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3 years ago

4m square - 8mn+3n ( resolve into factors)

Mathematics

2 answers:

vesna_86 [32]3 years ago

8 0

Step-by-step explanation:

your answer will be ( 2m-3n)(2m-n)

Explanation is in the attachment

hope it is helpful to you

marshall27 [118]3 years ago

8 0

Step-by-step explanation:

$4 {m}^{2} - 8mn + 3 {n}^{2} \\ 4 {m}^{2} - (2 + 6)mn + 3 {n}^{2} \\ 4 {m}^{2} - 2mn + 6mn + 3 {n}^{2} \\ 2m(2m - n) - 3n(2m - n) \\( 2m - 3n) \: (2m - n)$

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An English teacher needs to pick 1111 books to put on his reading list for the next school year. He has narrowed down his choice

forsale [732]

Answer:

There are 3,659,040 ways he can choose the books to put on the list.

Step-by-step explanation:

There are

12 novels

8 plays

12 nonfiction.

He wants to include

5 novels

4 plays

2 nonfiction

The order in which the novels, plays and nonfictions are chosen is not important. So we use the combinations formula to solve this problem.

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

How many ways can he choose the books to put on the list?

Novels:

5 from a set of 12. So

$C_{12,5} = \frac{12!}{5!7!} = 792$

Plays:

4 from a set of 8. So

$C_{8,4} = \frac{8!}{4!4!} = 70$

Nonfiction:

2 from a set of 12

$C_{12,2} = \frac{12!}{2!10!} = 66$

Total:

Multiplication of novels, plays and nonfiction.

$T = 792*70*66 = 3,659,040$

There are 3,659,040 ways he can choose the books to put on the list.

4 0

3 years ago

Which best describes the centroid of a triangle?

aivan3 [116]

Answer:

Option: B is the correct option:

B. The point where the three medians of the triangle intersect

Step-by-step explanation:

We know that the centroid of a triangle is the point where the three medians of the triangle intersect.

<em>The centroid of a triangle is also known as the center of gravity of the triangle.</em>

The median of a triangle is a line segment that is drawn form a vertex of a triangle such that it meets the opposite site of the triangle at the mid-point.