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3 years ago

Point Z is the incenter of triangle RST. What is the value of x? x = 2 x = 3 x = 5 x = 8

Mathematics

2 answers:

lawyer [7]3 years ago

8 0

Answer:

$x=5$

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

The <u><em>incenter</em></u> is the point where the three angle bisectors of a triangle meet

therefore

In this problem

$(5x-9)\°=16\°$

Solve for x

$5x=16+9$

$5x=25$

$x=5$

Zinaida [17]3 years ago

4 0

The value of x is 5

<h3>Further explanation</h3>

Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

<h3>sin ∠A = opposite / hypotenuse</h3><h3>cos ∠A = adjacent / hypotenuse</h3><h3>tan ∠A = opposite / adjacent </h3>

Let us now tackle the problem!

<em>The incenter of triangle RST</em><em> is the intersection between all of the angle bisectors from the three vertices of triangle.</em>

<em>From the attachment , it can be concluded that:</em>

∠ZAS = ∠ZBS = 90°

∠ZSA = ∠ZSB

ZS of ΔZSA is coincided with ZS of ΔZSB

<em>∴ </em><em>ΔZSA is congruent to ΔZSB</em>

$\texttt{ }$

<em>From the information above , then :</em>

∠ZSA = ∠ZSB

( 5x - 9 )° = ( 16 )°

5x = 16 + 9

5x = 25

x = 25 ÷ 5

$\texttt{ }$

<h2>Conclusion:</h2>

The value of x is 5

$\texttt{ }$

<h3>Learn more</h3>

Calculate Angle in Triangle : brainly.com/question/12438587
Periodic Functions and Trigonometry : brainly.com/question/9718382
Trigonometry Formula : brainly.com/question/12668178

<h3>Answer details</h3>

Grade: College

Subject: Mathematics

Chapter: Trigonometry

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle , Congruent

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zheka24 [161]

Answer:

Neither

Step-by-step explanation:

Since we only know the measure of the angles, we can only say the triangles are similar, not congruent. We need at least one side measurement on each triangle to determine if the triangles are congruent. And it would have to be the same side measurement. Then we could use ASA (Angle side Angle) or AAS ( Angle Angle side) to determine congruence.

The triangles are similar

62+39 +79 = 180

The three angles are the same

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<B = 39 = <Y = 39

<C = 79 = <Z = 79

This is shown by AAA similarity

5 0

3 years ago

Which ordered pair is the best estimate for the solution of the system of equations

Colt1911 [192]

The ordered pair that is the best estimate for the solution of the system of equations is (7, 1/2)

The given system of equations is:

$y=-\frac{1}{2}x + 4.......................(1)\\\\y = \frac{1}{2}x-3..........................(2)$

Equate equations (1) and (2)

$-\frac{1}{2}x + 4=\frac{1}{2}x -3$

Solve for x in the equation above

$-\frac{1}{2}x -\frac{1}{2}x =-3-4\\\\-x=-7\\\\x=7$

Substitute x = 7 into equation (1)

$y=-\frac{1}{2}x + 4\\\\y=-\frac{1}{2}(7) + 4\\\\y=\frac{1}{2}$

The ordered pair that is the best estimate for the solution of the system of equations is (7, 1/2)

Learn more on system of equations here: brainly.com/question/13729904

5 0

2 years ago

PLEASE HELP ASAP!!! (ii only)

mixer [17]

The equation of the tangent line can be found using slope formula and fact that slope = dy/dx.

$\frac{dy}{dx} = \frac{y - y_0}{x - x_0}$

where (x0,y0) is point A ---> (0,-1)

Then rearrange equation into slope-intercept form:
$y = \frac{dy}{dx}(x - 0) -1$

Finally sub in x=0 into dy/dx to get slope at the point (0,-1)

$y = 3x -1$