Answer:
1) -15·a·(5·b² + c)
2) h < 4
3) 4·x² - 9
4) 1792
5) 156°
6) 2t cm
7) 2·a·m·(2·m - 3)
8) 10 cm
9) 0.00051
10) #47,250
11) -10·p·q
12) 1.35 × 10⁻⁴
13) 320°
14) 20 cm
15) 12·x²·y²
16) 6.36 × 10⁵
17) 4 cm
18) 225°
19) 1034 cm²
20) 29
Explanation:
1) The given expression is -75·a·b - 15·a·c
Which can be expressed as -15·a·(5·b² + c)
2) The height, h < 2 × 12/6 = 4
h < 4
3) (2·x - 3)·(2·x + 3) = 4·x² - 9
4) The selling price = 1.12 × 200 × 8 = 1792
5) The interior angle of a polygon is given by the relation;
(n - 2)×180/n for 15, we get;
(15 - 2)×180/15 = 156°
6) 2t cm
7) 4·a·m² - 6·a·m = 2·a·m·(2·m - 3)
8) Slant height = √(8² + 6²) = 10 cm
9) 51 × 10⁻⁵ = 0.00051
10) Cash price = #54,000 × (1 - 0.125) = #47,250
11) -40·p·q÷(-2)² = -10·p·q
12) 0.003 × 0.045 = 1.35 × 10⁻⁴
13) N40°W = 320°
14) The base diameter of the cylinder = √(4 × (700×π cm³/7)/π) = 20 cm
15) The LCM of 2·x²·y, 3·x·y² is 12·x²·y²
16) 636,000 = 6.36 × 10⁵
17) 1/3·π·r²·h₁ = π·r²·h₂
h₂/h₁ = 1/3·π·r²/( π·r²) = 1/3
h₂/12 = 1/3
h₂ = 12/3 = 4 cm, the height of the cylinder = 4 cm
18) The angle = 180 + 45 = 225°
19) The total surface area = 22/7×14²/4 + 22/7 ×14 × 20 = 1034 cm²
20) The number is 58/2 = 29.