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3 years ago

12

Write the polynomial as a product: p^2q+r^2–pqr–pr Thanks so much! Love you all who help!

1 answer:

Anarel [89]3 years ago

5 0

Factor the equation so...
(r^2-pr) and (p^2q-pqr)

Factor out (r^2-pr) = r(r-p)
Factor out (p^2q-pqr) = pq(p-r)

Add a negative to r(r-p) to make it -r(p-r)

(pq-r)(p-r) is the answer... I'm sorry I can't explain things well, but I tried.

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10. Determine the open interval(s) on which the function f(x) = 12x - x^3 is increasing.

Gre4nikov [31]

Answer:

$\large\boxed{x\in(-2,\ 2)}$

Step-by-step explanation:

$f(x)=12x-x^3$

Calculate the derivative of the function:

$f'(x)=\left(12x-x^3\right)'=(12x)'-\left(x^3\right)'=12-3x^2$

Calculate the zeros of the derivative:

$f'(x)=0\Rightarrow12-3x^2=0\qquad\text{add}\ 3x^2\ \text{to both sides}\\\\3x^2=12\qquad\text{divide both sides by 3}\\\\x^2=4\to x=\pm\sqrt4\\\\x=\pm2$

Let's check the derivative sign:

$f'(x)>0\iff12-3x^2>0\qquad\text{use the distributive property}\\\\-3(x^2-4)>0\\\\-3(x^2-2^2)>0\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\-3(x-2)(x+2)>0\\^{\qquad x=2\qquad x=-2$

Sketch a parabola open down

(before the brackets there is the number -3 < 0)

Look at the picture.

Where the derivative is negative, the function decreases.

Where the derivative is positive, the function increases.

Therefore your answer is:

$x\in(-2,\ 2)$

3 0

3 years ago

How do I solve this puzzle?

Zarrin [17]

Answer: use division

Step-by-step explanation:

8 0

3 years ago

At the beginning of March, a store bought a rake at a cost of 9$ and marked it up 130%. At the end of the month, the rake had no

docker41 [41]

Answer:

the new discounted price is $5.85

Step-by-step explanation:

First convert 130% into a decimal: 130 ÷ 100 = 1.3

Next multiply 1.3 by 9: 9 x 1.3 = 11.7

Then convert 50% into a decimal: 50 ÷ 100 = 0.5

Last multiply 11.7 by 0.5: 11.7 x 0.5 = 5.85

8 0

2 years ago

The sum of Andy and Brett's ages is 44. Andy's age is 8 more than twice Bret's age. Find the solution.

kap26 [50]

Andy is 32, and Brett is 12. You gotta set up an equation.
a+b=44
a=2b+8
2b+8+b=44
b=12
a=32

4 0

3 years ago

What is the area of this figure?<br><br><br> Enter your answer in the box.

pav-90 [236]

Answer:

532

Step-by-step explanation:

18x18+0.5(18)(16)+0.5(8)(16)

532

5 0

2 years ago

Read 2 more answers