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3 years ago

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Points b and c lie on a circle with center o and radius equals 5. If the length of arc BC is 10.91 units, what is the measuremen

t of angle BOC in radians?

1 answer:

sergey [27]3 years ago

4 0

Check the picture below

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Determine which of the lines are parallel and which of the lines are perpendicular. Select all of the statements that are true.

slega [8]

Answers:

Line A is parallel to line D.

Line A is perpendicular to line C.

Line C is perpendicular to line D.

=====================================================

Explanation:

Let's use the slope formula to calculate the slope of the line through (-1,-17) and (3,11)

$(x_1,y_1) = (-1,-17) \text{ and } (x_2,y_2) = (3,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - (-17)}{3 - (-1)}\\\\m = \frac{11 + 17}{3 + 1}\\\\m = \frac{28}{4}\\\\m = 7\\\\$

The slope of line A is 7

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Now let's find the slope of line B.

$(x_1,y_1) = (0,4) \text{ and } (x_2,y_2) = (7,-5)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{-5 - 4}{7 - 0}\\\\m = -\frac{9}{7}\\\\$

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Now onto line C.

$(x_1,y_1) = (7,1) \text{ and } (x_2,y_2) = (0,2)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{2 - 1}{0 - 7}\\\\m = \frac{1}{-7}\\\\m = -\frac{1}{7}\\\\$

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Lastly we have line D.

$(x_1,y_1) = (-1,-6) \text{ and } (x_2,y_2) = (1,8)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{8 - (-6)}{1 - (-1)}\\\\m = \frac{8 + 6}{1 + 1}\\\\m = \frac{14}{2}\\\\m = 7\\\\$

------------------------------

Here's a summary of the slopes we found

$\begin{array}{|c|c|} \cline{1-2}\text{Line} & \text{Slope}\\\cline{1-2}\text{A} & 7\\\cline{1-2}\text{B} & -9/7\\\cline{1-2}\text{C} & -1/7\\\cline{1-2}\text{D} & 7\\\cline{1-2}\end{array}$

Recall that parallel lines have equal slopes, but different y intercepts. This fact makes Line A parallel to line D.

Lines A and C are perpendicular to one another, because the slopes 7 and -1/7 multiply to -1. In other words, -1/7 is the negative reciprocal of 7, and vice versa. These two lines form a 90 degree angle.

Lines C and D are perpendicular for the same reasoning as the previous paragraph.

Line B unfortunately is neither parallel nor perpendicular to any of the other lines mentioned.

You can use a graphing tool like Desmos or GeoGebra to verify these answers.

6 0

1 year ago

Which expressions are equivalent to (5g+3h+4) . 2

Elza [17]

Answer:

2(5g+3h+4)

10g+6h+8

Please that is the answer

3 0

2 years ago

Plz help i need to find slope here

Aleksandr-060686 [28]

The answer is d which is 6/5

3 0

3 years ago

Using two independent samples, two population means are compared to determine if a difference exists. The population standard de

ANTONII [103]

Answer:

Hence the degrees of freedom are associated with the critical value is 25.

Step-by-step explanation:

Using two independent samples, two population means are

compared to determine if a difference exists, the population standard deviation is equal.

sample size 1 = $n_{1}$ = 15 and sample size 2 = $n_{2}$ = 12

since, population standard deviations are equal, required degrees of freedom

$= n_{1} + n_{2} - 2 \\= 15 + 12 - 2\\ = 25$

8 0

2 years ago

Select the correct answer.

Usimov [2.4K]

Applying the law of sines, the approximate length of side YZ is: A. 15.7 units.

<h3>How to Apply the Law of Sines?</h3>

Law of sines is expressed as follows: x/sin X = y/sin Y = c/sin Z.

Given the following:

x (YZ) = ?
X = 32°
z = 24
Z = 180 - 32 - 94 = 54°

Plug in the values

x/sin 32 = 24/54

x = (sin 32 × 24)/sin 54

x ≈ 15.7 units.

Learn more about the law of sines on:

brainly.com/question/27174058

#SPJ1

4 0

1 year ago