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3 years ago

What is the perimeter of a rectangle with length 16.8 units and the width 9.6 units

1 answer:

5 0

Hey there! :) In order to find the perimeter, you must add all 4 sides. You first do 16.8 + 16.8 + 9.6 + 9.6 which is 52.8.

Hope it helps!

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14. If a chicken farm sold 3,000 dozen eggs last week, how many individual eggs were sold?

Nuetrik [128]

The answer is 36000...3000x 12

7 0

3 years ago

Read 2 more answers

Helpp I’ll give brainilest to whoever answers first

grigory [225]

Answer:

4×5

Step-by-step explanation:

Four is being added five times by itself, so it is similar to being multiplied 5 times. I hope this helps!

7 0

3 years ago

Find a polynomial $f(x)$ of degree $5$ such that both of these properties hold: $\bullet$ $f(x)$ is divisible by $x^3$. $\bullet

frosja888 [35]

There seems to be one character missing. But I gather that f(x) needs to satisfy

• $x^3$ divides $f(x)$

• $(x-1)^3$ divides $f(x)^2$

I'll also assume f(x) is monic, meaning the coefficient of the leading term is 1, or

$f(x) = x^5 + \cdots$

Since $x^3$ divides $f(x)$ , and

$f(x) = x^3 p(x)$

where $p(x)$ is degree-2, and we can write it as

$f(x)=x^3 (x^2+ax+b)$

Now, we have

$f(x)^2 = \left(x^3p(x)\right)^2 = x^6 p(x)^2$

so if $(x - 1)^3$ divides $f(x)^2$ , then $p(x)$ is degree-2, so $p(x)^2$ is degree-4, and we can write

$p(x)^2 = (x-1)^3 q(x)$

where $q(x)$ is degree-1.

Expanding the left side gives

$p(x)^2 = x^4 + 2ax^3 + (a^2+2b)x^2 + 2abx + b^2$

and dividing by $(x-1)^3$ leaves no remainder. If we actually compute the quotient, we wind up with

$\dfrac{p(x)^2}{(x-1)^3} = \underbrace{x + 2a + 3}_{q(x)} + \dfrac{(a^2+6a+2b+6)x^2 + (2ab-6a-8)x +2a+b^2+3}{(x-1)^3}$

If the remainder is supposed to be zero, then

$\begin{cases}a^2+6a+2b+6 = 0 \\ 2ab-6a-8 = 0 \\ 2a+b^2+3 = 0\end{cases}$

Adding these equations together and grouping terms, we get

$(a^2+2ab+b^2) + (2a+2b) + (6-8+3) = 0 \\\\ (a+b)^2 + 2(a+b) + 1 = 0 \\\\ (a+b+1)^2 = 0 \implies a+b = -1$

Then $b=-1-a$ , and you can solve for a and b by substituting this into any of the three equations above. For instance,

$2a+(-1-a)^2 + 3 = 0 \\\\ a^2 + 4a + 4 = 0 \\\\ (a+2)^2 = 0 \implies a=-2 \implies b=1$

So, we end up with

$p(x) = x^2 - 2x + 1 \\\\ \implies f(x) = x^3 (x^2 - 2x + 1) = \boxed{x^5-2x^4+x^3}$

6 0

3 years ago

What is -16=p/-3+(-9)

satela [25.4K]

Answer:

192?

Step-by-step explanation:

-16 = p ÷ [-3 + (-9)]

-16 × [-3 + (-9)] = p

-16 × - 12 = p

192 = p

7 0

3 years ago

Guided Practice

NARA [144]

Answer:

1 ≤ w ≤ 5

Step-by-step explanation:

Move all terms not containing

from the center section of the inequality.

Inequality Form:

1 ≤ w ≤ 5

Interval Notation:

[ 1 , 5 ]

4 0

3 years ago