24, 4×8=32, 6×8=48)
1.) 60-(20% of 60)
60-(.2 * 60)
60-12
48
The pants are $48
2.)30% of x = 20
.3x = 20
.3x/.3= 20/.3
x = 66.6666666...
The pants were $66.67
3.) 25 + (20% of 25)
25+(.2*25)
25+5
30
The magazine is now $30.
X=301/275
y=13/220
SolutionPlease find the attached image to get the complete solution.
I used online calculator to solve the system