Rewrite the underlined part of the sentences below without a subject. どういう意味ですか？

合同式を使った「証明」で、解説では表を使ってひとつひとつの項について丁寧に説明されているのですが、 2枚目のように一気に代入するような形で表すのは危険ですか？

496 演習 例題 123 合同式を利用した証明 (1) a,bは3で割り切れない整数とする。 このとき, d+α2b+64 は3で割り切れる ことを証明せよ。 200 1000円) 倉敷芸科大] 指針▷基本例題 117, 118 で似た問題を扱ったが,ここでは 合同式を利用して証明してみよう。 aが3で割り切れない整数とは,αを3で割った余りは1または2ということである ( 6 に ついても同じ)。 このことから,問題を合同式で表すと,次のようになる。 1997 「α=1 (mod 3) またはa=2 (mod3) b=1 (mod3) または 6≡2(mod 3) のとき である。 a+α²62+64=0 (mod3) であることを証明せよ。」 愛界に使える なお、証明では, 解答のように表を用いると簡明である。 【CHART 201 決まった数の割り算や 倍数に関係する問題 解答 a,bは3で割り切れない整数であるから, 3を法として [1] a=1, b=1 [2] a=1,b=2 の [3] a=2, b=1 [4] a=2, b=2 [1]~[4] の各場合について, α' +α'b' + b を計算すると,次の 表のようになる。 16 aª a262 [1] 14=1 12･12=1 64 1¹=1 a¹ + a²b² +64 3=0 よって いずれの場合も 合同式を利用すると簡明 [2] 14≡1 12･22=1 24≡1 3=0 [3] 24=1 22・12=1 22.22=1 14≡1 24=1 3=0 3=0 a+a²b²+b=0 (mod 3) (8 [4] 24=1 したがって, a4 + α'b' + 64 は3で割り切れる。 p.492 基本事項 ③ (SI bom) 式が煩雑になるので,O (mod3) は省略した。 ただし, 下線のように最初 に断っておくこと｡ (e bo bor Wa bod) 124=16=1 (mod 3) 2²=4=1 (mod 3) 「 BJ FODOS (1) |A=B (mod m), C(C=D (mod m) s (N) ならば A+C=B+D (mod m)

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(1) None of us knew ( which 1 2 (2) Stratford-upon-Avon is the town (₁) Shakespeare was born. 1 which 2 where 3 in that 4 when (3) I will never forget the holidays ( 1 when where (5)( ) she remained silent then. why 1 Whoever (4) (…) I've wanted is not money but love. 2 That 1 Who (7) The subject in ( 1 which (6) I bought a new book yesterday, ( 1 that 2 which (8) This is ( 1 which ) you may say, I won't change my mind. (2) Whomever (2) 3 when Bidan 4 whom ) I stayed with her. adal 3 why (9) We stayed in an old house, ( 1 which 2 who (10) Who was the person to ( 1 who whom Mid 3 Whosem 4 What ali gan4 which 3 Whatevers 4 Wherever ) I found very interesting. (3) what ) I was interested in my school days is mathematics that where 4 when (3) ) we came to understand each other. 2 who (3 for which 4 who M (8) 4 how 01 las of ) roof was covered with snow. (3) whose whom ) you were speaking yesterday? 3 that whose

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natural surroundings of meaningful activity.) Little African children are OVE Leitne not paraded up and down with bundles of sticks on their heads in order to teach them how to balance such objects. Rather, when they are old

