Answer:
(6, - 4)
Step-by-step explanation:
A translation of 4 units right is equivalent to adding 4 to the x- coordinate
A translation of 3 units up is equivalent to adding 3 to the y- coordinate
(x, y) → (x + 4, y + 3) ← translation rule
Hence
(2, - 7) → (2 + 4, - 7 + 3) → (6, - 4)
Answer:
Step-by-step explanation:
<u>Equation of the line</u>
A line can be expressed in many forms.
The equation of the line in slope-intercept form is:
y=mx+b
Being m the slope and b the y-intercept.
The point-slope form of the equation of a line is:
y-k=m(x-h)
Where m is the slope and (h,k) is a point through which the line passes.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
We are required to find a line with slope m=4 passing through the origin (0,0).
Using the point-slope form:
y-0=4(x-0)
Simplifying
Answer:
60 mph
Step-by-step explanation:
We don't know how far Jimmy drives in each direction. Let this distance be d. Then, d = rate * time, and d = r(2 hours) (where r represents his speed while driving to the ferry).
But it's also true that d = (r - 20 mph)(3 hours).
Equating d = r(2 hours) and d = (r - 20 mph)(3 hours), we get:
r(2) = (r - 20)(3), or 2r = 3r - 60.
Subtracting 2r from both sides yields 0 = r - 60, so that r = 60 mph.
Jimmy averaged 60 mph on the outbound trip.
The frog's jump represent a geometric series.
The sum of finite geometric series can be solved using the equation:
Sn = ao ( (1-r^n)/(1-r) )
Plugging in the values,
S8 = 1 ( (1-2^8)/(1-2) )
S8 = 255
Therefore, after 8 hops, the frog will have traveled 255 inches
