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3 years ago

Please help me solve these problems

Mathematics

1 answer:

vovangra [49]3 years ago

5 0

Will do first question of each concept only because the rest of the questions are the same concept (the same few repeat but whatever).

1. Total angle = (n - 2) * 180 --> 4 * 180 = 360°

70 + 130 + 120 + θ = 360 --> 320 + θ = 360 --> θ = 40

4. Total angle = (10 - 2) * 180 --> 8 * 180 = 1440

1440/10 = 144°

6. Interior: (n - 2) * 180 --> 10 * 180 = 1800

Exterior: 12 * 180 = 2160 --> 2160 - 1800 = 360

9. (n - 2) * 180 --> 3 * 180 = 540

90 + 90 + 150 + 160 + θ = 540 --> 490 + θ = 540 --> θ = 50

13. Interior: (n - 2) * 180 --> 2 * 180 = 360

Exterior: n * 180 - (n - 2) * 180 --> 180n - 180n + 360 --> 360 (always the same)

16. 7r + 4r + 8r + 5r = 360 --> 24r = 360 --> r = 15

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3 years ago

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3 years ago

Estimate the area of Alberta in square miles. Show your reasoning

ella [17]

Answer: About $278,250\ mi^2$

Step-by-step explanation:

The missing figure is attached.

Notice in the first picture that Alberta has a complex shape.

You can calculate the area of a complex shape by decomposing it into polygons whose areas can be calculated easily.

Observe the second picture. Notice that it can be descompose into two polygons: A trapezoid and a rectangle.

The area of the trapezoid can be calcualted with the formula:

$A_t=\frac{h}{2}(B+b)$

Where "h" is the height, "B" is the long base and "b" is short base.

And the area of the rectangle can be found with the formula:

$A_r=lw$

Wkere "l" is the lenght and "w" is the width.

Then, the apprximate area of Alberta is:

$A=\frac{h}{2}(B+b)+lw$

Substituting vallues, you get:

$A=(\frac{(410\ mi-180\ mi)}{2})(760\ mi+470\ mi)+(180\ mi)(760\ im)\\\\A=141,450\ mi^2+136,800\ mi^2\\\\A=278,250\ mi^2$

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3 years ago

Solve the proportion. 3/6 = 7/d

AysviL [449]

To solve this proportion:

$\frac{3}{6} =\frac{7}{d}$

Simplify 3/6, it reduces to 1/2

$\frac{1}{2} =\frac{7}{d}$

Then do the Criss cross method

1d = 7 ×2

d=14

Hope it helps!

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1 year ago

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