Please help me and explain this.

We want to find a polynomial

f(x) = a x³ + b x² + c x + d

such that the roots of f are x = -3, x = -1, and x = 4, and f(x) takes on a value of -24 when x = -2.

The factor theorem for polynomials tells us that we can factorize f(x) as

a x³ + b x² + c x + d = a (x + 3) (x + 1) (x - 4)

Expand the right side:

(x + 3) (x + 1) (x - 4) = x³ - 13x - 12

So we have

a x³ + b x² + c x + d = a x³ - 13a x - 12a

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

a = a (of course)

b = 0 (there is no x² term on the right)

c = -13a

d = -12a

We also have that f (-2) = -24, which means

f (-2) = a (-2 + 3) (-2 + 1) (-2 - 4)

-24 = 6a

a = -4

which in turn tells us that c = 52 and d = 48.

So we found

f(x) = -4x³ + 52x + 48

Answer:

Greatest Common Factor: 24

Step-by-step explanation:

The greatest common factor is found by multiplying all the factors which appear in both lists: So the GCF of 24 (2x2x2x3) and 48 (2x2x2x2x3) is 2x2x2x3 which is 24.

The greatest common factor of 24 and 48 is 24.

Here, we have,

To find the greatest common factor (GCF) of 24 and 48,

we can use the prime factorization method:

Step 1: Find the prime factorization of each number.

Prime factorization of 24:

24 = 2 * 2 * 2 * 3

Prime factorization of 48:

48 = 2 * 2 * 2 * 2 * 3

Step 2: Identify the common prime factors and their lowest exponents.

Common prime factors: 2 * 2 * 2 * 3

Step 3: Multiply the common prime factors with their lowest exponents.

GCF(24, 48) = 2 * 2 * 2 * 3 = 24

So, the greatest common factor of 24 and 48 is 24.

To learn more on GCF click:

brainly.com/question/30685324

#SPJ6

Answer:

The Trench or The Mariana Trench is the deepest part of the ocean.

Answer:

B) trench

Step-by-step explanation:

The deepest part of the ocean is called the Challenger Deep and is located beneath the western Pacific Ocean in the southern end of the Mariana Trench

I hope this helped you! If it did, please consider rating, pressing thanks, and giving my answer 'Brainliest.' Have a great day! :)

Answer:

here hope this helps please mark brainly

Step-by-step explanation:

Answer:

Step-by-step explanation:

4, because multiplying 2 1/3 by 4 would get you up to 9 1/3 just 1/3 below how much he had

Answer: f(2)=15, f(-2)=18, all real #s

Step-by-step explanation:

1. f(2)=4(2)^2-2+1=16-1=15

2. f(-2)=4(-2)^2-(-2)+1=16+3=18

Answer:

C??

Step-by-step explanation:

a says that y is bigger than -3

b says that 13 is less than or equal to y

c says y is smaller than 8

and d says y is equal to or smaller than 8

IM NOT SURE SKSJNSMS

Answer:

Y=21

X=8

Step-by-step explanation:

In the middle there is a right angle

therefore 27 +3y=90

Y will be 21

Then x+27+63+8x+18=180

x=8

Hence 8+27+3(21)+8(8)+18=180

Step-by-step explanation:

27 + 3y = 90

3y = 90 - 27

y = 21

27 + (21×3) + x + 8x + 18 = 180 ( angles on a straight line sum up to 180)

9x + 108 = 180

9x = 180 - 108

9x = 72

x = 72/9

x = 8 degrees

Answer:

x=3

Step-by-step explanation:

5(2x-3)=15

10x-15=15

10x=30

x=3

Answer:

x=3

Step-by-step explanation:

5(2x -3) = 15

10x-15=15

10x-15+15=15+15

10x=30

To find the x divide 10 to 30 so that is why 30÷10=3.

Answer:

kr3kf,,xdk,xe3,ke,kex,ks,l,sl,r4kf

Step-by-step explanation:

 nyjogtqGTKJMIYTRFEWDGTYU87R4EW2ERT5YUIO0IUJHYGFREDRGHJKL.BBRTBTRN

Answer:

Step-by-step explanation:

(2,3)

4+1+1=6

Step-by-step explanation:

she already has 4 necklaces so than she got 2 for a dollar so that equals 6.

Answer:

slope equals 2

Step-by-step explanation:

graph points and calculate rise over run

Answer:

2+x=O

x= -2

x€ Real number [-2+ infinite )

Answer:

[tex]x\geq -2[/tex]

Step-by-step explanation:

[tex]g(x)=\sqrt{2+x}[/tex]

We know we can only take the square root of a number greater than or equal to 0.

[tex]2+x\geq 0\\x\geq -2[/tex]

Answer:

hxdjgcfmv,hjb.kn

Step-by-step explanation:

hrzdxjcgfmv,guvmcdcfvmtfbudufuv,gh

Answer:

so i'm assuming you'd use Pythagoras:

so 15^2-12^2=81

square root it=9 which is I

to find T we do 41^2-9^2=1600

square root that is 40 so T=40

Answer: No

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

They don't have the same size.

The number of ways of distinct orders can be seated if two people of the same party are considered identical should be 5,544 ways.

