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3 years ago

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

Mathematics

2 answers:

MaRussiya [10]3 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:

Learn more about inverse of the function brainly.com/question/1632445.
Learn more about equation of circle brainly.com/question/1506955.
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]3 years ago

5 0

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

Look at the image down below!!

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a) $P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

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Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=4, p=1-0.25=0.75)$

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Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Part a

$P(X=0)=(4C0)(0.75)^0 (1-0.75)^{4-0}=0.0039$

$P(X=1)=(4C1)(0.75)^1 (1-0.75)^{4-1}=0.0469$

$P(X=2)=(4C2)(0.75)^2 (1-0.75)^{4-2}=0.211$

$P(X=3)=(4C3)(0.75)^2 (1-0.75)^{4-3}=0.422$

$P(X=4)=(4C4)(0.75)^2 (1-0.75)^{4-4}=0.316$

Part b

The expected value is givn by:

$E(X) = np = 4*0.75=3$

Part c

For the standard deviation we have this:

$Sd(X) =\sqrt{np(1-p)}=\sqrt{4*0.75*(1-0.75)}=0.866$

Part d

For this case the sample size needs to be higher or equal to 9. Since we need a value such that:

$P(X \geq 3) \geq 0.98$

And the dsitribution that satisfy this is $X\sim Binom(n=9,p=0.75$

We can verify this using the following code:

"=1-BINOM.DIST(3,9,0.75,TRUE)" and we got 0.99 and the condition is satisfied.

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