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Scorpion4ik [409]
3 years ago
14

Three angles of an irregular octagon are 100 degrees, 120 degrees, and 140 degrees. The remaining angles are congruent. Find the

size of each of the remaining angles
Mathematics
1 answer:
STatiana [176]3 years ago
7 0

Answer:

144°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° × (n - 2) ← n is the number of sides

Here n = 8 ( octagon ), hence

sum = 180° × 6 = 1080°

let the measure of 1 congruent angle be x

Then sum the 8 angles and equate to 1080

100 + 120 + 140 + 5x = 1080

360 + 5x = 1080 ( subtract 360 from both sides )

5x = 720 ( divide both sides by 5 )

x = 144

Thus each of the 5 congruent angles is 144°

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Sushilis now 4 times as old as Sunil. 5 years ago Sushilwas 7 times as old as Sunil was then. Find the present ages of each of t
Illusion [34]

Answer:

Sunil = 10 and Sushil= 40

Step-by-step explanation:

Present ages-

Sushil= 4x

Sunil= x

5 years ago-

Sushil = 4x - 5

Sunil = x - 5

4x - 5 = 7(x - 5) = 4x - 5 = 7x - 35

                        = -5 = 3x - 35

                        = 30 = 3x

                        = 10 = x

So substitute the xs for 10-

Present Sushil= 4 x 10 = 40

Present Sunil= 10

6 0
4 years ago
3. What are some of the goods that were in high demand and traded throughout the Afro-Eurasian
maxonik [38]

Step-by-step explanation:

Afro Eurasian network of trade basically encompassed all the major routes of trade before the discovery of Americas and thus meant that the tarde of many things was being done in different parts of it and from different parts of it.

The African coasts were rich in minerals and gold so it was traded from there while India and China were rich in silk, cotton, grain along with the very valuable salt which was also a commodity of the eastern and south eastern part of Asia.

The European trade route largely contributed to metals and non metals required for construction as well as other elements.

7 0
3 years ago
Help with this question, please!
uranmaximum [27]

Answer:

52 ft

Step-by-step explanation:

For each chord, the product of segment lengths is a constant. We can find that constant as the product of the segment lengths of the bisected chord:

(24 ft)·(24 ft) = 576 ft^2

Then the missing segment length (DX) of the diameter chord is ...

DX·(36 ft) = 576 ft^2

DX = (576 ft^2)/(36 ft) = 16 ft

So, the total length of the diameter chord is ...

DX +XL = 16 ft + 36 ft

DL = 52 ft

_____

We know DL is a diameter because the perpendicular bisector of any chord intersects the center of the circle.

5 0
3 years ago
Describe fully the single transformation that takes shape p onto shape q
Arturiano [62]

Answer:

The single transformation that takes shape 'p' onto shape 'q' is a dilation by a scale factor of 3 with the center point (1, 0)

Step-by-step explanation:

The coordinates of the vertices of shape ΔP are;

A(2, 3), B(2, 1), C(3, 1)

The length AB = 3 - 1 = 2

The length CB = 3 - 2 = 1

∴ The length AC = √(2² + 1²) = √5

The coordinates of the vertices of shape ΔQ are;

A'(4, 9), B'(4, 3), C'(7, 3)

The length A'B' = 9 - 3 = 6

The length C'B' = 7 - 3 = 3

∴ The length A'C' = √(6² + 3²) = √(45) = 3·√5

∴ Figure Q ΔA'B'C' is a dilation of figure P ΔABC by a scale factor of A'B'/AB = 6/2 = 3

The distance of point B(2, 1) from the point (1, 0) = √((2 - 1)² + 1²) = √2

The distance of point B'(4, 3) from the point (1, 0) = √((4 - 1)² + 3²) = 3·√2

Therefore, the distances of points on figure Q from (1, 0) = 3 × the distances of points on figure from (1, 0)

Therefore, figure 'Q' can be obtained from figure 'P' by a dilation of figure 'P' by a scale factor of 3 with the center of dilation at point (1, 0).

5 0
3 years ago
SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school are given below
kvasek [131]

Answer:

The value of test statistics is 25.

Step-by-step explanation:

We are given below the SAT reading and writing section scores of a random sample of twenty 11th-grade students in a certain high school;

380, 520, 480, 510, 560, 630, 670, 490, 500, 550, 400, 350, 440, 490, 620, 660, 700, 730, 740, 560

<em>Let </em>\sigma<em> = population standard of the reading and writing section SAT score of the students in this school</em>

So, Null Hypothesis, H_0 : \sigma \leq 100     {means that the reading and writing section SAT score of the students in this school is lesser than or equal to 100}

Alternate Hypothesis, H_A : \sigma<em> </em>> 100     {means that the reading and writing section SAT score of the students in this school is higher than 100}

The test statistics that would be used here is <u>One-sample Chi-square</u> test statistics;

                        T.S. =  \frac{(n-1)s^{2} }{\sigma^{2} }  ~ \chi^{2} __n_-_1

where, s^{2} = sample variance =  \frac{\sum (X-\bar X)^{2} }{n-1}  = 13135.8

            n = sample of 11th-grade students = 20

So, <u><em>the test statistics</em></u>  =  \frac{(20-1)\times 13135.8^{2} }{100^{2} }

                                     =  24.96 ≈ 25

Hence, the value of test statistics is 25.

5 0
4 years ago
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