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kow [346]
3 years ago
10

Lorie correctly determines that for the triangles below, the statement pg and the statement both describe the relationship betwe

en the two triangles.
Which best describes why both similarity statements are correct?
Each triangle has two congruent angles: and m.
Each triangle has two similar angles: and .
The triangles each have two given angle measures and one unknown angle measure.
All statements, regardless of the order of the vertices, define the same triangles

Mathematics
2 answers:
Tasya [4]3 years ago
7 0

Answer:

The correct option is 1.

Step-by-step explanation:

Two triangles are called similar if all the corresponding angles are congruent or all corresponding sides are in same proportion.

In triangle MNO and triangle RTS.

\angle M\cong\angle R=54.4^{\circ}          (Given)

\angle N\cong\angle T=71.2^{\circ}            (Given)

According to the angle sum property, the sum of all interior angles of a triangle is 180 degree. Since two corresponding angles are congruent, therefore third angle is also congruent.

\angle O\cong\angle S=54.4^{\circ}

Since all corresponding angles are congruent, therefore the triangles MNO and RTS similar.

The triangle are congruent by AA rule of similarity. Each triangle has two congruent angles, therefore both triangles are similar. Option 1 is correct.

DanielleElmas [232]3 years ago
4 0

Answer:

A

Step-by-step explanation:

You might be interested in
The average systolic blood pressure was found to be 140 mm for people who have high responsibility jobs, specifically investment
defon

Answer:

t = -1.428

Step-by-step explanation:

Average blood pressure among people with high responsibility jobs = u = 140 mm

Number of people sampled for the study = n = 51

Average blood pressure of the sample = x = 139 mm

Standard deviation of the sample = s = 5 mm

The claim is that practicing yoga decreases the blood pressure. So we have to test that after practicing yoga, the average blood pressure will be lesser than 140. Based on this we can formulate the null and alternate hypothesis as:

Null Hypothesis: \mu \geq 140

Alternate Hypothesis: \mu < 140

Since population standard deviation is not known, we cannot use z-distribution for this test. We are given the value of sample standard deviation, so t-test will be used for this case.

Test statistic is calculated as:

t=\frac{x-u}{\frac{s}{\sqrt{n} } }

Using the values in this formula gives us:

t=\frac{139-140}{\frac{5}{\sqrt{51}}}\\\\ t=-1.428

Therefore, the value of test statistic is -1.428

4 0
2 years ago
(15) The ratio of boys to girls at the school is 3:5. If there are 160 students at 1 point the school, how many of them are girl
elixir [45]

Answer:

100

Step-by-step explanation:

160 * (5/8) = 100

4 0
3 years ago
Sabina bought a samsung mobile set for rs.15750 after getting the discount of 10%. Find the price of mobile set before discount.
Elanso [62]

Answer:

Step-by-step explanation:

90/100 * x = 15750

0.9 x = 15750

x = 15750/0.9

x = 17500

Now check this by taking 10% off. Do you get 15750?

Let's see

10/100 of 17500 = 1750

Subtract that from 17500

17500 - 1750 = 15750 which is exactly what you should get.

7 0
2 years ago
What is the effect on the graph of the function f(x) =5x when f(x) is replaced with f(x) + 9?
Nimfa-mama [501]

Answer:

When we add 9 to the function we are shifting the function up 9 units.


Step-by-step explanation:

If it were added inside the function, it woulds shift it left or right.

But since it is outside the function, we will shift it up or down

When we add 9 to the function we are shifting the function up 9 units.

5 0
3 years ago
If you are reading this please help!!!!
Soloha48 [4]

Given:

1.  -3 x^{2}\left(4 x^{3}-7\right)\\$2. $(6 x-5)(2 x+3)$\\3. $(3 x-1)\left(x^{2}+5 x-2\right)$

To find:

The product of the polynomials.

Solution:

1. -3 x^{2}\left(4 x^{3}-7\right) =-3 x^{2}(4 x^{3}) -3 x^{2}(-7)

Multiply the numerical coefficient and add the powers of x.

                          =-12 x^{5}+21 x^{2}

2. (6 x-5)(2 x+3)=6 x(2 x+3)-5(2x+3)

Multiply each term of first polynomial with each term of 2nd polynomial.

Multiply the numerical coefficient and add the powers of x.

                              =12 x^2+18x-10 x-15

                              =12 x^2+8x-15

3. (3 x-1)\left(x^{2}+5 x-2\right)=3 x(x^{2}+5 x-2)-1(x^{2}+5 x-2)

Multiply each term of first polynomial with each term of 2nd polynomial.

Multiply the numerical coefficient and add the powers of x.

                                      =3x^{3}+15 x^2-6x-x^{2}-5 x+2

Add or subtract like terms together.

                                      =3x^{3}+14 x^2-11x+2

The answer for multiplying polynomials:

1. -12 x^{5}+21 x^{2}

2. \  12 x^2+8x-15

3. \ 3x^{3}+14 x^2-11x+2

3 0
3 years ago
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