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
Tasya [4]
3 years ago
7

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
You might be interested in
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
Other questions:
  • Use a paragraph, flow chart, or two-column proof to prove that ZX is the perpendicular bisector of side WY.
    15·1 answer
  • With regard to mathematics, what is in excepted statement of fact that is used to prove other statements
    15·1 answer
  • Help now please help help help
    12·1 answer
  • (03.07)
    15·2 answers
  • Help me with this problem!
    6·1 answer
  • HELP!!!! I don’t know what to do
    6·1 answer
  • To attend the football game, it costs $8 for parking plus $59 per ticket. If Bryan paid $362, how many tickets did he purchase?
    5·1 answer
  • Can someone please tell me why we write a number as 'difference' in math?
    8·1 answer
  • A square pyramid has a slant height of 15 cm. A side length of the base is 20 cm. What is the surface area of the pyramid? Enter
    15·1 answer
  • Christian conducted a survey to find the favorite hobby of her classmates from 4 choices. He surveyed the same number of girls a
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!