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.
Answer:
3
Step-by-step explanation:
10.50 x 3 = 31.5
15 x 13 = 195
195 + 31.5 = 226.50
An acute angle is an angle that is less than 90°. An angle bisector is a ray drawn along an angle that bisects it into two equal and adjacent parts. Now, if the total angle is, say 270°, which is more than a half circle, it would result to two 135-degree angles. In this case, the angle is no longer acute, but obtuse.
Answer:
10 big and 27 small
Step-by-step explanation:
First do a random amount and move closer to the answer by changing the amount of bottles
110/5=22
3 x 7 = 21
Bottles too little so less big water bottles
50/5=10
81/3=27
37 bottles so Liz sold 10 big bottles and 27 small bottles.
Answer:
The answer is x = 13.
Step-by-step explanation:
first, move the constant to the right and change its sign, (+15)
3.75 x = 63.75 -15
next, subtract the numbers, (65.75 -15)
3.75x = 48.75
then, divide both sides of the equation by 3.75,
final answer, x = 13
