What is the sum of the interior angles of a regular polygon with 13 sides?

giving 20 points!!

Segment addition postulate states that given points X, and Z, on a line, a point Y, can be located between X, and Z, ony if we have;

XZ = XY + YZ

The length of the segment BD is 36  cm

The reason the above value is correct is as follows:

Known:

The ratio in which the points A, B, C, and D divide the line segment = 4:3:1

The length of segment AD = 72 cm

Required:

The length of BD

Method:

Calculate the length of BC and CD and add their values to get BD

Solution:

Let the ratios be given unit proportions of the segment AD such that we have;

AB = 4 units

BC = 3 units

CD = 1 unit

By segment addition postulate, we have;

AD = AB + BC + CD

∴ AD = 4 units + 3 units + 1 unit = 8 units = 72 cm

∴ 1 unit = 72 cm/8 = 9 cm

1 unit = 9 cm

BD = BC + CD by segment addition postulate

BC = 3 units = 3 × 1 unit

∴ BC = 3 × 9 cm = 27 cm

BC = 27 cm

CD = 1 unit

∴ CD = 9 cm

∴ BD = 27 cm + 9 cm = 36 cm

The length of segment BD = 36 cm

Learn more about segment addition postulate here:

https://brainly.com/question/17015321

Part (a)

This is the empty set

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Explanation:

It doesn't matter what set A is composed of. Intersecting any set with the empty set Ø will always result in the empty set.

This is because we're asking the question: "What does some set A and the empty set have in common?". The answer of course being "nothing" because there's nothing in Ø. Not even the value zero is in this set.

We can write Ø as { } which is a set of curly braces with nothing inside it.

=========================================================

Part (b)

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Explanation:

When you union the universal set with any other set, you'll get the universal set.

The rule is [tex]A \cup B = B[/tex] where I've made B the universal set to avoid confusion of the letter U and the union symbol [tex]\cup[/tex] which looks nearly identical.

Why does this rule work? Well if an item is in set [tex]\overline{A}[/tex], then it's automatically in set U (everything is in set U; it's the universe). So we're not adding anything to the universe when applying a union involving this largest set.

It's like saying

we can see that [tex]\overline{A} \cup U[/tex] will basically form the set of every item, aka the universal set.

Answer:

5m

Step-by-step explanation:

5^(k-1)+5^(k-1)=m

Going to combine like terms on left:

2×5^(k-1)=m

Law of exponents applied:

2×5^k×5^(-1)=m

Reciprocal:

2×5^k×1/5=m

Multiply 5 on both sides to obtain the requested:

2×5^k=5m

In any artihmetic sequence, consecutive terms differ by a fixed constant c. So given the first term a, the second term is a + c, the third terms is a + 2c, and so on, up to the n-th term a + (n - 1)c.

If the 15th term is 40, then

40 = -12 + (15 - 1) c   ==>   c = 52/14 = 26/7

We can then write the n-th term as

-12 + (n - 1) 26/7 = (26n - 110)/7

The sum of the first 15 terms is then

[tex]\displaystyle \sum_{n=1}^{15}\frac{26n-110}7 = \frac{26}7\sum_{n=1}^{15}n - \frac{110}7\sum_{n=1}^{15}n = \boxed{210}[/tex]

Another way to compute the sum: let S denote the sum,

S = -12 - 58/7 - 32/7 + … + 228/7 + 254/7 + 40

Reverse the order of terms:

S* = 40 + 254/7 + 228/7 + … - 32/7 - 58/7 - 12

Notice that adding up terms in the same position gives the same result,

-12 + 40 = 28

-58/7 + 254/7 = 28

-32/7 + 228/7 = 28

so that

S + S* = 2S = 28 + 28 + 28 + … + 28 + 28 + 28

There are 15 terms in the sum, so

2S = 15×28   ==>   S = 15×28/2 = 210

Answer:

(2x+3y)^2

= (2x)^2 + 2(2x)(3y) + (3y)^2

= 4x^2 + 12xy + 9y^2

Answer:

4x^2 12xy +9y^2

Step-by-step explanation:

(2x+3y)^2

(2x+3y)(2x+3y)

FOIL

4x^2 + 6xy+6xy + 9y^2

4x^2 12xy +9y^2

Answer:

B. Never

Step-by-step explanation:

When a number is irrational, it means that it cannot be written as a fraction.

I hope this helps!

pls ❤ and mark brainliest pls!

Answer:

c) when it is improper fraction

Answer:

length = 13

Step-by-step explanation:

length =x-4

width = 8

perimeter =2( x-4) + 2× 8 = 34

= 2x - 8 + 8 =34

= 2x =34

= x = 17

Answer:

x = 13

Step-by-step explanation:

The opposite sides of a rectangle are equal, then

2(x - 4) + 2(8) = 34 ← distribute parenthesis and simplify left side

2x - 8 + 16 = 34

2x + 8 = 34 ( subtract 8 from both sides )

2x = 26 ( divide both sides by 2 )

x = 13

Answer:

Justin did not eat 7/12 of the pizza

Step-by-step explanation:

Marc eats 1/6 × 24 = 4, 24 - 4 = 20 left over

Claudine eats 1/4 × 20= 5, 20 - 5 = 15 left over

Sylvia eats 1/3 × 15 = 5, 15 - 5 = 10 left over

Justin eats 10.

