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3 years ago

Essential Question: How can you use models to find factors.

Mathematics

1 answer:

Elina [12.6K]3 years ago

6 0

Answer:

by models you mean drawings?

Step-by-step explanation:

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X^2-8xy+16y^2 factor completely

kicyunya [14]

Neato
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what 2 numbers multiply to get 16 and add to get -8
-4 and -4
(x-4y)(x-4y)
(x-4y)²

7 0

3 years ago

Read 2 more answers

The figure represents a doorstop in the shape of a triangular prism. What is the volume of the doorstop in cubic inches?

Makovka662 [10]

Answer:

7 times 5

divided by two

17.5

times 3

52.5 cubic inch

7 0

3 years ago

2. In how many ways can 3 different novels, 2 different mathematics books and 5 different chemistry books be arranged on a books

insens350 [35]

The number of ways of the books can be arranged are illustrations of permutations.

When the books are arranged in any order, the number of arrangements is 3628800
When the mathematics book must not be together, the number of arrangements is 2903040
When the novels must be together, and the chemistry books must be together, the number of arrangements is 17280
When the mathematics books must be together, and the novels must not be together, the number of arrangements is 302400

The given parameters are:

$\mathbf{Novels = 3}$

$\mathbf{Mathematics = 2}$

$\mathbf{Chemistry = 5}$

(a) The books in any order

First, we calculate the total number of books

$\mathbf{n = Novels + Mathematics + Chemistry}$

$\mathbf{n = 3 + 2 + 5}$

$\mathbf{n = 10}$

The number of arrangement is n!:

So, we have:

$\mathbf{n! = 10!}$

$\mathbf{n! = 3628800}$

(b) The mathematics book, not together

There are 2 mathematics books.

If the mathematics books, must be together

The number of arrangements is:

$\mathbf{Maths\ together = 2 \times 9!}$

Using the complement rule, we have:

$\mathbf{Maths\ not\ together = Total - Maths\ together}$

This gives

$\mathbf{Maths\ not\ together = 3628800 - 2 \times 9!}$

$\mathbf{Maths\ not\ together = 2903040}$

(c) The novels must be together and the chemistry books, together

We have:

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the novels in:

$\mathbf{Novels = 3!\ ways}$

Next, arrange the chemistry books in:

$\mathbf{Chemistry = 5!\ ways}$

Now, the 5 chemistry books will be taken as 1; the novels will also be taken as 1.

Literally, the number of books now is:

$\mathbf{n =Mathematics + 1 + 1}$

$\mathbf{n =2 + 1 + 1}$

$\mathbf{n =4}$

So, the number of arrangements is:

$\mathbf{Arrangements = n! \times 3! \times 5!}$

$\mathbf{Arrangements = 4! \times 3! \times 5!}$

$\mathbf{Arrangements = 17280}$

(d) The mathematics must be together and the chemistry books, not together

We have:

$\mathbf{Mathematics = 2}$

$\mathbf{Novels = 3}$

$\mathbf{Chemistry = 5}$

First, arrange the mathematics in:

$\mathbf{Mathematics = 2!}$

Literally, the number of chemistry and mathematics now is:

$\mathbf{n =Chemistry + 1}$

$\mathbf{n =5 + 1}$

$\mathbf{n =6}$

So, the number of arrangements of these books is:

$\mathbf{Arrangements = n! \times 2!}$

$\mathbf{Arrangements = 6! \times 2!}$

Now, there are 7 spaces between the chemistry and mathematics books.

For the 3 novels not to be together, the number of arrangement is:

$\mathbf{Arrangements = ^7P_3}$

So, the total arrangement is:

$\mathbf{Total = 6! \times 2!\times ^7P_3}$

$\mathbf{Total = 6! \times 2!\times 210}$

$\mathbf{Total = 302400}$

Read more about permutations at:

brainly.com/question/1216161

8 0

2 years ago

peter has 6/7 of a stack of baseball cards left. If he is planning on splitting what he has left into stacks that are each 3/28

DIA [1.3K]

<h3>Answer: 8</h3>

=======================================================

Work Shown:

Let's say there are 28 cards in a full stack.

6/7 = 24/28 after multiplying top and bottom by 4

Since he has 24/28 of a stack left, this means he has 24 cards left.

He wants to arrange the remaining cards into piles so that each pile consists of 3/28 of a full stack. In other words, he wants each pile to have 3 cards.

So this must mean he will get 24/3 = 8 piles

(8 piles)*(3 cards per pile) = 8*3 = 24 cards total

3 0

2 years ago

Read 2 more answers

What is the interest earned on $3000 at a rate of 0.04 for three years? The formula is interest equals (principal) (rate) (time)

bekas [8.4K]

Answer:

The interest after 3 years is $360

Explanation:

Given the principal amount (P) = $3000

Rate of interest (R) = 0.04

Time period (T) is given as 3 years

The Simple Interest is calculated by the formula;

$SI = Principal \times Rate of Interest \times Time$

Substituting the values in the above formula,

$SI = 3000 \times 0.04 \times 3$

SI = $360

Therefore, the interest after 3 years is $360

5 0

3 years ago