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3 years ago

Solve the eqaution 6 - 6x =5x - 9x -2.

2 answers:

8 0

Simplifying
6 + -6x = 5x + -9x + -2

Reorder the terms:
6 + -6x = -2 + 5x + -9x

Combine like terms: 5x + -9x = -4x
6 + -6x = -2 + -4x

Solving
6 + -6x = -2 + -4x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4x' to each side of the equation.
6 + -6x + 4x = -2 + -4x + 4x

Combine like terms: -6x + 4x = -2x
6 + -2x = -2 + -4x + 4x

Combine like terms: -4x + 4x = 0
6 + -2x = -2 + 0
6 + -2x = -2

Add '-6' to each side of the equation.
6 + -6 + -2x = -2 + -6

Combine like terms: 6 + -6 = 0
0 + -2x = -2 + -6
-2x = -2 + -6

Combine like terms: -2 + -6 = -8
-2x = -8

Divide each side by '-2'.
x = 4

Simplifying
x = 4

I hope this helps!

Aleksandr [31]3 years ago

6 0

You want to get the variable, x, onto one side of the equation so you can solve for it.

6 - 6x = -4x - 2

Add 6x to both sides

Don’t actually use the brackets, it’s just to simplify

6 ( - 6x + 6x ) = (- 4x + 6x) - 2

6 = 2x - 2

Add 2 to both sides

6 + 2 = 2x (-2 + 2)

8 = 2x

Divide both sides by 2

8/2 = 2x/2

4 = x

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3 years ago

To find the distance AB across a river, a surveyor laid off a distance BC=361 m on one side of the river. It is found that B=111

zhannawk [14.2K]

Answer:

91.87m

Step-by-step explanation:

We are given that

BC=361 m

Angle B= $111^{\circ}20'=111+\frac{20}{60}=111.33^{\circ}$

1 degree= 60 minute

Angle C= $12^{\circ} 15'=12+\frac{15}{60}=12.25^{\circ}$

We have to find the value of AB.

Sum of angles of triangle=180 degrees

$\angle A+\angle B+\angle C=180$

$\angle A=180-(\angle C+\angle B)=180-(111.33+12.25)=56.42^{\circ}$

By using law of sine

$\frac{AB}{sin C}=\frac{BC}{sin A}$

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4 years ago

Solve for x: x - 24 = 25 *

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f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

$P(X \geq 2) = P(X = 2) + P(X = 3)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

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