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【ⅢI】 次の(A), (B)の設問に答えよ。 (A)14点,(B) 6点) (A) 次の英文を読んで下の設問に最も適切な解答をせよ。 特に指示のない選択式の設問は記 号を1つ選んで答え, "You may choose more than one option." と指示のある設問に対して複 数の記号を選ぶ場合は, アイウエオ順に解答すること｡ Mike: Hello Alex, long time no see! Alex: Hi, it's been almost two years since we last met each other! How were you doing? Mike: Until recently, I was frustrated that I could not meet my friends at university, but I was able to spend more time with my family, so I was okay. By the way, how did you like the online classes? Alex: Personally, I did not like them. It was difficult for me to maintain my concentration at home. Also, I could not resist the temptation of using my smartphone, because there was no supervisor at home who checked whether I was working hard or not. Mike: If you use your phone during class, the professor will definitely tell you off! Mo Alex: Another reason why I prefer in-person classes is that I can ask questions or have discussions with my friends. In the Pre-covid-19 era, when I had questions, I went up to my friend Thomas, one of the best students in our faculty and he taught me everything that I did not understand. Mike: That was a huge issue for me as well. If I have questions piled up, then I am more likely to dislike the subject and have more anxiety towards it. So, my friends and I decided to have meetings online on a regular basis and this helped me to worry less about online learning. Alex: That was really ( 1 ) of you, I should have done that! So, are you in favor of online learning? Mike: Yes, although I have less face-to-face interaction with friends, I like online learning more because I do not have to spend a lot of time commuting to school. I live far away from university and it takes two hours for me to get here by train. B(A) Alex: Really! I did not know that, what time do you wake up? Mike: I usually wake up at 5 am. Alex: That's so early! What do you do on the train? Mike: I just do netsurfing and I do not feel that I use my time productively on the train. If we can continue to take online classes wherever we want, we can get more flexibility in our schedules, We won't have take the time to commute to the university to attend classes, or if we like it, we may even be able to watch lecture videos on our phones while traveling by train. Alex: I understand your opinion, but didn't you have any technical problems? Mike: I only had a few. Besides, most of the professors posted recorded videos of lectures after class. So, I watched the recordings when I missed some parts. Furthermore, I could study at my own pace and the videos allowed me to digest what I had learned. Alex: That's a good point, but it had an adverse effect on my learning. Mike: How? Alex: I started skipping my online classes because I thought I could just watch those recorded videos later. So, just before exams, I had so many videos to watch. Mike: Maybe, traditional classroom settings might be better for people like you. Alex: I think so. Oh, it's time to go to class. Mike: Oh, yeah, have a good day. Alex: You too! 問1 NOTES Topic of the conversation: (2) Standpoint Basis Mike (3) (5) Choose the best one to complete blank 1. 7 because cruel clever I kind 2 Choose the best title to complete blank 2. 7 How to get good results at university Technical issues in online classes Safe remote learning at home I Online learning or learning face to face Alex (4) (6) -11-

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【Ⅲ】 次の(A), (B)の設問に答えよ。 ((A)14点,(B)6点) (A) 次の英文を読んで,下の設問に最も適切な解答をせよ。 特に指示のない選択式の設問は記 号を1つ選んで答え, "You may choose more than one option." と指示のある設問に対して複 数の記号を選ぶ場合は、 アイウエオ順に解答すること。 Mike: Hello Alex, long time no see! Alex: Hi, it's been almost two years since we last met each other! How were you doing? Mike: Until recently, I was frustrated that I could not meet my friends at university, but I was able to spend more time with my family, so I was okay. By the way, how did you like the online classes? Alex: Personally, I did not like them. It was difficult for me to maintain my concentration at home. Also, I could not resist the temptation of using my smartphone, because there was no supervisor at home who checked whether I was working hard or not. Mike: If you use your phone during class, the professor will definitely tell you off! Hot Alex: Another reason why I prefer in-person classes is that I can ask questions or have discussions with my friends. In the Pre-covid-19 era, when I had questions, I went up to my friend Thomas, one of the best students in our faculty and he taught me everything that I did not understand. Mike: That was a huge issue for me as well. If I have questions piled up, then I am more likely to dislike the subject and have more anxiety towards it. So, my friends and I decided to have meetings online on a regular basis and this helped me to worry less about online learning. Alex: That was really (1) of you, I should have done that! So, are you in favor of online learning? Mike: Yes, although I have less face-to-face interaction with friends, I like online learning more. because I do not have to spend a lot of time commuting to school. I live far away from university and it takes two hours for me to get here by train. Alex: Really! I did not know that, what time do you wake up? Mike: I usually wake up at 5 am. ant mo Alex: That's so early! What do you do on the train? Mike: I just do netsurfing and I do not feel that I use my time productively on the train. If we can continue to take online classes wherever we want, we can get more flexibility in our schedules, We won't have to take the time to commute to the university to attend classes, or if we like it, we may even be able to watch lecture videos on our phones while traveling by train. Alex: I understand your opinion, but didn't you have any technical problems? Mike: I only had a few. Besides, most of the professors posted recorded videos of lectures after class. So, I watched the recordings when I missed some parts. Furthermore, I could study at my own pace and the videos allowed me to digest what I had learned. Alex: That's a good point, but it had an adverse effect on my learning. Mike: How? Alex: I started skipping my online classes because I thought I could just watch those recorded videos later. So, just before exams, I had so many videos to watch. Mike: Maybe, traditional classroom settings might be better for people like you. Alex: I think so. Oh, it's time to go to class. Mike: Oh, yeah, have a good day. Alex: You too! 問1 NOTES Topic of the conversation: ( 2 ) Standpoint Basis Mike (3) (5) Choose the best one to complete blank 1. 7 because cruel clever I kind 2 Choose the best title to complete blank 2. 7 How to get good results at university Technical issues in online classes Safe remote learning at home I Online learning or learning face to face Alex ( 4 ) (6) -11- 18

