112.1 陰で見ずらくてすみません。 記述これだとダメですよね？？

480 HA 00000 基本例題112 互いに素に関する証明問題 (1) (1) nは自然数とする。 n +3は6の倍数であり, n+1は8の倍数であるとき、 n+9は24の倍数であることを証明せよ。 (2) 任意の自然数nに対して, 連続する2つの自然数nとn+1は互いに素であ ることを証明せよ。 (2) 指針 (1) 次のことを利用して証明する。 a, b, kは整数とするとき p.476 基本事項 ②. 基本 111 【CHART α, 6 は互いに素で, ak が6の倍数であるならば,kは6の倍数である。 (2) +1は互いに素⇔nとn+1の最大公約数は 1 nとn+1の最大公約数をg とすると n=ga, n+1=gb(a,bは互いに素) この2つの式からnを消去してg=1を導き出す。 ポイントは A,Bが自然数のとき, AB=1 ならば A=B=1 解答 (1) n+3=6k,n+1=81(k, lは自然数) と表される。 n+9=(n+3)+6=6k+6=6(k+1) n+9=(n+1)+8=81+8=8(+1) よって 6(k+1)=8(+1) すなわち 3 (k+1)=4(+ ! 3と4は互いに素であるから, k+1は4の倍数である。 したがって, k+1=4m (mは自然数) と表される。 ゆえに n+9=6(k+1)=6.4m=24m したがって, n +9は24の倍数である。 (2) nとn+1の最大公約数をgとすると a,bは ①1 ak=blならばんは6の倍数, I αの倍数 互いに素 2 aとbの最大公約数は 1 練習 112 と表される。 n=ga をn+1=gbに代入すると ga+1=gb すなわち g (6-α)=1 n=ga,n+1=gb (a,bは互いに素である自然数) 重要 114, g=1 よって, nとn+1 の最大公約数は1であるから, nとn+1 は互いに素である。 注意 (2) の内容に関連した内容を、 次ページの[参考] で扱っている。 このとき, 1+1は3の倍数 である。 したがって, 1+1=3m² と表されるから, n+9=8.3m=24m としてもよい。 g, a,b は自然数で, n <n+1 より b-a>0であるからn=ga,n+1=gb 積が1となる自然数は1だ けである。 (1) は自然数とする。 n +5 は7の倍数であり, n +7は5の倍数であるとき、 +12を3で割った余りを求めよ。 (2) nを自然数とするとき, 2n-1と2n+1は互いに素であることを示せ。 [ (1) 中央大 (道] p.484 EX 79 基本 自然数の とを証明 指針▷ at そこ at. なお CHAR 解答 a+b と ab 数』を公約 a+b= と表される ② から,c aがpの倍 このとき, bもの倍 これはαと bがpの倍 aとbが したがって 参考 前ペ の問題を 問題 素 [証明] ni る ※各自 n 素数が無 上の 法である 練習 a, ③113 (1)

至急お願いします 教えてください！

3 次の各組の文がほぼ同じ意味になるように, (2) (3) に適する語を書きなさい。 (5) It is important to study English every day. English every day He didn't say goodbye, and went out. He went out important. She can play the piano well. She is at the piano. (4) I talked with Jane, and I enjoyed it very much. with Jane very much. You helped me yesterday. Thank you for that. Thank you goodbye. me yesterday. ( 8点×5)

働いていますということは、ingがつくと思ったんですけど、何故workingではなく、 worksなのですか？ 教えていただきたいです。

私の姉は病気の人々を助けるために一生懸命に働いています。 (三重 (例) My sister works hard to help sick people.

高一の動名詞の問題です。 日本語に合うように(　)に入れます。 分かりません。教えて下さい。できるだけベストアンサーにします。！❢

(5) 私は彼のスピーチを聞いて泣かずにはいられなかった. I( ) not ( ) ( (6) 彼と議論してもむだだ. ) is ( )over his speech. ) *arguing with him. (7) 駅に着くとすぐに私は母に電話をした. ( (8) 明日映画に行きませんか. How ( ) ( (9) 彼女は早起きには慣れていない. She is not used ( (10) 将来何が起こるかはわからない. There is ( ) ( )() at the station, I called my mother. ) to the movies tomorrow? *「議論する 」 ) what will happen in the future. up early.

