50 POINTS PLUS BRAINLIEST

Answer:

[tex]a = -6, b = - 8[/tex]

Remaining factor = [tex]x+4[/tex]

Step-by-step explanation:

Given that:

Two polynomials:

[tex]x^{2} -x-2[/tex] and [tex]x^3 +3 x^2 +ax +b[/tex]

[tex]x^{2} -x-2[/tex] is a factor of [tex]x^3 +3 x^2 +ax +b[/tex].

To find:

The values of [tex]a[/tex] and [tex]b[/tex] from the cubic equation and the remaining factor.

Solution:

Let us first of all, factorize [tex]x^{2} -x-2[/tex].

[tex]x^{2} -2x+x-2=0\\\Rightarrow x(x-2)+1(x-2)=0\\\Rightarrow (x+1)(x-2)=0\\\Rightarrow x = -1, 2[/tex]

There are two factors of the given quadratic equation.

These two factors must also be factors of the cubic equation as well.

Putting [tex]x = 2[/tex]:

[tex]2^3 +3 \times 2^2 +a\times 2 +b =0\\\Rightarrow 2a+b=-20 ..... (1)[/tex]

Putting [tex]x = -1[/tex]:

[tex](-1)^3 +3 \times (-1)^2 +a\times (-1) +b =0\\\Rightarrow -a+b=-2 ..... (2)[/tex]

Subtracting (2) from (1):

[tex]3a = -18\\\Rightarrow a = -6[/tex]

From equation (1):

[tex]2\times (-6) + b=-20\\\Rightarrow b = -8[/tex]

Putting the values of [tex]a[/tex] and [tex]b[/tex] in the cubic equation, we get:

[tex]x^3 +3 x^2 -6x -8[/tex]

Dividing the cubic equation with quadratic, we get:

[tex]\dfrac{x^3 +3 x^2 -6x -8}{x^{2} -x-2} = x+4[/tex]

Answer:

the last one. hope I help u

Answer:

S<30

need explain that?

Answer:

10 units

Step-by-step explanation:

LMNO is a square.

All sides of square are equal

MN = LM

3x + 1 = x + 7

3x - x = 7 - 1

2x = 6

x = 6/2

x = 3

LM = x + 7 = 3 + 7 = 10

LM = 10 units

Answer:

A.  $5

B.  $7

C.  $40

D.  $4

Step-by-step explanation:

To find the unit rate, you need to divide the cost by the amount.

A.  $25/5 = $5 for a movie ticket

B.  $35/5 = $7 for one yard

C.  $240/6 = $40 for a calculator

D.  $8/2 = $4 for a can of tuna

Answer:

-12

Step-by-step explanation:

Step 1: Add 18 to both sides.

−2x−18+18=6+18

−2x=24

Step 2: Divide both sides by -2.

−2x

−2

=

24

−2

x=-12

Answer:

-2x -18=6

+18. +18

-2x=24

÷-2. ÷-2

×= -12

7x+4y-28=0 is the answer

Answer:

A

Step-by-step explanation:

If you were to dilate a point by a scale factor of 2, then if you have the point (-4,0), both the x value and the y value would be multiplied by 2, giving a coordinate of (-8,0). If you do this to the other point, you get (0,4).

Now graph it out, and you get a parallel line that is not right on top, eliminating answer B. It's not C because it is parallel, not intersecting. And it's not D because they are related, they're parallel.

Hope this helps!

Answer:

-2 wholes 4/25

Step-by-step explanation:

I used calculator. btw its -2 4/25

hope this helps! mark as brainliest!

Answer:

-2 4/25

Step-by-step explanation:

Answer: The answer is C on edge

Step-by-step explanation:

Answer:

$1,200

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

lil mosey

Step-by-step explanation:

Answer:

82.8

Step-by-step explanation:

Formula

multiply the length value by 36

Answer:

the line through the points negative 6 comma 0 and 0 comma negative 2

Step-by-step explanation:

Rewrite the equation to something you are familiar with such as the slope intercept form; y = mx + b. This means you need to solve for y.

3x + 9y = -18 --- divide everything by 3.

x + 3y = -6

3y = -6 - x

y = -2 - 1/3x

your slope is -1/3 and your y intercept is - 2.

remember, y-intercept is when x = 0. therefore, when x = 0, y = -2.

write as an ordered pair (0, -2). the only option that has (0, -2) is the second one.

Therefore, the line through the points negative 6 comma 0 and 0 comma negative 2.

Answer:0.01944444444 if it is like that then there is going to be a line above 4 for repeating.

Step-by-step explanation:

please let me know if this helps I had questions like this but I don't know if that what they are asking for you to do too! have a great day and I dont mean to be greedy but may i please have BRAINLIEST?    

Answer:

A and C

Step-by-step explanation:

Answer: The answer is 7-b=-y

Step-by-step explanation: You subtract b from one side to the other, and then do the same with y

Answer:

B

Step-by-step explanation:

If a point is on the line of origin it doesn't count as being in any quadrant.

Answer:

y = 3 /7 x − 17 /7

Step-by-step explanation:

Answer:

your x's will be -2, -1 , 0 , 1, 2

and your y's will be -5, -2, 1, 4, 7

Answer:

56.25 minutes

Step-by-step explanation:

1 mile is 6.25 minutes

9 miles is _____?

6.25 minutes x 9 miles =

56.25 minutes

Find Unit Rate to help solve

Hope this helps :)

Answer:

-19

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define Expression

3² + (9 - 16)(4)

Step 2: Evaluate

Answer:

Step-by-step explanation:

BODMAS=bracket

O=of

D=division

M=multiplication

A=addition

S=subtraction

3*3=9

9+(9-16)(4)

9+(7)(4)

9-28

-19

Answer:

Four

Step-by-step explanation:

29 plus 7 = 36 divided by 4= 9

Answer: See explanation

Step-by-step explanation:

Number of red marbles = 42

Number of blue marbles = 36

Total number of marbles = 42 + 36 = 78

There are 21 odd numbers between 1 - 42.

There are 18 odd numbers between 1 - 36.

(a) Probability that the marble is red will be:

P(red)= 42 / 78 = 7 / 13

(b) Probability that the marble is odd-numbered will be:

= 39 / 78 = 1/2

(c) Probability that the marble is red or odd-numbered will be:

P(red or odd) = P(red) + p(odd) - P(odd and red)

= (42/78) + (39/78) - (21/78)

= 60/78

= 10/13

(d) Probability that the marble is blue or even-numbered.

= P(blue) + P(even) - P(blue and even)

= 36/78 + 39/78 - 18/78

= 57/78

= 19/26

Answer:

-8m

Step-by-step explanation:

Combine like terms

−

−

7

{\color{#c92786}{-m}}{\color{#c92786}{-7m}}

−m−7m

−

8

{\color{#c92786}{-8m}}

−8m

Answer:

1. x= 10x6-9 Sherry is 51 apparently

2. $71.40

Step-by-step explanation: