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3 years ago

Select the postulate or theorem

Mathematics

1 answer:

VladimirAG [237]3 years ago

5 0

Answer: SAS similarity Theorem.

Explanation:

1) SAS stands for Side-Angle-Side

2) SAS Theorem postulates that when two sides of a triangle are proportional to two sides of other triangle and one angle of one triangle is congruent to one angle of other triangle then the two triangles are similar.

3) In this case you can verify the SAS theorem and conclude that the triangles are similar by:

3.1) proportionality of sides:

6 3
--- = ----
4 2

3.2) angle congruency

at point M the angles are opposite by the vertex, which means that the angles are congruent.

So, you have shown that the two triangles are similar in virtue of SAS Theorem.

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What are the next two numbers for 486, 162, 54, 18,

Andru [333]

Each number is 1/3 of the number before it.

After 18 come 6, 2, 2/3, 2/9, 2/27, 2/81, ... etc.

6 0

4 years ago

Solve the triangle.<br> A = 32°, a = 19, b = 14

Paha777 [63]

Answer:

A = 32°, a = 19, b = 14, B=22.98°, C = 125.02°, c = 29.36

Step-by-step explanation:

We have two sides of the triangle and we have an angle.

A = 32 °, a = 19, b = 14

We use the sine theorem to find the angle B.

We know that according to the sine theorem it is true that:

$\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}$

$\frac{sin(32\°)}{19}=\frac{sin(B)}{14}$

$sin(B)=14*\frac{sin(32\°)}{19}\\\\B=Arcsin(14*\frac{sin(32\°)}{19})\\\\B=22.98\°$

We know that the sum of the internal angles of a triangle is always equal to 180.

So:

$C=180-32-22.98\\\\C=125.02\°$

Finally we find the c side

$\frac{sin(A)}{a}=\frac{sin(C)}{c}$

$\frac{sin(32\°)}{19}=\frac{sin(125.02)}{c}$

$0.02789=\frac{sin(125.02)}{c}$

$c=\frac{sin(125.02)}{0.02789}\\\\c=29.36$

8 0

3 years ago

Geometric sequence find common ratio 0.45,0.9,1.8

prisoha [69]

Answer:

<h3>The common ratio is 2</h3>

Step-by-step explanation:

To find the common ratio of the geometric sequence divide the previous term by the next term

That's

0.9 / 0.45 = 2

1.8 / 0.9 = 2

Therefore the common ratio is 2

Hope this helps you

7 0

3 years ago

HELP PLEASE!!! 25 Points & Brainliest!

Citrus2011 [14]

Answer:

(1) $f(x)=3x+4$

Ad g(x) represent f(x) after horizontal translation 2 units to the left.

$g(x)=3(x+2)+4$

$g(x)=3x+6+4$

$g(x)=3x+10$ is the required translation.

(2) $f(x)=\frac{-2x}{3}+2$

$f(\frac{1}{2})=\frac{-2}{3}\cdot(\frac{1}{2})+2$

$f(\frac{1}{2})=\frac{5}{3}$

(3) We have been given a point (1,-9); slope 2

We will use the equation:

$y-y_1=m(x-x_1)$

m is the give slope.

$y-(-9)=2(x-1)$

$y+9=2(x-1)$

Therefore, Option (a) is correct.

6 0

3 years ago

Read 2 more answers

How much smaller is the sum of the first 1000 natural numbers than the sum of the first 1001 natural numbers?

aleksandr82 [10.1K]

ANSWER

1001

EXPLANATION

The sum of the first n - natural numbers is

$S_n= \frac{n}{2} (2a + d(n - 1))$

The sum of the first 1000 terms is

$S_{1000}= \frac{1000}{2} (2(1) + 1(1000 - 1))$

$S_{1000}=500 (1001)$

$S_{1000}=500500$

The sum of the first 1001 terms is

$S_{1001}= \frac{1001}{2} (2(1) + 1(1001 - 1))$

$S_{1001}= 1001 \times (501)$

$= 501501$

The difference is

$501501 - 500500= 1001$

5 0

3 years ago

Read 2 more answers