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Musya8 [376]
2 years ago
8

How do the lengths of the corresponding sides compare? How do you know?

Mathematics
1 answer:
ra1l [238]2 years ago
7 0

Step-by-step explanation:

if two have the same shape, they are called "similar". When two figures are similar, the ratio of the lengths of their corresponding sides are equal. To determine if the triangles show are similar, compare their corresponding sides. Triangles ABC is similar to triangle DEF.

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Prove that C(50,3) + C(50,4) = C(51,4)
valkas [14]

By definition of the binomial coefficient,

C(n,k) = \dfrac{n!}{k!(n-k)!}

so we have

C(50,3) + C(50,4) = \dfrac{50!}{3!47!} + \dfrac{50!}{4!46!} \\\\ = \dfrac{50!}{3!46!} \left(\dfrac1{47} + \dfrac14\right) \\\\ = \dfrac{50!}{3!46!} \times \dfrac{51}{188} \\\\ = \dfrac{51!}{3!46!} \times \dfrac1{4\times47} \\\\ = \dfrac{51!}{4!47!} \\\\ = \dfrac{51!}{4!(51-4)!} = C(51,4)

as required.

5 0
2 years ago
The process of paying off the principal on the loan is called a(n) _.
NISA [10]
The answer is amortization
3 0
3 years ago
Read 2 more answers
3. The area of a rectangular deck, in square meters, is given by the polynomial 40p2 + 24p.
lorasvet [3.4K]

Answer:

Length = 5p + 3

Perimeter = 26p + 6

Step-by-step explanation:

Given

Area = 40p² + 24p

Width = 8p

Solving for the length of deck

Given that the deck is rectangular in shape.

The area will be calculated as thus;

Area = Length * Width

Substitute 40p² + 24p and 8p for Area and Width respectively

The formula becomes

40p² + 24p = Length * 8p

Factorize both sides

p(40p + 24) = Length * 8 * p

Divide both sides by P

40p + 24 = Length * 8

Factorize both sides, again

8(5p + 3) = Length * 8

Multiply both sides by ⅛

⅛ * 8(5p + 3) = Length * 8 * ⅛

5p + 3 = Length

Length = 5p + 3

Solving for the perimeter of the deck

The perimeter of the deck is calculated as thus

Perimeter = 2(Length + Width)

Substitute 5p + 3 and 8p for Length and Width, respectively.

Perimeter = 2(5p + 3 + 8p)

Perimeter = 2(5p + 8p + 3)

Perimeter = 2(13p + 3)

Open bracket

Perimeter = 2 * 13p + 2 * 3

Perimeter = 26p + 6

4 0
3 years ago
A boat travels 432km in 24 hours how far can it travel in 16 hours?
pickupchik [31]
The answer is 288 km!

3 0
3 years ago
The guitar that you always wanted is on sale in the music store. It costs 2/3 the original price. The guitar now costs $1996.67,
AysviL [449]

Answer:

3,327.9

Step-by-step explanation:

now: 1996.67

original: 3,327.9

1996.67/.6 = 3,327.9

4 0
3 years ago
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