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3 years ago

P(x)⋅Q(x)=R(x); if P(x)=x+2 and R(x)=x3−2x2−6x+4, what is Q(x)?

Mathematics

1 answer:

STatiana [176]3 years ago

7 0

Answer: Q(x) = x² - 4x + 2

Step-by-step explanation:

P(x) · Q(x) = R(x) ⇒ Q(x) = R(x)/P(x)

R(x) = x³ - 2x² - 6x + 4 ÷ P(x) = x + 2

I will use synthetic division (but you can also use long division).

-2 | 1 -2 -6 4

| ↓ -2 8 -4

1 -4 2 0 ← remainder

The reduced polynomial is: x² - 4x + 2

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A fish starts swimming at -50m and increases 13m. Which equation best represents the situation and the fish's final elevation? a

marta [7]

Answer:

Step-by-step explanation:

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3 years ago

F(n)=4n g(n)=n2+2n find f(g(-6))

ELEN [110]

Answer:

When f(n) = 4n and g(n) = n² + 2n, f(g(-6)) = 96.

Step-by-step explanation:

To evaluate f(g(-6)), first find g(-6).

g(n) = n² + 2n

Substitute value.

g(-6) = (-6)² + 2(-6)

Square -6. Remember that (-x)² = x²

g(-6) = 36 + 2(-6)

Multiply 2 and -6.

g(-6) = 36 - 12

Subtract 12 from 36.

g(-6) = 24.

Now knowing this, substitute that value into f(n).

f(g(-6)) = f(24)

f(n) = 4n

Substitute value.

f(24) = 4(24)

Multiply 4 and 24.

f(24) = 96.

8 0

2 years ago

Don’t understand this question help please

yulyashka [42]

I think the answer is the second one. A reflection over the x-axis and the a 90° counterclockwise rotation about the origin.

4 0

3 years ago

Age c) The group is planning to build a fence around the garden. How many yards of fencing materials do they need for the fence?

FromTheMoon [43]

Answer:

Step-by-step explanation:

The perimeter is obtained by taking the sun of the fence :

Outer fencing :

Let's obtain b :

From Pythagoras :

b² = 15² - 12²

b = sqrt(225 - 144)

b = 9

Outer fencing = 2(12+6) + 2(8+9)

= 2(18) + 2(17)

= 36 + 34

= 70

Inner fencing :

(8 + 9 + 12 + 6 + 15 + 10) = 60

(70 + 60) = 130 yards

3 0

3 years ago

A bacterial culture grows exponentially according to the function n(t)=n(e^n), where n(t) is the quantity after t hours and n is

mart [117]

Answer:

$n(t=2) = 2 e^{1.386294361(2)}=32 grams$

So then after 2 hours we will have 32 grams.

Step-by-step explanation:

For this case we have the followin exponential model:

$n(t) = n e^{rt}$

n(t) is the quantity after t hours, n is the original quantityand t represent the hours and r the rate constant.

For this case we know that n(0) = 2 grams and n(3) = 128 grams and we want to find n(2)=?

From the initial condition we know that n = 2, and we have the model like this:

$n(t) = 2 e^{rt}$

Now if we apply the other conditionn(3) = 128 we got:

$128 = 2 e^{3r}$

If we divide both sides by 2 we got:

$64= e^{3r}$

If we apply natural log for both sides we got:

$ln(64) = 3r$

$r = \frac{ln(64)}{3}=1.386294361$

And our model is this one:

$n(t) = 2 e^{1.386294361t}$

And if we replace t = 2 hours we got:

$n(t=2) = 2 e^{1.386294361(2)}=32 grams$

So then after 2 hours we will have 32 grams.

5 0

2 years ago