1) When Mrs.Smith came home yesterday, she saw that her daughter had cooked supper and was waiting for her with the table laid.
2) Where is Nick? -He isn't at home, he has gone to the cinema. Wait for him, he will come in half an hour.
3) It was very late. I had gone to bed and had fallen asleep when my father returned home.
4) I'll join you when I have drunk my tea.
5) When I came, he was living in the same old house where I had first met him. He told me he had been waiting for me for already some time.
6) The pupils had done a lot of exercises before they learnt to write dictations well.
7) I could not hear a sound: they had stopped talking.
ответ: 1. 5¹⁰ +5⁸ -5⁹ =5⁸(5² +1 -5) = 5⁸*21 =5⁷*5*21 =5⁷*105 || делится на 105|| .
2. √(1 24/25 ) -√(0,09)*√81 +√(3² +4²)*√(0,0625) =√(49/25) -√(9/100) *√9² +√5² *√(0,25)² =7/5 -9/10*9 +5*0,25 =
1,4 -8,1+1,25 = -5,45.
3. a =13q₁ +8 ; b=13q₂ +10 .
a*b = (13q₁ +8)(13*q₂ +10) = 13² q₁q₂ +13*10q₁ + 13*8q₂+ 80 =.
13² q₁q₂ +13*10q₁ + 13*8q₂+ 13*6 + 2 =13(13 q₁q₂ +10q₁ + 8q₂+ 6) +2 . || r =2||.
4.√((7-4√3)/(5-2√6)) -√((6-4√2)/(5+2√6)) -4√2 =√((2²-2*2√3 +(√3)²)/(3-2√3*√2 +2)) -√((4-2*2*√2 +2)/(3+2√3*√2 +2) ) - 4√2 = √((2-√3)²)/(√3-√2)² ) -√((2-√2)²/(√3+√2)²) - 4√2 = (2-√3)/(√3-√2) -(2-√2)/(√3+√2) - 4√2 = (2-√3)(√3+√2) -(2-√2)(√3-√2) - 4√2 =
2√3+2√2 -3 -√3*√2 -2√3 +2√2 +√3*√2 -2 - 4√2 = - 5.
5. (x² +x√2)/(x² +2) *( x/(x-√2) -√(2) / (x+√2) ) =
(x² +x√2)/(x² +2) *(x(x+√2) -√(2) * (x-√2) ) / (x+√2) (x-√2) )=
(x² +x√2)/(x² +2) *(x²+x√2 -x√2 +2 ) / (x² -2) )=
(x² +x√2)/(x² +2) *(x² +2 ) / (x² -2) ) = x(x+√2) / (x +√2)(x -√2) =x /(x -√2) .
6. ( √(19 +8√3) +√(7-4√3) ) *x√y /(√x²y³ +√x³y²) =
( √(4+√3)² +√(2 -√3)² ) *x√y /xy(√y +√x) =( 4+√3 +2 -√3 ) *1 / √y(√y +√x ) =
6/√y (√y +√x )= || x =121 , y =16 || = 6/(√16(√16 +√121 )) =6/(4(4+11)) =
=6/(4*15) =6/60 = 0,1.
объяснение: если ты не туп! й то объяснение тебе не надо!
2. He always (prepares) his homework carefully.
3. We always (plays) tennis on Saturdays.
4. She (speaks) several foreign languages.
5. The children (play) in the park every afternoon.
6. Helen (works) very hard.
7. They (take) a lot of trips together.
8. We always (travel) by car.
9. I (eat) lunch in the cafeteria every day.