All categories

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 incenter 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!

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

From the attachment , it can be concluded that:

∠ZAS = ∠ZBS = 90°

∠ZSA = ∠ZSB

ZS of ΔZSA is coincided with ZS of ΔZSB

∴ ΔZSA is congruent to ΔZSB

$\texttt{ }$

From the information above , then :

∠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

You might be interested in

Hassam plotted Point M in the coordinate plane below

ki77a [65]

Answer:

The answer to your question is the second option, both coordinates should be negative.

Step-by-step explanation:

The point Hassam plotted was (-0.5, -0.25). If he wanted to plot point (0.5, 0.25):

-First, he should have counted two squares to the right

- then one square up.

Because both coordinates are positive this point must be in the first quadrangle not in the third.

4 0

3 years ago

Read 2 more answers

Solve 3x − x + 2 = 12.

astra-53 [7]

X=5 is ur answer my guy it’s simple math

5 0

3 years ago

Read 2 more answers

Need help plzz! will give best answer brainliest!!!

german

Second graph because there are positive

and functioning

7 0

2 years ago

Read 2 more answers

The original value of a sculpture is $950, and the value decreases by 15% each year. Find the value of the sculpture in 8 years.

german

Answer:

The value of the sculpture in 8 years is $258.865

Step-by-step explanation:

The original value of sculpture = $950

we are given that the value decreases by 15% each year.

Formula : $N(t)=N_0(1-r)^t$

Where N(t)=Value after t years

$N_0 =$ Initial value

r = rate of decrease in decimals

t = time

We are supposed to find the value of the sculpture in 8 years.

Substitute the values in the formula :

So, $N(t)=950(1-0.15)^8=258.865$

Hence the value of the sculpture in 8 years is $258.865

5 0

3 years ago

I will give brainiest to whom answers correct and the fastest and a thanks

german

Answer:

(D) The bottom graph, and (A) The top table.

Step-by-step explanation:

The easiest way to pick out the wrong answers is simply through substitution. Substitute the input into the x part of the equation that is given and if it doesn't match up with y everytime, then it is incorrect.

From table A (top table), the input x can be substituted into y = x + 2 which will come out as the output so it is correct.

For table A:

x = -3 → y = x + 2 → y = (-3) + 2 → y = -1 = -1

x = -2 → y = x + 2 → y = (-2) + 2 → y = 0 = 0

x = -1 → y = x + 2 → y = (-1) + 2 → y = 1 = 1

x = 0 → y = x + 2 → y = (0) + 2 → y = 2 = 2

x = 1 → y = x + 2 → y = (1) + 2 → y = 3 = 3

Since the table matches up with the inputs and outputs of the table, it is a correct answer.

For table B:

x = 3 → y = x + 2 → y = (3) + 2 → y = 5 = 5

x = 4 → y = x + 2 → y = (4) + 2 → y = 6 ≠ 7

x = 5 → y = x + 2 → y = (5) + 2 → y = 7 ≠ 9

x = 6 → y = x + 2 → y = (6) + 2 → y = 8 ≠ 11

x = 7 → y = x + 2 → y = (7) + 2 → y = 9 ≠ 13

5 out of the 6 y values of the table do not match the equation, so table B must be incorrect.

Graph C:

Notice how you can see the line cross the x, and y axis. When the line crosses the x axis, it is an x intercept which means y is 0. When the line crosses the y axis, it is a y intercept which means x is 0.

Since the line crosses the y axis at 2, this means that an x of 0 must lead to a y of 2 which it does.

x = 0 → y = x + 2 → y = (0) + 2 → y = 2 = 2.

But the x intercept doesn't match up as shown here.

y = 0 → y = x + 2 → (0) = x + 2 →

0 – 2 = x + 2 – 2 → -2 = x → x = -2 ≠ -1

When graphing the line y = x + 2, it's x intercept should be (-2,0). While on this graph, it's (-1,0). This means that this graph is incorrect which leads to D being another correct answer.

✓ Table A: y = x + 2

× Table B: y = 2x – 1

× Graph C: y = 2x + 2

✓ Graph D: y = x + 2

8 0

3 years ago