1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
____ [38]
2 years ago
10

The two triangles are similar. What is the value of x? Enter your answer in the box.

Mathematics
2 answers:
MaRussiya [10]2 years ago
8 0

The value of \text{x} is \boxed{x = 5}.

Further Explanation:

There are many similarity rules and are as follows.

1. Angle Angle (AA)

2. Side SideSide (SSS)

3. Side Angle Side (SAS)

If two triangles are similar to each other than the ratios of the corresponding sides are equal.

Explanation:

The similar triangles are those in which all the corresponding angles are equal and the sides are proportional.

The \Delta {\text{ACB}} and \Delta {\text{ACE}} are similar to each other. Therefore, the ratios of the corresponding sides are equal.

\begin{aligned}\frac{{{\text{AC}}}}{{{\text{DC}}}} &= \frac{{{\text{EC}}}}{{{\text{BC}}}} \\\frac{{{\text{AD}} + {\text{DC}}}}{{{\text{DC}}}} &= \frac{{{\text{EC}}}}{{{\text{BC}}}} \\\frac{{12 + 3}}{{12}} &= \frac{{4x}}{{3x + 1}}\\\frac{{15}}{{12}} &= \frac{{4x}}{{3x + 1}}\\\end{aligned}

Further solve the above equation.

\begin{aligned}\frac{5}{4}&=\frac{{4x}}{{3x + 1}}\\5\left( {3x + 1} \right) &= 4\left( {4x} \right)\\15x + 5 &= 16x\\5&= 16x - 15x\\5&= x\\\end{aligned}

The value of \text{x} is \boxed{x = 5}.

Kindly refer to the image attached.

Learn more:

  1. Learn more about inverse of the function brainly.com/question/1632445.
  2. Learn more about equation of circle brainly.com/question/1506955.
  3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Triangle

Keywords: congruent, angles, triangle, similar, value, x, two right triangles, one smaller, right angles, straight angle, two acute angles, overlapping, legs, labeled, 20, extends, smaller triangle, larger triangle, ray, 3x.

ra1l [238]2 years ago
5 0

Just took the test and got the the correct answer *\(♡°▽°♡)/*

Look at the image down below!!


You might be interested in
I need help on this one. Thanks.
murzikaleks [220]
I think it would have to be an irrational number.
4 0
2 years ago
If f(x)=2x-6 and g(x)=x^3 what is (g f)(0)
marin [14]

ANSWER

(g \circ \: f)(0) = - 216

EXPLANATION

The functions are:

f(x) = 2x - 6

g(x) =  {x}^{3}

(g \circ \: f)(x) =g(f(x))

(g \circ \: f)(x) =g(2x - 6)

We substitute f(x) into g(x) to obtain:

(g \circ \: f)(x) =(2x - 6)^{3}

We now substitute x=0 to obtain;

(g \circ \: f)(0) =(2(0) - 6)^{3}

(g \circ \: f)(0) =(- 6)^{3}

This simplifies to:

(g \circ \: f)(0) = - 216

4 0
2 years ago
Consider the angles: 30°,30°,x° .
Elina [12.6K]
There are 180° in a triangle so you do
180- (30+30)
=180 - 60
=120

Therefore the answer is x = 120
8 0
2 years ago
Please help me out!!!!!!!!!!!!
Savatey [412]
(700/8)%. ............
4 0
3 years ago
Read 2 more answers
What are the factors of 42??
Tom [10]
The factors of 42 are: 1,2,3,6,7,14,21,42
4 0
3 years ago
Other questions:
  • 13 plus 5 times a number is no more than 30
    10·1 answer
  • LINEAR ALGEBRA<br><br> List four variables and link them using one equation
    10·1 answer
  • ON TIMER ONLY 2 MIN LEFT PLEASE HELP!!!!
    11·1 answer
  • Please help me with this question :)
    12·1 answer
  • Find the area for each figure to the nearest tenth
    15·1 answer
  • Pedro has 5 jars of marbles. Each jar is 2/3 filled with marbles. How many full jars of marbles does Pedro have? Write an equati
    14·1 answer
  • Which of these statements about the function is true?
    10·1 answer
  • PLISSSSSS HELP!!!!!!!!!!!!! <br> i will give brainliest.....
    11·1 answer
  • To create a graph from an equation, evaluate the function at different ______. Use the input-output pairs to identify and plot _
    11·1 answer
  • Solve each of the following quadratic equations<br><br> 3x=0.5x^2<br><br><br> 0=5x^2-2x+6
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!