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基本 日本 本 (1) None of us knew ( 1 which 2 (2) Stratford-upon-Avon is the town ( where which ) she remained silent then. why when 2 (3) I will never forget the holidays ( ) I stayed with her. 1 when 2 where 3 why (4) (4) ( ) I've wanted is not money but love. 1 Who 2 That (6) I bought a new book yesterday, ( 1 that which ) Shakespeare was born. in that 4 when (5) ( ) you may say, I won't change my mind. 1 Whoever 2 Whomever (7) The subject in ( 1 which den 2 that 3 Whose (9) We stayed in an old house, ( 1 which (2) who 4) whom (8) This is () we came to understand each other. 1 which 2 who 3 for which which What (3) Whatever 4 Wherever ) I was interested in my school days is mathematics. (3) where 4 when ) I found very interesting. (3) what 4 who how ) roof was covered with snow. whose (3) (4) whom (10) Who was the person to ( ) you were speaking yesterday? (3) that (4) 1 who (2) whom whose

object weighing about one ton. このweighingは現在分詞らしいのですがよく分かりません。。 重さがある、という意味の動詞がなぜ現在分詞になれるのか教えて欲しいです🙇‍♀️

このAの正しい答えがわかる方がいたら教えて欲しいです。

10 15 5 20 Practice A Complete the sentences using the words in brackets. 1. Every year, about 1.3 million people (are killed) in traffic accidents around the world. [kill] 2. It is said but I've never seen any. [say] 3. TIME magazine ( ) that there are some bears in the mountains, every week since 1923. [publish] 4. Last week's solar eclipse be seen ) from Japan. [cannot see] 5. I don't know how I'm going to get to work while my car ). [repair] ( B Rewrite each sentence using the underlined words as the subject. 1. They teach three foreign languages at Kate's school. 2. Our professional staff will look after your child. 3. Someone saw two women enter the building. 4. Graham Bell invented the telephone in 1876. 5. We can use many different types of oil to make soap. House) Put the words in brackets in the correct order. 1. What [in/flower/ called /is/ this] English? It's called a sunflower. - 2. [any/be/station kiosk / newspapers / at / can / bought]. 3. The party [has/next/put/been / Wednesday /until/off]. 4. His latest book [is/into/being / Chinese / translated] by a Taiwanese publisher. 5. Une famous tree there, Jomonsagi, fold/be/3,000 years/is/to/ said / over]. .............

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A129 (1) 白玉4個, 赤玉6個が入っている袋から,玉を1個取り出 それをもとに戻さないで, 続いてもう1個を取り出す。 最初 まとめ 玉が白であるという事象をA, 2回目の玉が赤であるという 象をBとする。次の確率を求めよ。 (ア) PA(B) (イ) PA (B) (ウ) P(B) (2) 当たりくじ4本を含む 20本のくじがある。 引いたくじはも [ に戻さないで, A,B,Cの3人がこの順に1本ずつくじを引 (ア) Bが当たる確率を求めよ。 (イ) AとBでは当たる確率はどちらが高いか。 (ウ) Cがはずれる確率を求めよ。