9514 1404 393
Answer:
f(x) = -1/3x +23/3
Step-by-step explanation:
You can use the linear regression function of a graphing calculator or spreadsheet to show you the equation of the line through these points:
f(x) = -1/3x +23/3
__
Approaching this in the usual way, we recognize we have points ...
(-1, 8) and (5, 6)
The slope of the line through those points is ...
m = (y2 -y1)/(x2 -x1)
m = (6 -8)/(5 -(-1)) = -2/6 = -1/3
Then the point-slope equation of the line is ...
y - 8 = -1/3(x +1)
Adding 8 gives us a form we can use for a function definition:
f(x) = -1/3(x +1) +8
f(x) = -1/3x +7 2/3
Answer:
Distance to appointment point = 5 miles
Step-by-step explanation:
Let s be the distance to the appointment point,
We have Maria drove to a business appointment at 50mph in the morning.
Time taken in the morning
Her average speed on the return trip in the afternoon was 40 mph.
Time taken in the afternoon
Given that the return trip took 1/4hr longer because of traffic.
That is
Substituting
Distance to appointment point = 5 miles
Answer:
y value = 49
Step-by-step explanation:
You are going to be completing the square
y = - x^2 - 10x + 24 Take a minus outside the brackets for the first 2 terms.
y = - (x^2 + 10x) + 24
Take 1/2 the linear term (1/2 10 and square it. Put that value inside the brackets. 1/2* 10 =5; 5^2 = 25
y = - (x^2 + 10x + 25) + 24
Add 25 outside the brackets.
y = -(x^2 + 10x + 25) + 24 + 25. You should stop here and consider why you are adding 25 outside the brackets. It is because there is a - sign in front of the trinomial and what is inside the brackets is really - 25 when the brackets are removed. Therefore to balance that, you add 25.
Now complete the square.
y = - ( x + 5)^2 + 49
The value you seek is 49.
=============
I'll confirm this with a graph.
Answer:the square footage of the parallelogram is 299 square feet.
Step-by-step explanation:
The formula for determining the area of a parallelogram is expressed as
Area of parallelogram = length × perpendicular height.
From the digram shown,
Length of the parallelogram is 23 feet.
perpendicular height of the parallelogram is 13 feet
Area of parallelogram = 23 × 13 = 299 square feet.
