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expeople1 [14]
4 years ago
7

Austin collects rare Pokémon cards. He currently has 42 cards in his collection. His parents buy him 3 rare cards every year on

his birthday. How long will it take him to collect 78 Pokémon cards?
A: 3p+42=78
B: 78p-3=78
C: 42p+3=78
D: 3p-78=42
Mathematics
2 answers:
barxatty [35]4 years ago
8 0

Answer:

i believe the answer is A. hope this helped.

Step-by-step explanation:

Naya [18.7K]4 years ago
3 0

Answer: option A is the correct answer.

Step-by-step explanation:

Let p represent the number of years for which his parents bought him rare Pokémon cards.

His parents buy him 3 rare cards every year on his birthday. This means that in p years, he would be getting 3p rare cards from his parents.

He currently has 42 cards in his collection. This means that the number of cards that he would have in his collection in p years is

3p + 42

Therefore, the time it will take him to collect 78 Pokémon cards would be

3p + 42 = 78

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The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. The length of the h
Alex17521 [72]

Answer:

Step-by-step explanation:

Let x represent the length of the hypotenuse.

Let y represent the length of the the shorter leg.

Let z represent the length of the longer leg.

The length of the longer leg of a right triangle is 20 inches more than twice the length of the shorter leg. It means that

z = 2y + 20

The length of the hypotenuse is 22 inches more than twice the length of the shorter leg. It means that

x = 2y + 22

We would apply Pythagoras theorem which is expressed as

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Therefore,

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= 4y² + 44y + 44y + 484 = y² + 4y² + 40y + 40y + 400

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4y² + 88y + 484 = 5y² + 80y + 400

5y² - 4y²+ 80y - 88y + 400 - 484

y² - 8y - 84 = 0

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y(y + 6) - 14(y + 6)

y - 14 = 0 or y + 6 = 0

y = 14 or y = - 6

The shorter length cannot be negative hence y = 14 inches

The length of the shorter side is 14 inches.

The length of the hypotenuse is

(2 × 14) + 22 = 50 inches

The length of the longer side is

(2 × 14) + 20 = 48 inches

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