# Tutor profile: Emily Z.

## Questions

### Subject: Geometry

Find the area of a regular octagon, described as follows. There is a line, called line A, from the center of the octagon to a side of the octagon. This line is perpendicular to the side. This line measures 63 inches. The side that it touches measures 53 inches.

Draw lines from the center of the octagon to each of the corners. If you look at Line A, you may notice that it forms the height of a triangle. Its base is a side of the octagon. Find the area of that triangle. Half of Base times Height. 1/2 x b x h. b = side = 53. h = line A = 63. 1/2 x 53 x 63. The area of that triangle is 1669.5 inches. You can count the number of triangles in the polygon, and you will get 8. Otherwise, you can just count the number of sides, and that’s how many triangles there will be. Area of one triangle x total number of triangles = area of the octagon. That means 1669.5 x 8 = 13,356. The area of the polygon is 13,356 square inches.

### Subject: Pre-Algebra

Solve the following system of equations using elimination: 4x - 4y = 4 and -9x + 8y = -27

Multiply each term in the first equation by 2. This gives you 8x - 8y = 8. Add the matching terms of each equation. 8x - 9x = -x. -8y + 8y = 0. 8 - 27 = -19. The equation you get is -x + 0 = -19. That is -x = -19. multiply each term by -1. You get x = 19. Now plug the 19 back into one of the original equations. 4 (19) - 4y = 4. Solve for y. 76 - 4y = 4. 76 - 4 = 4y. 72 = 4y. y = 18. So the answer is x = 19 and y = 18.

### Subject: Basic Math

What is 1035 x 82?

2 times 5 is 10. Write the zero and carry the 1 Write the 1 above the 3. 2 x 3 = 6. 6 + 1 = 7. Write the 7 to the left of the zero. 2 x 0 = 0. 2 x 1 = 2. You should have 2070 written below the 82. Write a 0 below the 0 of 2070. 8 x 5 = 40. Write the 0 to the left of the other 0. Carry the 4. Write it above the 3. 8 x 3 = 24. 24 + 4 = 28. Write the 8 to the left of the two zeros. Carry the 2. Write it above the 0. 8 x 0 = 0. 0 + 2 = 2. Write the 2 to the left of the 800. 8 x 1 = 8. Write the 8 to the left of the 2. You should have 2,070 + 82,800. This equals 84,870.

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