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77julia77 [94]
4 years ago
11

Use the Rational Zeros Theorem to write a list of all potential rational zeros. f(x) = x3 - 5x2 + 8x - 24

Mathematics
2 answers:
masha68 [24]4 years ago
6 0
If I remember correctly this would be  obtained from the factors of  -24

so i think its +/-1, +/-2, +/- 3, +/- 4, +/- 8, +/- 6 , +/-12, +/-24

Sorry but i cant be sure
murzikaleks [220]4 years ago
5 0
ANSWER

All the potential rational zeros are:

\pm1,\pm2,\pm3,\pm4,\pm6,\pm8,\pm12,\pm24

EXPLANATION

The given polynomial function is

f(x) =  {x}^{3}  - 5 {x}^{2}  + 8x - 24
The leading coefficient is
1
The constant term of the polynomial is
- 24


According to the rational zeros theorem, the possible rational zeros of the given polynomial are all the factors of -24 expressed over all the factors of 1 in the simplest form.

The possible rational zeros are,

\pm1,\pm2,\pm3,\pm4,\pm6,\pm8,\pm12,\pm24
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If theta is a positive acute angles find theta when <br>2 sin^2 theta + 3 cos theta =3​
MArishka [77]

Answer:

Theta = 0, 60 degrees.

Step-by-step explanation:

2 sin^2 theta + 3 cos theta = 3​

Using the identity sin ^2 theta = 1 - cos^2 theta :

2(1 - cos^2 theta) + 3 cos theta  = 3

2 - 2cos^2 theta) + 3 cos theta  = 3

2 cos^2 theta - 3 cos theta   + 3 - 2 = 0

2 cos^2 theta - 3 cos theta   + 1 = 0

(2 cos theta - 1)(cos theta - 1) = 0

cos theta = 1/2 , cos theta = 1

Theta = 60 degrees or theta = 0

6 0
3 years ago
In a parenting magazine, Mrs. Smith read an advertisement about all the different ways that bleach can be used to kill bacteria.
babymother [125]

Question:

(a) How many bacteria would be found in 24 hours

(b) How many bacteria would be found in 2 days

(c) How long for 1000 bacteria to be found

Answer:

(a) 282429536481 bacteria

(b) 7.97*10^{22 bacteria

(c) 6 days

Step-by-step explanation:

The question illustrates an exponential function

y = ab^x

Where

a = Initial\ Value = 1

b=Rate = 3 --- i.e. triples

x = number\ of\ hours

Solving (a): Bacteria in 24 hours

In this case:

x = 24

Substitute x = 24, b = 3 and a = 1

So:

y = ab^x

y = 1 * 3^{24

y = 1 * 282429536481

y = 282429536481 bacteria

Solving (b): Bacteria in 2 days

2\ days =48\ hours

So:

x = 48

Substitute x = 48, b = 3 and a = 1

So:

y = ab^x

y = 1 * 3^{48

y =7.97*10^{22 bacteria

Solving (c): How long for 1000 bacteria

In this case:

y = 1000

Substitute y = 1000, b = 3 and a = 1

So:

y = ab^x

1000 = 1 *3^x

1000 = 3^x

Take Log of both sides

Log1000 = Log3^x

This gives:

Log1000 = xLog3

Make x the subject

x = \frac{Log1000}{Log3}

x \approx 6

<em>Hence: It takes 6 days</em>

8 0
3 years ago
I am not usre what the answer could be
lakkis [162]

Answer:

x \le 5

Step-by-step explanation:

Given

Shape: Cube

Dimensions: x, 3x and 2x

Volume < 900

Required

Show that x \le 5

First, calculate the volume

Volume = x * 3x * 2x

Volume = 6x^3

Volume < 900 becomes

6x^3 < 900

Divide both sides by 9

x^3 < 150

For x^3 < 150, the value of x as to be: 1, 2, 3, 4 or 5

Hence:

x \le 5

3 0
3 years ago
the total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. predict the total sales after 41 m
Nikitich [7]
You make each into an ordered pair so you will get (3,25,000) and (23,68,000)
So then you will plug it into the slope formula of y2-y1
 68,000-25,000        43,000                                --------
-------------------- =   ----------  = 2150                    x2-x1                                   
         23-3                     20
 now you plug it in 
y=2150x+b
25,000=2150(3)+b
25,000=6450+b
-6,450  -6,450
--------------------
18,550=b
put everything together 
y=2150x+18,550
y=2150(41)+18,550
y=88,150+18,550
y=106,700  dollars for 41 months 
7 0
4 years ago
What is 9 ×7 plus 1500
dolphi86 [110]
Just times 9 x 7 = 63 so, just add it to 1500, which leaves you with your answer. Which is.... 1563 

Hope that helped u!!!!!

3 0
3 years ago
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