Answer:
k = 11.
Step-by-step explanation:
y = x^2 - 5x + k
dy/dx = 2x - 5 = the slope of the tangent to the curve
The slope of the normal = -1/(2x - 5)
The line 3y + x =25 is normal to the curve so finding its slope:
3y = 25 - x
y = -1/3 x + 25/3 <------- Slope is -1/3
So at the point of intersection with the curve, if the line is normal to the curve:
-1/3 = -1 / (2x - 5)
2x - 5 = 3 giving x = 4.
Substituting for x in y = x^2 - 5x + k:
When x = 4, y = (4)^2 - 5*4 + k
y = 16 - 20 + k
so y = k - 4.
From the equation y = -1/3 x + 25/3, at x = 4
y = (-1/3)*4 + 25/3 = 21/3 = 7.
So y = k - 4 = 7
k = 7 + 4 = 11.
So first you have to find the perfect square that matches up with x^2 + 6x
so half of 6, and square it. your perfect square is 9
x^2 + 6x + 9 = 7 + 9
then, condense the left side of the equation into a squared binomial:
(x + 3)^2 = 16
take the square root of both sides:
x + 3 = ± √16
therefore:
x + 3 = ± 4
x = - 3 ± 4
so your solution set is:
x = 1, -7
X = 96
100 137.4
137.4x=(100)(96)
137.4x=9600
137.4x/137.4=9600/137.4
x=70%
Hi there!
Looking at the graph, we can see exactly where the line crosses the y-axis (vertical line). The y-intercept is where the line goes through one point on the y-axis. The purple line goes perfectly through the point (0,4). Since the line goes through this point and the point is on the y-axis, the point (0,4), is the y-intercept.
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
