1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832:1 x 832, 2 x 416, 4 x 208, 8 x 104, 13 x 64, 16 x 52, 26 x 32
x2 - 10x + 25 = 64 Or x2 - 10x + 25 = 64? If the first, move all over to 1 side; x2 - 10x + 25 - 64 = 0 x2 - 10x + -39 = 0 Then make it into quadratic equations; (x - 13)(x + 3) = 0 Therefore x = 13 or x = -3. If the second, 8x = -39 -39/8 = -9.75 = x
13
Equation: 8x^2 -26x +15 =0 I Divide all terms by 8: x^2 -26/8 +15/8 = 0 and complete the square as follows:- (x -13/8)^2 -169/64 +15/8 = 0 => (x-13/8)^2 = 49/64 Square root both sides: x-13/8 = -/+ 7/8 Add 13/8 to both sides: x = 13/8 -/+ 7/8 Therefore solutions are: x = 5/2 or x = 3/4
3x+1+2x-2 = 64 3x+2x = 64-1+2 5x = 65 x = 13
16 x 4 = 64 77 - 64 = 13 4 times with 13 remaining
Using the vertex (h, k) the equation of the quadratic would be: y = a(x - h)² + k → y = a(x - 8)² + 2 → y = a(x² - 16x + 64) + 2 → y = ax² -16ax + 64a + 2 Using the y-intercept of (0, -11): -11 = a 0² - 16a 0 + 64a + 2 → 64a = -13 → a = -13/64 Thus the quadratic could be: y = (-13/64)x² - 16(-13/64)x + 64(-13/64) + 2 → y = (-13/64)x² + (13/4)x - 11 Or, removing the fractions: 64y = -13x² + 208x - 704
1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 832:1 x 832, 2 x 416, 4 x 208, 8 x 104, 13 x 64, 16 x 52, 26 x 32
x2 - 10x + 25 = 64 Or x2 - 10x + 25 = 64? If the first, move all over to 1 side; x2 - 10x + 25 - 64 = 0 x2 - 10x + -39 = 0 Then make it into quadratic equations; (x - 13)(x + 3) = 0 Therefore x = 13 or x = -3. If the second, 8x = -39 -39/8 = -9.75 = x
33 = 2726 = 647 x 13 = 91
13
Equation: 8x^2 -26x +15 =0 I Divide all terms by 8: x^2 -26/8 +15/8 = 0 and complete the square as follows:- (x -13/8)^2 -169/64 +15/8 = 0 => (x-13/8)^2 = 49/64 Square root both sides: x-13/8 = -/+ 7/8 Add 13/8 to both sides: x = 13/8 -/+ 7/8 Therefore solutions are: x = 5/2 or x = 3/4
You find numbers that divide evenly into 64, such as for example, 1, 2, 4, 8, 16, 32, and 64. Then sharpen your pencil and start writing. 1 x 64 = 64 2 x 32 = 64 4 x 16 = 64 8 x 8 = 64 2 x 2 x 16 = 64 2 x 4 x 8 = 64 4 x 4 x 4 = 64 2 x 2 x 2 x 8 = 64 2 x 2 x 4 x 4 = 64 2 x 2 x 2 x 2 x 4 = 64 2 x 2 x 2 x 2 x 2 x 2 = 64
The first ten positive integer multiples of 64 are:1 x 64 = 642 x 64 = 1283 x 64 = 1924 x 64 = 2565 x 64 = 3206 x 64 = 3847 x 64 = 4488 x 64 = 5129 x 64 = 57610 x 64 = 640
58
These numbers multiply to equal 832: 1, 2, 4, 8, 13, 16, 26, 32, 52, 64, 104, 208, 416, 8321 x 832, 2 x 416, 4 x 208, 8 x 104, 13 x 64, 16 x 52, 26 x 32
8 x 8 = 64 32 x 2 = 64 63 + 1 = 64 100 - 36 = 64