Write the number in expanded form: Three hundred twenty-six thousand, five hundred eight and nine hundredths?

Factor f(x) = 15x^3 - 15x^2 - 90x completely and determine the exact value(s) of the zero(s) and enter them as a comma separated

Illusion [34]

Answer:

$x=-2,0,3$

Step-by-step explanation:

We have been given a function $f(x)=15x^3-15x^2-90x$ . We are asked to find the zeros of our given function.

To find the zeros of our given function, we will equate our given function by 0 as shown below:

$15x^3-15x^2-90x=0$

Now, we will factor our equation. We can see that all terms of our equation a common factor that is $15x$ .

Upon factoring out $15x$ , we will get:

$15x(x^2-x-6)=0$

Now, we will split the middle term of our equation into parts, whose sum is $-1$ and whose product is $-6$ . We know such two numbers are $-3\text{ and }2$ .

$15x(x^2-3x+2x-6)=0$

$15x((x^2-3x)+(2x-6))=0$

$15x(x(x-3)+2(x-3))=0$

$15x(x-3)(x+2)=0$

Now, we will use zero product property to find the zeros of our given function.

$15x=0\text{ (or) }(x-3)=0\text{ (or) }(x+2)=0$

$15x=0\text{ (or) }x-3=0\text{ (or) }x+2=0$

$\frac{15x}{15}=\frac{0}{15}\text{ (or) }x-3=0\text{ (or) }x+2=0$

$x=0\text{ (or) }x=3\text{ (or) }x=-2$

Therefore, the zeros of our given function are $x=-2,0,3$ .

7 0

4 years ago

A population of rabbits on a farm grows by 12% each year. Assume that this increase occurs as new baby rabbits at the beginning

jolli1 [7]

Answer:

a) r₁₂ = 104.36

In general, rₙ = arⁿ⁻¹

b)

- rabbit food consumed during the 10th year is approximately 832 pounds

- rabbit food consumed in total for the 1st through 10th years is approximately 5265 pounds

Step-by-step explanation:

Given that:

r1 = 30 and a farm grows by 12%

a = 30 and the common ratio r = 1.12

now

n r

1 30.00

2 33.60

3 37.63

4 42.15

5 47.21

6 52.87

7 59.21

8 66.32

9 74.28

10 83.19

11 93.18

12 104.36

Therefore r₁₂ = 104.36

In general, rₙ = arⁿ⁻¹

b)

if each rabbit consume 10 lbs of rabbit food each year

n r food consumed(lbs)

1 30.00 300

2 33.60 336

3 37.63 376

4 42.15 422

5 47.21 472

6 52.87 529

7 59.21 592

8 66.32 663

9 74.28 743

10 83.19 832

total 5265

Therefore, the rabbit food consumed during the 10th year is approximately 832 pounds

And the rabbit food consumed in total for the 1st through 10th years is approximately 5265 pounds

6 0

3 years ago

The latest online craze is a new game, Khan on Seven. You get 100 points for playing the game. In addition, you get 50 points fo

Anettt [7]

The inequality would be 50w + 100 >_ 18,000 ( the _ goes under the > but I cannot do that on my phone )

7 0

3 years ago

Read 2 more answers

If you rolled two dice, what is the probability

Softa [21]

Answer:

2/36 or 1/18 simplified

Step-by-step explanation:

you have all the combinations listed which is good.

probability = number of successful events / number of total events

look for the sums that are 11 and count them (there are 2 - 5,6 and 6,5).
total the number of all events (36)
so you then get the 2/36

there are

5 0

3 years ago

Help please really needed

Anarel [89]

Answer:

Either :

1/2 10x+1/2 20y+1/2 10z

or

5x+10y+5z

Step-by-step explanation:

You're just multiplying everything by 1/2

7 0

3 years ago