24 - 10 = 14

Justin did not eat 14/24 = 7/12

Answer:

-4

Step-by-step explanation:

a = 3

b = -4

c = -2

2a + 3b - c

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

= 6 + (-12) + 2

= -4

Answer:

[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]

Step-by-step explanation:

We are given that:

[tex]\displaystyle \tan A = \frac{2ab}{a^2 - b^2}[/tex]

And we want to find the value of cos(A) and sin(A).

Recall that tangent is the ratio of the opposite side to the adjacent side.

Therefore, the opposite side measures 2ab, and the adjacent side measures a² - b².

Using the Pythagorean Theorem, solve for the hypotenuse:

[tex]\displaystyle \begin{aligned} c^2 &= a^2 + b^2 \\ \\ c&= \sqrt{(2ab)^2 + (a^2-b^2)} \\ \\ &= \sqrt{(4a^2b^2)+(a^4-2a^2b^2+b^4)} \\ \\ &= \sqrt{a^4 + 2a^2b^2 + b^4 } \\ \\ &= \sqrt{(a^2 +b^2)^2} \\ \\ &= a^2 + b^2\end{aligned}[/tex]

Thus, our hypotenuse is given by a² + b².

Cosine is the ratio between the adjacent side and the hypotenuse. Thus:

[tex]\displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}[/tex]

And sine is the ratio between the opposite side and the hypotenuse. Thus:

[tex]\displaystyle \sin A = \frac{2ab}{a^2 + b^2}[/tex]

In conclusion:

[tex]\displaystyle \displaystyle \cos A = \frac{a^2-b^2}{a^2 + b^2}\text{ and } \sin A = \frac{2ab}{a^2 + b^2}[/tex]

Answer:

Step-by-step explanation:

[tex]sec^2A-tan^2A=1\\sec^2A=1+tan^2A=1+\frac{4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2-b^2)^2+4a^2b^2}{(a^2-b^2)^2} =\frac{(a^2+b^2)^2}{(a^2-b^2)^2} \\cos^2A=\frac{(a^2-b^2)^2}{(a^2+b^2)^2} \\cos A=\frac{a^2-b^2}{a^2+b^2} \\sin A=\sqrt{1-cos^2A} =\sqrt{1-(\frac{a^2-b^2}{a^2+b^2} )^2} =\sqrt{\frac{(a^2+b^2)^2-(a^2-b^2)^2}{(a^2+b^2)^2} } =\sqrt{\frac{4a^2b^2}{(a^2+b^2)^2} }=\frac{2ab}{a^2+b^2}[/tex]

Answer:

sorry

Step-by-step explanation:

polynomial is not given

question is incomplete

Answer:

528 cm squared

Step-by-step explanation:

A parallelogram (slanted shape at the bottom) is essentially the same area as a rectangle.

Therefore, both shapes have the same measurements.

Multiply the length and height of the rectangle to get its area: 22cm×12cm =264cm squared

Since the area of the rectangle corresponds geometrically to the area of the parallelogram, just multiply the area of the rectangle (264cm squared), by 2.

So 264×2, = 528cm squared

Ta da...

Answer:

- 2 x y^2+3 x^2 y -xy

-120

Step-by-step explanation:

xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2

Combine like terms

xy – 2xy + 3x^2 y — 4x y^2 + 2xy^2

- x y+3 x^2 y - 2 x y^2

Let x = 4 y = -2

-(4)(-2) +3(4)^2 (-2) -2(4)(-2)^2

Exponents first

-(4)(-2) +3(16) (-2) -2(4)(4)

Multiply

+8 -96-32

Add and subtract

-120

Answer:

[tex]P(x \ge 5) = 0.60[/tex]

Step-by-step explanation:

Given

[tex]S = \{5, 2, 7, 2, 3, 4, 10, 6,4,6,3, 6, 6, 4, 8,5,7,7,1,5\}[/tex]

[tex]n(S) = 20[/tex]

Required

[tex]P(x \ge 5)[/tex]

First, we count the number of trials that are at least 5

[tex]x = \{5, 7, 10, 6,6, 6, 6, 8,5,7,7,5\}[/tex]

So, we have:

[tex]n(x \ge 5) = 12[/tex]

So, we have:

[tex]P(x \ge 5) = \frac{n(x \ge 5)}{n(S)}[/tex]

This gives

[tex]P(x \ge 5) = \frac{12}{20}[/tex]

[tex]P(x \ge 5) = 0.60[/tex]

Answer:

8 cm

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

So first let's write the information we got

Angle BAC = 90 degrees

Midpoint of BC = M

AC = 6cm

Am= 5cm

Also I found MC = BM, since it has a line that represents both lines are same

so to find it we have to Pythagoras theorem (A^2 + B^2 = C^2), well it is question we have the 'A value and C Value', also we need to find the value of B to find the length of MC and BM

A = 5

C = 6

so therefore to find B^2, we have to do the reverse, we don't add but subtract

C^2 - A^2 = B^2

___________________________________________________________

Moving on to Calculation

6^2 - 5^2 = B^2

36 - 25 = B^2

B^2 = 9

B = √9

B = 3

MC and BM Length =  3 cm

____________________________

Now, we know the length we again need to use Pythagoras theorem to solve this.

