Consider the function f(x) = x³ − 13x² +44x − 32. a. use the fact that x − 4 is a factor of f to factor this polynomial. b. find the x-intercepts for the graph of f. c. at which x-values can the function change from being positive to negative or from negative to positive? d. to sketch a graph of x, we need to consider whether the function is positive or negative on the four intervals x < 1, 1 < x < 4, 4 < x < 8, and x > 8. why is that? e. how can we tell if the function is positive or negative on an interval between x-intercepts? f. for x < 1, is the graph above or below the x-axis? how can you tell? g. for 1 < x < 4, is the graph above or below the x-axis? how can you tell? h. for 4 < x < 8, is the graph above or below the x-axis? how can you tell? i. for x > 8, is the graph above or below the x-axis? how can you tell?

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

~

what is the question?

step-by-step explanation: