Answer:
n=2
Step-by-step explanation:
2000 pounds = 1 ton 600000 pounds = X tons Hence X tons = (600000 x 1) ÷ 2000 = 300 tons 3 x 10ⁿ = 300 Hence 3 x 10ⁿ = 3 x 10² Hence n= 2
N - Nicholes money
M - Marys money
(1) N + M = 4800 ⇒ N = 4800 - M
(2) N - 800 = M - 2/5M ⇒ N - 800 = 3/5M
subtitute (1) to (2)
4800 - M - 800 = 3/5M
4000 - M = 3/5M
-M - 3/5M = -4000
-8/5M = -4000 |multiply both sides by (-5/8)
M = 2500
subtitute the value of M to (1)
N = 4800 - 2500
N = 2300
Answer: Mary had at first $2500. (Nichole: $2300).
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: <em><u>C. the base period amount.</u></em>
<u><em>Explanation: </em></u>While implementing a horizontal analysis on a given income statement, we compute a percentage change in any individual item by dividing the dollar amount of change from base to current time period with <u><em>the base period amount.</em></u>
i.e. % Change in Individual item = 
<u><em>Therefore, the correct option in this case is (c)</em></u>
The axis of symmetry of a parabola like
is a vertical line of the form
where k is the x coordinate of the vertex of the parabola.
In particular, the x coordinate of the vertex of the parabola is given by
which in your case becomes
So, the axis of symmetry is the line
