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3 years ago

What are the two variations of the Pythagorean theorem to use? (short and long side)

Mathematics

1 answer:

Tju [1.3M]3 years ago

5 0

Step-by-step explanation:

the Pythagorean Theorem only works with right triangles. You can use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle if you know the length of the triangle's other two sides, called the legs.

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Being financially prepared for retirement requires planning. true false

igor_vitrenko [27]

True, because without the preparation for retirement, there will be nowhere to store retirement funds.

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3 years ago

Read 2 more answers

Prove that 1+cosθ+sinθ/1+cosθ-sinθ = 1+sinθ/cosθ

marusya05 [52]

Step-by-step explanation:

(1 + cos θ + sin θ) / (1 + cos θ − sin θ)

Multiply by the reciprocal:

(1 + cos θ + sin θ) / (1 + cos θ − sin θ) × (1 + cos θ + sin θ) / (1 + cos θ + sin θ)

(1 + cos θ + sin θ)² / [ (1 + cos θ − sin θ) (1 + cos θ + sin θ) ]

(1 + cos θ + sin θ)² / [ (1 + cos θ)² − sin² θ) ]

Distribute and simplify:

(1 + cos θ + sin θ)² / (1 + 2 cos θ + cos² θ − sin² θ)

[ 1 + 2 (cos θ + sin θ) + (cos θ + sin θ)² ] / (1 + 2 cos θ + cos² θ − sin² θ)

(1 + 2 cos θ + 2 sin θ + cos² θ + 2 sin θ cos θ + sin² θ) / (1 + 2 cos θ + cos² θ − sin² θ)

Use Pythagorean identity:

(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (sin² θ + cos² θ + 2 cos θ + cos² θ − sin² θ)

(2 + 2 cos θ + 2 sin θ + 2 sin θ cos θ) / (2 cos² θ + 2 cos θ)

(1 + cos θ + sin θ + sin θ cos θ) / (cos² θ + cos θ)

Factor:

(1 + cos θ + sin θ (1 + cos θ)) / (cos θ (1 + cos θ))

(1 + cos θ)(1 + sin θ) / (cos θ (1 + cos θ))

(1 + sin θ) / cos θ

3 0

3 years ago

Solve for x: 6 over x equals 4 over 8

Talja [164]

Answer:

For the given expression, x = 12.

Step-by-step explanation:

Here, in the given expression:

6 over x equals 4 over 8.

Now, 6 over x = $\frac{6}{x}$

and 4 over 8 = $\frac{4}{8}$

So, here $\frac{6}{x} =\frac{4}{8}\\ \implies x = \frac{6 \times 8}{4} = 12$

⇒ x = 12

Hence, for the given expression, x = 12.

5 0

3 years ago

What is the value of x in the equation x - y = 30, when y = 15? O4 O 8 O 80 O 200

olganol [36]

$\frac{1}{5}x - \frac{2}{3} y = 30 \\$

Putting the value of Y = 15

$\frac{1}{5} x - \frac{2}{3} \times 15 = 30 \\ \frac{1}{5} x = 30 + 10 \\ \frac{1}{5} x = 40 \\ x = 5 \times 40 \\ x = 200$

So, X = 200

6 0

3 years ago

P/9 - 1 < -2 ... Solve for p

love history [14]

Step-by-step explanation:

first collect terms, while the < remains unchange

P < 1-2

cross examine and get the answer

P < -1

9 1

P = -9

7 0

3 years ago