Since we know

A = 5

B = 3

So..

A^2 + B^2 = C^2

5^2 + 3^2 = C^2

25 - 9 = C^2

C^2 = 16

C = √16

C = 4

The statistical question is; "What are the ages of the students in this class?

A statistical question is always aimed at data collection which can subsequently used for analysis and decision making. Statistical questions are asked in the course of research.

Among the two questions, the statistical question is; "What are the ages of the students in this class?

Learn more about statistics:https://brainly.com/question/8058700

#SPJ1

Answer:

hope this might help you

Answer:

16

Step-by-step explanation:

If the teacher had 23 but then 7 had to go away for a trip, then all you do is subtract 23 and 7:

23-7= 16

Thus, the teacher had 16 students that day after the 7 went away.

Answer:

see explanation

Step-by-step explanation:

Using x and y to represent the 2 numbers with x > y , then

x + y = 15 → (1)

x - y = 11 → (2)

Adding the 2 equations term by term to eliminate y

2x = 26 ( divide both sides by 2 )

x = 13

Substitute x = 13 into (1)

13 + y = 15 ( subtract 13 from both sides )

y = 2

The 2 numbers are 13 and 2

[tex]\\ \sf\longmapsto (-42)+15+(-63)[/tex]

[tex]\\ \sf\longmapsto -42+15+(-63)[/tex]

[tex]\\ \sf\longmapsto -27+(-63)[/tex]

[tex]\\ \sf\longmapsto -27-63[/tex]

[tex]\\ \sf\longmapsto -90[/tex]

Answer:

42 + 15 + (-63) = -90

Step-by-step explanation:

If you like my answer than please mark me brainliest thanks

Answer:

13.9

Step-by-step explanation:

For the 41° angle, x is the opposite leg, and 16 is the adjacent leg. The trig ratio that relates the opposite leg and the adjacent leg is the tangent.

tan A = opp/adj

tan 41° = x/16

x = 16 * tan 41°

x = 13.9085...

Answer: 13.9

Answer:

I think E

Step-by-step explanation:

You know the shortest building is 25 m.

to find the rest, use trigo so Tan(20)=opposite/adjacent.

Adjacent is 50. Do the math and add the answer with 25.

Answer:

The answer would be E. 43.2

According to TOA, The opposite side is tan(20) x adjacent side( 50m)

the answer is 18.2( to 1 dp). Add the height of the second building together with 18.2 and you will get ur answer. HOpe this helps:)

Answer:

2=124  124/2

4=248 248/4

5=310 310/5

8=496 496/8

Step-by-step explanation:

40 + 22 = 62

62 x 2 = 124

62 x 4 = 248

62 x 5 = 310

62 x 8 = 496

i think

Answer: B) 3 × 3 × 3 × 3 × 3

Concept:

In factorization, the easiest way is to divide the term multiple times by the least factor each time until the answer is not divisible. Then, multiply all the factors and the remainder together to get the factorization of a term.

Solve:

243 ÷ 3 = 81

81 ÷ 3 = 27

27 ÷ 3 = 9

9 ÷ 3 = 3

3 ÷ 3 = 1

Therefore, the prime factorization of 243 = 3 × 3 × 3 × 3 × 3

Hope this helps!! :)

Please let me know if you have any questions

Answer:

B

Step-by-step explanation:

how could it not be??

Answer: your answer should be 10.5130

Step-by-step explanation:

Answer:

Equation of line is y = -8x + 21

Step-by-step explanation:

Slope, m = -8

General equation of line:

[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]

At point (2, 5), y = 5 and x = 2:

[tex]{ \tt{5 = ( - 8 \times 2) + c}} \\ { \tt{c = 21}}[/tex]

Therefore:

[tex]{ \sf{y = - 8x + 21}}[/tex]

[tex]{ \underline{ \blue{ \sf{christ \:† \: alone }}}}[/tex]

Answer:

Klog earned $135.45 altogether.

Step-by-step explanation:

Hours

Monday - Friday : 5 days / 3.5 hours

Saturday : 1 day / 4 hours

3.5 · 5 + 4

= 17.5 + 4

= 21.5

Money

$6.30 per hours / 21.5 hours

6.30 · 21.5

= $135.45