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3 years ago

Which theorem or postulate proves that △ABC and △DEF are similar?

Mathematics

2 answers:

goldfiish [28.3K]3 years ago

5 0

Answer: SSS similarity theorem

Step-by-step explanation:

In the given figure we have two triangles ΔABC and ΔDEF.

Since we have given only the side lengths of the triangle.

Thus when we find the ratio of the corresponding sides we get,

$\frac{AB}{DE}=\frac{9}{15}=\frac{3}{5}\\\\\frac{BC}{EF}=\frac{6}{10}=\frac{3}{5}\\\\\frac{AC}{DF}=\frac{12}{20}==\frac{3}{5}\\\\\Rightarrow\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}=\frac{3}{5}$

So by SSS similarity theorem, we have

ΔABC is similar to ΔDEF.

SSS similarity theorem says that if the lengths of the corresponding sides of two triangles are proportional then the triangles are similar triangles.

Harlamova29_29 [7]3 years ago

3 0

3 sides proportional

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Find the volume of the following prism using the formula V = Bh.

Natali [406]

Answer:

1001.

Step-by-step explanation:

1. if B=11*13; h=7, then

2. V=11*13*7=1001.

6 0

2 years ago

Determine the slope of the line that has the following coordinates: (5, 9)(11, - 3)

AlladinOne [14]

Answer:

$x_1 = 5, x_2 =11, y_1 =9, y_2 = -3$

The slope can be founded with this formula:

$m =\frac{y_2 -y_1}{x_2 -x_1}$

And replacing we got:

$m =\frac{-3 -9}{11-5}= -2$

And the best answer for this case would be :

$m=-2$

Step-by-step explanation:

For this case we have the following two points given:

$x_1 = 5, x_2 =11, y_1 =9, y_2 = -3$

The slope can be founded with this formula:

$m =\frac{y_2 -y_1}{x_2 -x_1}$

And replacing we got:

$m =\frac{-3 -9}{11-5}= -2$

And the best answer for this case would be :

$m=-2$

7 0

3 years ago

In a sample of 70 stores of a certain company, 62 violated a scanner accuracy standard. It has been demonstrated that the condi

uysha [10]

Answer:

We need at least 243 stores.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error of the interval is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

$n = 70, p = \frac{62}{70} = 0.886$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

Determine the number of stores that must be sampled in order to estimate the true proportion to within 0.04 with 95% confidence using the large-sample method.

We need at least n stores.

n is found when M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.886*0.114}}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.886*0.114}$

$\sqrt{n} = \frac{1.96\sqrt{0.886*0.114}}{0.04}$

$(\sqrt{n})^{2} = (\frac{1.96\sqrt{0.886*0.114}}{0.04})^{2}$

$n = 242.5$

Rounding up

We need at least 243 stores.

5 0

2 years ago

Solve the equation 2x3 + 7x2 – 10x – 24 = 0 in the real number system.

Rom4ik [11]

Answer:

x = 2

x = -4

x = -3/2

Step-by-step explanation:

We need to find the roots of the equation

2x^3 + 7x^2 – 10x – 24 = 0

We can factorize the equation into

(x-2)(x+4)(2x + 3) = 0

Roots

x = 2

x = -4

x = -3/2

The answer to your question is also attached in the images below

4 0

2 years ago

Read 2 more answers

In the figure LMV is similar to UTK. what's the value of x the length of side LM?

Kipish [7]

To solve this problem, all we need to do is just set up a proportion. The two shapes are similar, which means that they are the same shape, but different sizes. Using the wording/letter arrangement in the problem, we can figure out which side of one triangle corresponds to which side of the other triangle.

Triangle LMV (with segments LM, MV, and VL) is similar to triangle UTK (with segments UT, TK, and KU).

Corresponding pairs:

LM(x) : UT(39)

MV(30) : TK(65)

VL : KU

However, we need only be interested in the first two pairs. Here is the proportion with letters:

LM / UT = MV / TK

and as numbers:

x / 39 = 30 / 65

Solve for x:

x / 39 = 30 / 65

Cross multiply:

(x)(65) = (39)(30)

Simplify:

65x = 1170

Divide:

65x/65 = 1170 / 65

Simplify:

x = 18

<h2>Answer:</h2>

The length of side LM (x) in triangle LMV is 18 units.

7 0

3 years ago