Afamily is traveling in a car at a constant average speed during a road trip. the function d(t)=70t+620 models the distance d, in miles, the family is from their house t hours after starting to drive on the second day of the road trip.
a) at what average speed is the family's car traveling?
-explain
b) what is the distance between the family's house and the point where they started driving on the second day
-explain

A.  70 miles per hour B.  620 miles from home

Step-by-step explanation:

This function is a linear equation, following the slope-intercept form of a line.  This standard form is y = mx + b, where m is the slope and b is the y-intercept.  The slope of a line is the rate at which the steepness of the line is changing.  The y-intercept is where the function is "starting".

In our case, the number in the rate of change position is 70.  It is being multiplied by t.  If t = 1, that means that after 1 hour, we have gone 70 miles.  If t = 2, that means after 2 hours we have gone 140 miles.  If t = 3, that means that after 3 hours, we have gone 210 miles; etc.  That number in the slope position represents the rate at which you are traveling PER HOUR; the slope.

The "starting" position of day 2 is found in the y-intercept.  Replacing x with 0, meaning NO time has gone by at all, at the beginning of the second day, we are starting 620 miles from home.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3