Answer:
The value of k=4
Step-by-step explanation:
we have
f(x)=0.4x
This function represent a linear direct variation (The line passes through the origin)
we know that
If f(x) is shifting up by 4 units
then
The y-intercept of the function will be the point (0,4)
therefore
The function g(x) will be -----> g(x)=0.4x+4 (equation of the line into slope
intercept form)
The rule of the translation
f(x) --------> g(x)
(x,y) -------> (x,y+4)
The translation is 4 units up
therefore
The value of k=4
<u>Directrix:</u>
If the vertex of the parabola is at (0, 0) and the focus is (0, -4) <em>which is 4 units down</em><em> </em>then the directrix will be the line 4 units UP.
Answer: y = 4
<u>Equation of parabola:</u>
; where p is the distance from the vertex to the focus.
As stated above, the focus is 4 units down, so p = -4
Answer: 
D is the answer for your question
Answer:
Center: (2,-1)
Radius: 4 units
Step-by-step explanation:
Equation of the circle in standard form is:
The radius of this circle is located at (-g, -f) and its radius is equal to:
The given equation of circle is:
Re-writing this equation in a form similar to the standard equation:
Comparing this equation with standard equation we can say:
g= -2
f = 1
c = -11
So, the center of the circle will be located at (-g, -f) = (2, -1)
And the radius will be = 
Thus the radius of the given circle is 4 units.
Answer:
Step-by-step explanation:
First we need to find their rate of speed.
r = d / t
For ant,
Convert millimeters to inches.
1 inch = 25.4 mm
18 mm = 0.7 inch
r = 0.7 / 5
r = 0.14 inches per second
For beetle,
r = 8 / 3
r = 2.7 inches per second
From the rates, you can tell that the beetle crosses the Garden first.
To know how long it takes for the ant to cross is by dividing the length by the rate.
1 yard = 36 inches
13 yards = 468 inches
468 ÷ 0.14 = 668.5 ≈ 669 seconds
In terms of minutes:
11 minutes and 15 seconds
The ant would cross the garden in 11 minutes and 15 seconds (or 669 seconds <em>up to you</em>).
