B: 2x + y = -6
C:x - 2y = 7
D:8x - 4y = -5
p = 11
p = 10
p = 12
p = 13
Answer:
(c) p = 12
Step-by-step explanation:
You may recall that (5, 12, 13) is a Pythagorean triple. That would tell you ...
p = 12
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If you have not memorized a few useful Pythagorean triples, you can use the Pythagorean theorem to solve for p. The sum of squares of the sides is the square of the hypotenuse:
5² +p² = (p+1)²
p² +25 = p² +2p +1
24 = 2p . . . . . . . . subtract p²+1 from both sides
p = 12 . . . . . . divide by 2
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Additional comment
Some of the Pythagorean triples commonly seen in algebra and geometry problems are ...
(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41)
Of course, multiples of these are used, too. For example, (6, 8. 10) is a multiple of the (3, 4, 5) triple.
Answer:
12
Step-by-step explanation:
5^2 + p^2 = (p+1)^2
25 + p^2 = p^2 + 2p + 1
25 = 2p + 1
24 = 2p
12 = p
Answer:
Step-by-step explanation:
the vertex of the function is (-2, -1)
The price of the notebook experienced a percentage increase of 7.9%.
The subject of this problem is in the area of mathematics, specifically on percentage increase. To find the percentage increase in the price of the notebook, you first find the difference in price. The difference is $3.40 - $3.15 = $0.25. Next, you divide the increase by the original price, which gives you: $0.25 / $3.15 = 0.079365. Then, to turn this into a percentage, multiply the result by 100 to get 7.9365%. Rounding this to the nearest tenth, we get 7.9%.
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