12) if x is 0, then it lies on the y-axis. If y is 0, then it lies on the x-axis.
a) (0, 4) lies on y-axis
b) (-2, 0) lies on x-axis
c) (3, 0) lies on x-axis
d) (0, -1) lies on y-axis
13) multiply each of them out and add them together. You will see that the first and last terms cancel, leaving you with the middle terms which each have a coefficient of 3.
3[xy(y - x) + yz(z - y) + xz(x - z)]
14) x³ - x
= x(x² - 1)
= x(x - 1)(x + 1)
15) Using synthetic division for 5x⁴ - x³ - 2x² + x + 9 ÷ x -
0.5 | 5 -1 -2 +1 +9
| 0.5 2.75 0.875 0.5625 0.78125
5.5 1.75 1.125 1.5625 9.78125
Remainder is: 9.78125
16) TRUE. This is known as the Triangle Angle Sum Theorem
17) Separate into two triangles, use Heron's formula to calculate the area for each triangle, then find their sum.
ΔABC: s = (6 + 7 + 9)/2 = 11, A = √(11)(5)(4)(2) ≈ 21
ΔCDA: s = (12 + 15 + 9)/2 = 18, A = √(18)(6)(3)(9) ≈ 54
ΔABC + ΔCDA: 21 + 54 = 75 cm
18) 3√45 - √125 + √200 - √50
= 9√5 - 5√5 + 10√2 - 5√2
= 4√5 + 5√2