Выполнение письменных упражнений 1. Преобразуйте выражение в тождественно равное ему, используя соответствующие свойства действий над числами: 1) -6,2a · 5; 2) 0,3 х · (-12у); 3) -23 · (2a – 3b + 1); 4) 1,5(-3x + 4y – 5z); 5) 13a + 7b – 2a – b; 6) -5,1 a – 4b – 4,9 a + b. 2. Выполните тождественные преобразования выражений: 1) x + (a – b) – (c + d); 2) a + (b – (c – d)); 3) (х – 1) + (12 – 7,5x); 4) 4(6 – 5х) + 17х – 10; 5) 0,2(3a – 1) + 0,3 – 0,6а; 6) -2,6(5 – с) – с + 8. 3. Является ли тождеством равенство (объясните, используя действия над числами): 1) ab + 16c = 16c + ab; 2) 5(b + c) = 5b + 5c; 3) a · 25b = 25ab; 4) (x – x)a = 0? 4. Запишите в виде равенства следующие утверждения: 1) произведение любого числа и нуля равно нулю; 2) сумма двух противоположных чисел равна нулю; 3) произведение двух чисел равно произведению чисел, им противоположных; 4) квадрат любого числа равен квадрату числа, ему противоположного. Есть ли записанные равенства тождественностями? Почему?
Объяснение:
WRITING Choose ONE of the topics and write. Topic 1: You are a charitable volunteer in your city and always give a hand to those who are in need: clean the apartments of the disabled people; bring food to animal refuges to feed homeless animals; organise campaigns to raise money and collect toys and clothes for the local orphanages. Your new idea is to write a formal letter to the local mayor to ask him/her for any help he/she can provide to help your charity organisation. Include in your letter the following information: • The title of your charity organisation: • What you have done/are doing aiready; • How you would like the mayor to help your charity organisation. Use appropriate style and examples in your letter.WRITING Choose ONE of the topics and write. Topic 1: You are a charitable volunteer in your city and always give a hand to those who are in need: clean the apartments of the disabled people; bring food to animal refuges to feed homeless animals; organise campaigns to raise money and collect toys and clothes for the local orphanages. Your new idea is to write a formal letter to the local mayor to ask him/her for any help he/she can provide to help your charity organisation. Include in your letter the following information: • The title of your charity organisation: • What you have done/are doing aiready; • How you would like the mayor to help your charity organisation. Use appropriate style and examples in your letter.WRITING Choose ONE of the topics and write. Topic 1: You are a charitable volunteer in your city and always give a hand to those who are in need: clean the apartments of the disabled people; bring food to animal refuges to feed homeless animals; organise campaigns to raise money and collect toys and clothes for the local orphanages. Your new idea is to write a formal letter to the local mayor to ask him/her for any help he/she can provide to help your charity organisation. Include in your letter the following information: • The title of your charity organisation: • What you have done/are doing aiready; • How you would like the mayor to help your charity organisation. Use appropriate style and examples in your letter.WRITING Choose ONE of the topics and write. Topic 1: You are a charitable volunteer in your city and always give a hand to those who are in need: clean the apartments of the disabled people; bring food to animal refuges to feed homeless animals; organise campaigns to raise money and collect toys and clothes for the local orphanages. Your new idea is to write a formal letter to the local mayor to ask him/her for any help he/she can provide to help your charity organisation. Include in your letter the following information: • The title of your charity organisation: • What you have done/are doing aiready; • How you would like the mayor to help your charity organisation. Use appropriate style and examples in your letter.WRITING Choose ONE of the topics and write. Topic 1: You are a charitable volunteer in your city and always give a hand to those who are in need: clean the apartments of the disabled people; bring food to animal refuges to feed homeless animals; organise campaigns to raise money and collect toys and clothes for the local orphanages. Your new idea is to write a formal letter to the local mayor to ask him/her for any help he/she can provide to help your charity organisation. Include in your letter the following information: • The title of your charity organisation: • What you have done/are doing aiready; • How you would like the mayor to help your charity organisation. Use appropriate style and examples in your letter.
Объяснение:
1). (x+3)(2-x)/x+6≥0 Умножим обе стороны неравенства на x+6 и получим (x+3)(2-x)≥0. Отсюда (x+3)≥0 и (2-x)≥0. Тогда x≥-3 и x≤2
2). 2х²+7х+5>0 Приравняем данное неравенство к равенству.
2х²+7х+5 = 0
D=-7²-4·2·5 = 49-40 = √9 = 3²
x1= (-7+3)/2·2 = -4/4 = -1
x2= (-7-3)/4 = - 2,5
3). (x-2)²(x²+6x-9)<0
(x-2)²<0 и (x²+6x-9)<0
Решим сначала (x-2)²<0
= x²-2·2·x+2²<0 = x²-4x+4<0 Приравняем данное неравенство к нолю и получим x²-4x+4=0
D=-4+²-4·1·4=16-16+ = √0 = 0
x1 = (4+0)/2·1= 4/2 = 2
x2 = (4-0)/2·1= 4/2 = 2
Теперь решим (x²+6x-9)<0. Приравняем данное неравенство к нолю и получим x²+6x-9=0
D= 6²-4·1·(-9) = 36+36 = √72
x1 = (-6+√72)/2 = -3+(√72/2)
x2 = (-6-√72)/2 = -3-(√72/2)
4). x²-5x+4/x³-64>0 Умножим обе стороны неравенства на x³-64 и получим: x²-5x+4>0. Приравняем данное неравенство к нолю.
x²-5x+4=0
D=-5²-4·1·4 = 25-16 = √9 = 3²
x1= (5+3)0/2= 8/2= 4
x2= (5-3)/2 = 2/2 = 1
5). (x-2)(2+x)(5-x)≤0 Отсюда (x-2)≤0 (2+x)≤0 (5-x)≤0
Тогда: x≤2, x≤-2 и x≥5