Mathematics, 11.01.2021 06:50 rakanmadi87

If T is the circumcenter of triangle MNP, find each measure.

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Applying the properties of circumcenter of a triangle and the Pythagorean Theorem, the measure of each given segments are calculated as:

8. TN = 22

9. RT = 12.8

Recall:

The point where the three perpendicular bisectors of a triangle meet is known as the circumcenter of the triangle.The perpendicular bisectors form right angles with each side it bisects. This means that there are two opposite right angles formed at point Q, S, and R.The circumcenter is also the point that is equidistant to all three vertices of the triangle. This means that, in the diagram given, MT, TN, and TP are equal.Pythagorean theorem can be used to solve for the missing side of a right triangle. It states that, if c is the hypotenuse (longest side that is directly opposite to the right triangle), and a and b are the two other smaller sides, therefore: c^2 = a^2 + b^2

8. Find TN

Given,

MT = 6x - 56TP = 3x - 17

Thus,

6x - 56 = 3x - 17 (MT = TN = TP, because they are equidistant from the circumcenter, T.)

Combine like terms

6x - 3x = 56 - 17

3x = 39

Divide both sides by 3

x = 13

TN = TP = 3x - 17

TN = 3x - 17

Plug in the value of x

TN = 3(13) - 17

TN = 22

9. Find RT

Given,

RN = 14TN = 4x - 17TP = x + 10

Thus,

4x - 17 = x + 10 (TN = TP)

Combine like terms

4x - x = 17 + 10

3x = 27

Divide both sides by 3

x = 9

TN = 4x - 17

Plug in the value of x

TN = 4(9) - 17

TN = 19

To find RT, apply the Pythagorean Theorem

$RT = \sqrt{TN^2 - RN^2}$

Substitute

$RT = \sqrt{19^2 - 14^2}\\\\\mathbf{RT = 12.8}$

In summary, applying the properties of circumcenter of a triangle and the Pythagorean Theorem, the measure of each given segments are calculated as:

8. TN = 22

9. RT = 12.8

Learn more about circumcenter of a triangle here:

link

If T is the circumcenter of triangle MNP, find each measure.

Answer from: mcmccann4317

8). TN = 22 units ; 9). √165

Step-by-step explanation:

The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.

8). 6x - 56 = 3x - 17

3x = 39

x = 13

TN = 22 units

9). 4x - 17 = x + 10

3x = 27

x = 9

TN = 19

RT = $\sqrt{TN^2 - RN^2}$

RT = $\sqrt{361-196}$ = √165 ≈ 12.8 units

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

Answer from: Quest

14.3

step-by-step explanation:

add all the numbers together.

9 + 12 + 15 + 16 + 17 + 17 = 86

now, divide 86 by how many numbers we have: 6.

86 / 6 = 14.3