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3 years ago

Which of the following reasons could be used to conclude that the lines are parallel based on the given information?

2 answers:

7 0

We have been given three statements. From those statements, we have to pick the statement that can conclude that that two lines are parallel.

Statement 1:

If right angles are formed, then lines are parallel.

This is not valid because if the angle formed is right angle then lines forming right angle will be perpendicular.

Statement 2:

If two lines are perpendicular to another line, then they are parallel.

This is valid because the line on which other two lines are perpendicular will work as transversal and the alternet interior angles will be equal. Hence the two perpendicular lines on given line will be parallel to each other.

Statement 3:

If alternate interior angles are equal, then lines are parallel.

This is valid as explained above.

Hence final answer are statement 2 and statement 3 both.

kompoz [17]3 years ago

7 0

Answer:

If two lines are perpendicular to another line, then they are parallel.

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Find g(1) if g(x) =x^2+1 A.4 B.2 C.3

kodGreya [7K]

Answer:

B.2

Step-by-step explanation:

g(1) if g(x) =x^2+1

= x^2 + 1 = (1)^2 + 1 = 1 + 1 = 2

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3 years ago

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Evaluate each expression |-16| -|-1|

Maslowich

Understanding the Absolute Value.

First, know what the absolute value is.

The absolute value is the value that determines how far the value is from 0.

For example, The absolute value of -5 is far from 0 5 units. Therefore the absolute value of -5 equals 5.

Basic Absolute Value Defines

| a | = a

- | a | = -a

| - a | = a

Back to the question. To evaluate those expressions, we use the defines of absolute value.

|-16| = 16

|-1| = 1

16-(1)

Then remove the brackets. 16 - 1 = 15

Therefore, the answer is 15.

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3 years ago

Suppose a rope is nailed to a pole 35 meters above the ground and extended away from the base of the pole. The distance from the

motikmotik

Answer:

$B. \: \boxed{66.8}$

Step-by-step explanation:

$to \: solve \: this \: little \: poblem : we \:apply \: the \: pythagrean \: rule \to \\ \boxed{SOH} \boxed{CAH} \boxed{TOA} \to \\ we \: are \: been \: given : \to \\ the \: \boxed{opp }\: of \: the \: required \: angle \: = 35. \\ the \: \boxed{adj }\: of \: the \: required \: angle \: = 15. \\ now \: lets \: apply \: \boxed{TOA}\to \: \tan( \theta) = \frac{opp}{adj} \to\\ \tan( \theta) = \frac{opp}{adj} = \frac{35}{15} = 2.3333333333 \\ \theta = \tan {}^{ - 1} (2.3333333333) \\ \boxed{\theta = 66.80}$

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3 years ago

\int (x+1)\sqrt(2x-1)dx

Nezavi [6.7K]

Answer:

$\int (x+ 1) \sqrt{2x-1} dx = \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15}(2x-1)^{\frac{5}{2}} + C$

Step-by-step explanation:

$\int (x+1)\sqrt {(2x-1)} dx\\Integrate \ using \ integration \ by\ parts \\\\u = x + 1, v'= \sqrt{2x - 1}\\\\v'= \sqrt{2x - 1}\\\\integrate \ both \ sides \\\\\int v'= \int \sqrt{2x- 1}dx\\\\v = \int ( 2x - 1)^{\frac{1}{2} } \ dx\\\\v = \frac{(2x - 1)^{\frac{1}{2} + 1}}{\frac{1}{2} + 1}} \times \frac{1}{2}\\\\v= \frac{(2x - 1)^{\frac{3}{2}}}{\frac{3}{2}} \times \frac{1}{2}\\\\v = \frac{2 \times (2x - 1)^{\frac{3}{2}}}{3} \times \frac{1}{2}\\\\v = \frac{(2x - 1)^{\frac{3}{2}}}{3}$

$\int (x+1)\sqrt(2x-1)dx\\\\ = uv - \int v du$

$= (x +1 ) \cdot \frac{(2x - 1)^{\frac{3}{2}}}{3} - \int \frac{(2x - 1)^{\frac{3}{2}}}{3} dx \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ u = x + 1 => du = dx \ ]$

$= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \int (2x - 1)^{\frac{3}{2}}} dx\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{3}{2} + 1}}{\frac{3}{2} + 1}) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{3} \times ( \frac{(2x-1)^{\frac{5}{2}}}{\frac{5}{2} }) \times \frac{1}{2}\\\\= \frac{1}{3}(x+1) (2x - 1)^{\frac{3}{2} } - \ \frac{1}{15} \times (2x-1)^{\frac{5}{2}} + C\\\\$

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3 years ago