Answer:
1) Slope-intercept form
2) 9200
3) 2 months
4) (0,200)
Step-by-step explanation:
A shelter had 200 animals in foster homes at the beginning of spring and the number of animals in foster homes at the end of the summer could be represented by
y=3000x+200 ............ (1)
Where x is the number of months and y is the number of animals.
1) The equation (1) is written in the slope-intercept form of a straight line equation.
2) After 3 months means x = 3 and the number of animals in the foster home after 3 months will be (3000 ×3 + 200) = 9200 (Answer)
3) Let after x months the animal population will become 6200.
So, 6200 = 3000x + 200
⇒ 3000x = 6000
⇒ x = 2 months (Answer)
4) If we put x = 0 in equation (1), then we get y = 200.
So, (0,200) is a point on the graph of the line. (Answer)
Let
x be the distance that the truck has left to travel
t be the the time
The total distance is 1675 miles
The average speed is 55 miles per hour
The equation that represents the distance that the truck has left to travel with respect to time is
55t + x =1675
x = -55t + 1675
Step-by-step explanation:
You have 5 digits.Youdonot say if duplication is allowed. I will assume not
For the first digit you have 5 choices. One of the 5 digits is gone.
You now have 4 digits to choose from. You pick one. Now you have but 3 left.
The total answer if 5*4*3*2*1 = 120
The x coordinate of the vertex will be the average of the two zeros, here -3 and 5, so x=(-3+5)/2 = 1, f(1)=(1+3)(1-5) = -16.
Answer: (1, -16)
Let's do it some other ways. How about completing the square to turn f in to vertex form?
f(x) = (x+3)(x-5) = x² - 2x - 15 = (x² - 2x + 1) - 1 - 15 = (x-1)² - 16
and now we can read off (1, -16) as the vertex.
The other method is the vertex is x= - b/2a = - (-2)/2(1) = 1.
Three methods, same answer. Good.