Question

Factorise -75ab² - 15ac

Answer 1

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

Step-by-step 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.