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4 years ago

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

2 answers:

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

Answer:

(a) 282429536481 bacteria

(b) $7.97*10^{22$ bacteria

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

Read 2 more answers