5y + 3y + 5 ≤ ‐2(2y + 4)

Answer:

2. Eunju is right

3. [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].

Step-by-step explanation:

Polynomial Remainder Theorem

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).

As a consequence, if a polynomial is divisible by x-a, f(a)=0.

Part 1:

Let's make:

[tex]f(x)=(x+b)^3+(x+c)^2-(b-c)[/tex]

To find out if x+b is a factor of f(x), we find f(-b):

[tex]f(-b)=(-b+b)^3+(-b+c)^2-(b-c)[/tex]

Operating:

[tex]f(-b)=(-b+c)^2-(b-c)[/tex]

The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).

Part 2:

We must find out if [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex] without using long division or synthetic division.

We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:

[tex]x^2+5x+6 =(x+2)(x+3)[/tex]

Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.

Let's make:

[tex]f(x)=x^4+5x^3+2x^2-20x-24[/tex]

Find f(-2):

[tex]f(-2)=(-2)^4+5(-2)^3+2(-2)^2-20(-2)-24[/tex]

[tex]f(-2)=16-5*8+2*4+40-24 =16-40+8+40-24=0[/tex]

Find f(-3):

[tex]f(-3)=(-3)^4+5(-3)^3+2(-3)^2-20(-3)-24[/tex]

[tex]f(-3)=81-5*27+2*9+60-24[/tex]

[tex]f(-3)=81-135+18+60-24 =0[/tex]

Since both f(-2) and f(-3) are zero, [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].

Answer:

17, 20, 23, 26, 29, 32,

Step-by-step explanation:

Answer:

17, 20, 23, 26, 29, 32, 35....

Step-by-step explanation:

cause that's how math was made

"don't have a good day, have a great day"

-Guy

Answer:

the crate weighs 26.31

Step-by-step explanation:

add 32.8 and 39.34 together and then subtract 98.45 from the sum. ^^

Answer:

the crate weighs 26.31

Step-by-step explanation:

add 32.8 and 39.34 together and then subtract 98.45 from the sum. ^^

Step-by-step explanation:

Answer:

n = -19/14

Step-by-step explanation:

Please transcribe this into a symbolic equation:

26n + 4 = 12n - 15

Then 14n = -19, or n = -19/14.

Answer:

F

Step-by-step explanation:

Answer:

As the x=-2 does not satisfy the inequality.

Therefore, the solution is False!

Step-by-step explanation:

Given the expression

[tex]x-10x+1<\:20+\:5x\:[/tex]

substituting the value x = -2

[tex]\left(-2\right)-10\left(-2\right)+1<20+5\left(-2\right)[/tex]

[tex]-2+20+1 < 20-10[/tex]

[tex]19 < 10[/tex]

As the x=-2 does not satisfy the inequality.

Therefore, the solution is False!

Answer:

81!    THANK YOU<3333333333333

Answer: 81

Step-by-step explanation: 9 x 9 = 81 Obviously

Answer:

-5 is the y intercept

Step-by-step explanation:

Answer:

You count something

Step-by-step explanation:

If you imagine 9 slots that are empty and you fill 3 of them then there is 6 empty slots so -6

Answer:

the origin is where the graph starts which is located at 0,0

Step-by-step explanation:

Answer:

its either 98 cm or 28 cm

Step-by-step explanation:

7 x 7 = 49 x 2 = 98 cm

14 x 2 = 28

Answer: 7

Step-by-step explanation:

3x (4 - 2) + 1

3x (2) + 1

6 + 1

7

Answer: x =5

Step-by-step explanation:

[tex]x + 3 + 3(x + 2) = - 24[/tex]

[tex]x + 3 + 3x + 6 = - 24[/tex]

[tex]4x + 9 = - 24[/tex]

[tex]4x = - 24 - 9[/tex]

[tex]4x = - 33[/tex]

[tex]x = \frac{ - 33}{4} [/tex]

Answer: 11. D 12.d 13. A

Step-by-step explanation:

Answer:

Evern though this isn’t a math question, I’ll still help you :)

11. Option D

12. Option D

13. Option B

Hope this helps! :)

Answer:

regular parabola but shifted up 3 on the y axis

Step-by-step explanation:

Answer:

There would be 30 black cars.

Since the ratio is 1:5

And we know that there are 6 red cars,

we basically just input it in our ratio

so it would look like 6:x

Now, we just have to plug in for x.

To do that, you have to multiply 6 by 5

To match the ratio.

So that would give us 6:30

And if we divide by 5 we should get our original ratio.

I know this seems confusing haha, but I hope you get it, it's not as hard as it looks !!

Answer:

y=2

Step-by-step explanation:

I think

it's been a while since I did functions

Answer:

the answer is y=2

Step-by-step explanation:

you add 8y+4y=12y

and then divide 12 on each side

which 24/12=2

Answer:

9?

Step-by-step explanation:

Answer:

sorry dont understaand

Step-by-step explanation:

Response:

I'll try if I can but

Answer:

2

Step-by-step explanation:

the two sides are 3 and its equal to 8..its 2

Answer:

A car takes 4 hours to reach a destination travelling at the speed of 63 km/h.

Speed = distance / time

Distance = speed × time

Distance it took the car, travelling for 4 hours to a destination at a speed of 63 kilometers per hour would be

4 × 63 = 252 kilometers.

if the car travels at a different speed of 56 kilometers per hour and the distance remains 252 kilometers, the time it takes will be

Time = distance / speed

= 252/56 = 4.5 hours

The time varies inversely with the speed. The more the speed, the lesser the time and the lesser the speed, the more the time.

Let speed = s and let time = t

s varies inversely with t

Introducing constant of inverse variation k, it becomes

s = k/t

When s = 56, t = 4.5

56 = k/4.5

k = 4.5 × 56 =252

This is the distance

Step-by-step explanation:

Answer:

$8.64

Step-by-step explanation:

Divide 3.24 by three to get the codt of one bottle,$1.08. multiply $1.08 by 8 and we get $8.64.

Answer:

y = 4x + 17

Step-by-step explanation:

y = mx + b              given points: (-3,5) (-5,-3)

[tex]\frac{5+3}{-3+5}[/tex] = [tex]\frac{8}{2}[/tex] = 4

y = 4x + 17

Answer:

6/8

Step-by-step explanation:

Answer:

1 -> 12s

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

zeros of the function are −2 and 3

Step-by-step explanation:

there is no -2 so H.3