What happens to (-9,3) when it is translated 3 units right and 4 units down?

expeople1 [14]

Simplified version would be 3 square root of 11

4 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

the ratio of hard problems to easy problems was 23 to 7. how many easy problems were there if the total number of problems was 9

il63 [147K]

Answer:

5

Step-by-step explanation:

I just know the answer is five

7 0

2 years ago

Write an equation for the line shown pictured in the graph.

guajiro [1.7K]

Answer:

4y = x + 13

Step-by-step explanation:

The general equation of the line y = mx + c

where m is the slope and c is constant represent y-intercept

The line shown in the graph pass through the points (3,4) , (-1,3)

The slope of the line = (y₂-y₁)/(x₂-x₁) = (3-4)/(-1-3) = -1/-4 = 1/4

∴ y = (1/4) x + c

Substitute with the point (3,4) to find c

∴ 4 = (1/4) 3 + c

∴ c = 4 - 3/4 = 13/4

∴ y = (1/4) x + 13/4 ⇒ multiply both sides by 4

∴ 4y = x + 13

So, The equation of the line in the graph: 4y = x + 13

The equation can be written as y = (1/4) x + 13/4 OR 4y - x = 13

8 0

4 years ago

The scatter plot below represents the weight of a bunch of bananas based on the number of bananas in the bunch. A trend line sho

Shalnov [3]

Answer:

Step-by-step explanation:3.0

3 0

2 years ago

Read 2 more answers