Solve for $x$, where $x > 0$ and $0 = -21x^2 - 11x + 40.$ Express your answer as a simplified common fraction.

Step-by-step explanation:

Hello, please consider the following.

The solutions are, for a positive discriminant:

Here, we have a = -21, b = -11, c = 40, so it gives:

So, we have two solutions:

We only want x > 0 so the solution is

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.