A central angle in a circle has a measure of 180°. The length of the arc it intercepts is 8 in.

Determine the measure of each segment then indicate whether the statements are true or false

kupik [55]

Answer:

$d_{AB}\ne d_{JK}$

$d_{AB}\ne \:d_{GH}$

$d_{GH}\ne \:d_{JK}$

Therefore,

Option (A) is false

Option (B) is false

Option (C) is false

Step-by-step explanation:

Considering the graph

Given the vertices of the segment AB

A(-4, 4)

B(2, 5)

Finding the length of AB using the formula

$d_{AB}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$=\sqrt{\left(2-\left(-4\right)\right)^2+\left(5-4\right)^2}$

$=\sqrt{\left(2+4\right)^2+\left(5-4\right)^2}$

$=\sqrt{6^2+1}$

$=\sqrt{36+1}$

$=\sqrt{37}$

$d_{AB}\:=\sqrt{37}$

$d_{AB}=6.08$ units

Given the vertices of the segment JK

J(2, 2)

K(7, 2)

From the graph, it is clear that the length of JK = 5 units

so

$d_{JK}=5$ units

Given the vertices of the segment GH

G(-5, -2)

H(-2, -2)

Finding the length of GH using the formula

$d_{GH}\:=\:\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

$=\sqrt{\left(-2-\left(-5\right)\right)^2+\left(-2-\left(-2\right)\right)^2}$

$=\sqrt{\left(5-2\right)^2+\left(2-2\right)^2}$

$=\sqrt{3^2+0}$

$=\sqrt{3^2}$

$\mathrm{Apply\:radical\:rule\:}\sqrt[n]{a^n}=a,\:\quad \mathrm{\:assuming\:}a\ge 0$

$d_{GH}\:=\:3$ units

Thus, from the calculations, it is clear that:

$d_{AB}=6.08$

$d_{JK}=5$

$d_{GH}\:=\:3$

Thus,

$d_{AB}\ne d_{JK}$

$d_{AB}\ne \:d_{GH}$

$d_{GH}\ne \:d_{JK}$

Therefore,

Option (A) is false

Option (B) is false

Option (C) is false

8 0

2 years ago

Two of the vertices of a triangle are located at (6,0) and (5,10) on the coordinate plane. The third vertex is located at (x,20)

Amiraneli [1.4K]

The answer is 1,1 . 3,-3, 5, -3

6 0

2 years ago

Round 4.675 to the nearest cent

Viktor [21]

Money is written out to the hundredths place, so when rounding to the nearest cent, round to the hundredths place. In 4.675, the 7 is in the hundredths place. The value to its right, 5, is greater than 4, so the 7 is rounded up to 8. So 4.675 to the nearest cent is 4.68

3 0

3 years ago

Which equation would you use to find how high the bird is flying

lisov135 [29]

Hi there! The fourth answer is correct.

In the picture we have to deal with facts:
1. The angle of 45°
2. The length of the opposite side
3. The length of the adjacent side.

Since we have to use the opposite and the adjacent side, we have to use the tangent of the angle. In a formula:
$\tan( \alpha ) = \frac{opposite}{adjecent}$

Filling in this formula, brings us to the following answer.
$\tan(45) = \frac{x}{1100}$

6 0

3 years ago

Sam is building a new deck. His decking material is sold by the square foot. At a cost of $3.90 per square foot, how much will i

AVprozaik [17]

It would be =18*14*3.90=982.8

6 0

3 years ago