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lilavasa [31]
3 years ago
9

Find the missing length of the triangle. If necessary, round your answer to the nearest tenth

Mathematics
2 answers:
lisov135 [29]3 years ago
8 0

Answer:

x = 30

Step-by-step explanation:

a^{2} = c^{2} - b^{2}

a^{2} = 50^{2} - 40^{2}

a^{2} = 2500 - 1600

a^{2} = 900

\sqrt{a^{2}} = \sqrt{900}

a = 30

Amiraneli [1.4K]3 years ago
4 0

Answer:

30

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem to find the missing side

a^2 +b^2 = c^2  where a and b are the sides and c is the hypotenuse

x^2 + 40^2 = 50^2

x^2 +1600 = 2500

x^2 = 2500-1600

x^2 = 900

Take the square root of each side

sqrt(x^2) = sqrt(900)

x = 30

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The lateral edge PA of a triangular pyramid ABCP is perpendicular to the base and PA = 2sqrt5 in. The base edges AB = 10 in, AC
DIA [1.3K]

Answer:

PQ = √84 = 2√21 in ≈ 9.165 in

Step-by-step explanation:

The base edges AB = 10 in, AC = 17 in, and BC = 21 in

Q ∈ BC and AQ is the altitude of the base.

Let BQ = x in ⇒ CQ = (21 - x) in

ΔAQB a right triangle at Q

∴ AQ² = AB² - BQ² = 10² - x²  ⇒(1)

ΔAQC a right triangle at Q

∴ AQ² = AC² - CQ² = 17² - (21-x)²  ⇒(2)

Equating (1) and (2)

∴  10² - x² = 17² - (21-x)²

∴ 10² - x² = 17² - (21² - 42x + x²)

∴  10² - x² = 17² - 21² + 42x - x²

∴ 10² - 17² + 21² = 42x

∴ 42x = 252

∴ x = 252/42 = 6

Substitute at (1)

∴ AQ² = AB² - BQ² = 10² - x² = 100 - 36 = 64 = 8²

∴ AQ = 8 in

∵ The lateral edge PA of a triangular pyramid ABCP is perpendicular to the base

∴ PA⊥AQ

∴ ΔPAQ is a right triangle at A,

PA = 2sqrt5 in  and AQ = 8 in

∴ PQ (hypotenuse) = √(PA² + AQ²)

∴ PQ = √[(2√5)² + 8²] = √(20+64) = √84 = 2√21 in ≈ 9.165 in

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2 years ago
Which of the following are solutions to | x + 4 |= 3x-5
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X= 9/2

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The dot plot shows the number of magazines sold. Determine the range of the data set.
solong [7]

Answer:

B

Step-by-step explanation:

The range is the difference between the largest and smallest members of the data set.

largest = 25 and smallest = 17

range = 25 - 17 = 8 → B

8 0
3 years ago
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