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Umnica [9.8K]
3 years ago
11

One leg of a right angel is 4 less than the other leg. The square of the hypotenuse of the right angel is 80. How long are the l

egs of the right triangle? Show your work.
Mathematics
1 answer:
Mice21 [21]3 years ago
8 0
Sometimes these problems are easier to work if you consider the average of the two leg lengths. Call that "x".
.. (x -2)^2 +(x +2)^2 = 80 . . . . . . . by the Pythagorean theorem
.. x^2 -4x +4 +x^2 +4x +4 = 80 . . eliminate parentheses
.. 2x^2 +8 = 80 . . . . . . . . . . . . . . . simplify
.. x^2 = (80 -8)/2 = 36
.. x = √36 = 6
Legs are this value ±2.

The leg lengths are 4 and 8.
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Complete parts (a) and (b) using the probability distribution below.
katen-ka-za [31]
Μ = (0×0.026) + (1×0.072) +(2×0.152) + (3×0.303) + (4×0.215) + (5×0.164) + (6×0.066) 
μ = 0 + 0.072 + 0.304 + 0.909 + 0.86 + 0.82 + 0.396
μ = 3.361 ≈ 3.4

We need the value of ∑X² to work out the variance
∑X² = (0²×0.026) + (1²×0.072) + (2²×0.152) + (3²×0.303) + (4²×0.215) + (5²×0.164) + (6²×0.066)
∑X² = 0+0.072+0.608+2.727+3.44+4.1+2.376
∑X² = 13.323

Variance = ∑X² - μ²
Variance  = 13.323 - (3.4)² = 1.763 ≈ 2

Standard Deviation = √Variance = √1.8 = 1.3416... ≈ 1.4

The correct answer related to the value of mean and standard deviation is the option D
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An employee works an average of 3.4 overtime hours per week with a standard deviation of approximately 1.4 hours.</span>
7 0
3 years ago
Un cable guía de 600 pies esta sujeto a la parte superior de una torre de comunicaciones. Si el cable forma un ángulo de 65° con
natita [175]

Answer:

La torre tiene 543.78 pies de altura.

Step-by-step explanation:

Podemos pensar en esta situación como si fuera un triángulo rectángulo, donde el cable es la hipotenusa y la torre es uno de los catetos. (Abajo se puede ver un dibujo de esta situación).

Nosotros queremos encontrar el valor de H, que es el cateto opuesto al ángulo conocido de 65°.

Entonces simplemente podemos usar la relación:

Sin(θ) = (cateto opuesto)/(hipotenusa)

donde:

cateto opuesto = H

θ = 65°

hipotenusa = 600 ft

sin(65°)  = H/600ft

sin(65°)*600ft = H = 543.78 ft

La torre tiene 543.78 pies de altura.

8 0
3 years ago
A circle has a radius of 3. An arc in this circle has a central angle of 60°.
MArishka [77]

Answer:

π

Step-by-step explanation:

s = (∅/360) * (2πr)

s = (60/360) * (2π*3)

s = (1/6) * (6π)

s = π

8 0
3 years ago
Enrique says is a rational number. Which of the following best describes if Enrique is correct?
olasank [31]

If a number is rational it means, it can be written in the form of \frac{p}{q}, where q≠0 and p and q can be any integers.

There are following properties possessed by Rational numbers

1. Decimal representation of  Rational numbers are either terminating or non terminating repeating i.e if the denominator is of the form 2^m or 5^n or (2^m \times 5^n) where m and n are any natural number.

2. Addition ,Subtraction ,Multiplication and Division of two rationals is always Rational.

3. The sum or difference of rational and irrational is always irrational.



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3 years ago
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What is the daily rate for a 20% ROI?​
strojnjashka [21]

Answer:look it up

Step-by-step explanation:

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