[tex]= \frac{12!}{1!5!6!} \\\\= \frac{12\times11\times10\times9\times8\times7\times6!}{6!\times5\times4\times3\times2\times1}\\\\= \frac{12\times11\times10\times9\times8\times7}{5\times4\times3\times2\times1}\\\\= 5,544[/tex]

= 5,544 ways

Learn more about the panel here: https://brainly.com/question/24546489

Answer:

Step-by-step explanation:

4.

Given:

10:s

6:y

8:13

Solve:

8/13 = 10/s

s = 65/4 or 16.25 cm

8/13 = 6/y

y = 39/4 or 9.75 cm

5.

Given:

70ft:88ft

o/90ft

n/53ft

Solve:

70/88 = o/90

o = 1575/22 or 71.59 ft

70/88 = n/53

n = 1855/44 or 42.16 ft

6.

Given:

5.7in:9.1in

9.6in:e

11.2in:t

Solve:

5.7/9.1 = 9.6/e

e = 15.33 in

5.7/9.1 = 11.2/t

t = 17.88 in

7.

Given:

74m:48m

43m:u

64m:y

Solve:

74/48 = 43/u

u = 1032/37 or 27.89 m

74/48 = 64/y

y = 1536/37 or 41.51 m

8.

Given:

16cm:o

11.8cm:101 (I can't see if that is a 101 or 10.1 but I can do it both ways)

6.2cm:t

Solve:

11.8cm/101 = 16cm/o

o = 136.95

or

11.8cm/10.1 = 16cm/o

o = 13.69

11.8cm/101 = 6.2cm/t

t = 53.07

or

11.8cm/10.1 = 6.2cm/t

t = 5.3

9.

Given:

AB:AC

AE:AD

EB:DC

ABE:ACD are right angles

DC = P

We know that:

13ft:30ft

AE:AD are unknown

8ft:DC

We are looking for P?

Solve:

13ft/30ft = 8ft/P

P = 240/13 or 18.46

Answer:

∅ = 40.3°

General Formulas and Concepts:

Trigonometry

Step-by-step explanation:

Step 1: Define

Looking for m∠A

Step 2: Identify

adjacent leg of ∠A = AC = 7.4

hypotenuse = AB = 9.7

Step 3: Find theta

Answer:

d. Reject the claim that mean is 40 MPG when it is actually 40 MPG.

Step-by-step explanation:

The type 1 error could be said to have been made if the null hypothesis is erroneously rejected.

In the scenario above :

The null hypothesis (H0) : mean = 40

Hence, if the Null hypothesis defined above is rejected when in fact the hypothesis that the mean miles per gallon is actually 40.

On the other hand, the type 2 error occurs when a null which is false is not rejected.

Hence, when a true null is rejected, a type 1 error is committed. Similarly, when a false null isn't rejected, then a type 2 error has been committed.

hope this photo helps.enjoy

Answer:

gating

Step-by-step explanation:

This is your answer

Answer:

78

Step-by-step explanation:

is it right

im sure it might be 78 the correct

sorry po Bobo po ako sa math ☹️

Step-by-step explanation:

wala eh

Answer:

it should be c. y = 5.0

Step-by-step explanation:

use the line of best fit to see at what point on the line that x = 7.

Answer:

3 ÷ 2/5 = 0.5

5/8 ÷ 3/4 = 0.05

3/10 ÷ 1/2 ÷ 6/5 = 0.5

8/7 ÷ 4 = 0.28

2/3 ÷ 5/9= 1.2

11/2 ÷ 10 ÷ 5/4 = 0.44

Step-by-step explanation:

....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ..... ...φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ.... ....φ(︶▽︶)φ....

Answer:

Squirrel has High BLood pressure

Step-by-step explanation:

Squirrels

Answer:

If one −5s−7(8s−1): -61s+7

If two −5s−7(8s−1): -112s+14

Step-by-step explanation:

-5s-7(8s-1)

Multiply -7 onto 8s and -1:

-5s-56s+7

add -5s and -56s:

-61s+7

−5s−7(8s−1)−5s−7(8s−1)

Multiply both -7 to 8s and -1

-5s-56s+7-5s-56s+7

add:

-112s+14

Answer:

The answer is below

Step-by-step explanation:

a) A linear function shows the relationship between variables. A linear equation is in the form: y = mx + b, where m is the rate of change, b is the value of y when x = 0, y is the dependent variable and x is an independent variable.

Let U represent the number of umbrellas and p the price of the umbrella. At $10 the number of umbrella sold is 18000, it can be represented as (10, 18000) i.e. (p, U)

At $16 the number of umbrella sold is 9000, it can be represented as (16, 9000).

The linear function is determined using:

[tex]U-U_1=\frac{U_2-U_1}{p_2-p_1}(p-p_1)[/tex]

Given (10, 18000) and (16, 9000):

[tex]U-U_1=\frac{U_2-U_1}{p_2-p_1}(p-p_1)\\\\U-18000=\frac{9000-18000}{16-10}(p-10)\\\\U-18000=-1500(p-10)\\\\U-18000=-1500p+15000\\\\U=-1500p+15000+18000\\\\U=-1500p+33000\\\\U(p)=-1500p+33000[/tex]

b) At p = $20, The number of umbrella is:

U(20) = -1500(20)+33000

U(20) = 3000 umbrella

Answer:

I think you need to know the value of X to get this answer.

Step-by-step explanation:

Answer:

$35

Step-by-step explanation:

1,500/43.35