A wire 2 meters long is cut into two parts and one part is twice as long as the other. The longer piece is bent into the shapeof a square and the other part is bent into the shape of a circle. Find the total area of the square and the total area of thecircle.
longer piece is 1 1/3.... shorter is 2/3 square: (1+1/3)/2 = 2/3 square is (2/3)^2 circle: r = 1/3π (π*1/3π)^2 total is 11.27m^2
x2 ‐ 7x ‐ 90 = 8
x^2 - 7x - 98 (x - 7)(x - 14)
negative values!
6, 7, 8, 9, 10, 11, 12, 13, 14, 15, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15
9.8
π^2
3x – 2y = 5 that goes through the point (4 , 5).
y = (3x-5)/2 + 1.5
equation of a line through
3 -7 y = - 7/3x + 23/3
x3 + 3x2 – 4x – 12
(x + 3)(x - 2)(x + 2)
4a^2 b^3 (1- 3ab)
5 3 4 21
x = 2 and x= -8
If x = 7, how long is the diagonal AC in rectangle ABCD above? Give your answer as a simplified root, not a decimal
3^2 + 11^2 = 9 + 121 = 130 ac = √130
Find a simplified formula for the area of rectangle ABCD whose sides have length x + 4 and x – 4
(x + 4)(x-4) = x^2 -16
(2x ‐1)2 + 5x = 3(x +2)
3x = 4 x = 1 1/3
26 12 4 3 2 16 6 2 42. Evaluate without a calculator: 1 2 3 2 36 1 22 3 10 3 2
-6- (-12+4) * 3 / 2 + 16 - 6 * (2-4)^2 = -2
2)
25/8 = 3.125 = 3.125
3 2 100x yx y
y and x are the same but one is negative or 0, x and y cannot be 0. there is 3x and 2y, x = -y -3y - 2y = 10 -5y=10 y = -2 => x = 2
B
What are the authors’ theses or claims? What/where is the best evidence the authors provide for their theses or additional claims? Where are the weak points in their arguments? What are the similarities and differences in these authors’ arguments? How would you evaluate the usefulness or reliability of these sources? What lessons can we draw as historians from these readings? What were you confused about in the reading? What do you need help understanding? What questions, observations, connections remain that you want to make?