こちらのプリントの回答教えてください。 よろしくお願いします。

4 eehaupbsorl elstog 空欄にあてはまるものを (A)~(D) の中から選んで記号を書きましょう。 rinom soon tundA (8) 1. My first of Toronto was very positive. (A) impressed (B) impressing (C)impressive (D) impression swdua vd oo visuay 1 (5) 3. 2. The special equipment was (A) originally (B) origin (C) original (D) originality 4. The manufacturer (A) produces vaboj alriemriserter prind soinom bib vilW..t A teacher's class. Sum ob incinu vertone (A) friendship (B) friendlily (C) friendly (D) friendliness Autoledad blow approach makes new students feel comfortable in their new es new students fee (B) has produced shwob trand enirkham y 5. It is necessary that the applicant 8. Would you mind (A) open made for those who have mobility problems. mismo2( bloo out a'fariT (8) Of(0) tripim men (8) TV sets in developing countries ten years ago. (D) has been produced (C) produced (A) fill (B) filled (C) fills (D) would fill 6. Tomoko invited me to see the musical with (A) she (C) (B) heraners 10. Is there anyone (A)whom blueWF Tesy jasi cio 7. The CEO by the charity foundation to speak at their annual conference, but he had to decline the request because of a scheduling conflict. (A) asked (D) had been asking (B) was asked (C) has asked 9. The meeting will be held (A) in dar out the form before the job interview. toy bollit need cen (A) admun orong olidam ym e'evgH (8) Jeneves need even ment (2) eldabil opening prupiolansi (B) whose blow reiwi at sol no (D) herself them. the window for me? vietne.m (C) to open (D) to be opening Houp (0) (B) on (C) for (D) at nismen (0) Meason (2) gribnstalue (8) 10:30 in the conference room. is against this alternative proposal? (D) which m) boysin .GP .er Deda briced OS eldialval (A) 11. Tim is as as Linda. (A) more intelligent (B) intelligent (C) less intelligent (D) better intelligent for storage. (A) designated (B) detained (C) reciprocated (D) signified 12. According to the proposal, a large block of rooms in the east wing of the new building will be

こちらのプリントの回答教えてください。 よろしくお願いします。

4 eehaupbsorl elstog 空欄にあてはまるものを (A)~(D) の中から選んで記号を書きましょう。 rinom soon tundA (8) 1. My first of Toronto was very positive. (A) impressed (B) impressing (C)impressive (D) impression swdua vd oo visuay 1 (5) 3. 2. The special equipment was (A) originally (B) origin (C) original (D) originality 4. The manufacturer (A) produces vaboj alriemriserter prind soinom bib vilW..t A teacher's class. Sum ob incinu vertone (A) friendship (B) friendlily (C) friendly (D) friendliness Autoledad blow approach makes new students feel comfortable in their new es new students fee (B) has produced shwob trand enirkham y 5. It is necessary that the applicant 8. Would you mind (A) open made for those who have mobility problems. mismo2( bloo out a'fariT (8) Of(0) tripim men (8) TV sets in developing countries ten years ago. (D) has been produced (C) produced (A) fill (B) filled (C) fills (D) would fill 6. Tomoko invited me to see the musical with (A) she (C) (B) heraners 10. Is there anyone (A)whom blueWF Tesy jasi cio 7. The CEO by the charity foundation to speak at their annual conference, but he had to decline the request because of a scheduling conflict. (A) asked (D) had been asking (B) was asked (C) has asked 9. The meeting will be held (A) in dar out the form before the job interview. toy bollit need cen (A) admun orong olidam ym e'evgH (8) Jeneves need even ment (2) eldabil opening prupiolansi (B) whose blow reiwi at sol no (D) herself them. the window for me? vietne.m (C) to open (D) to be opening Houp (0) (B) on (C) for (D) at nismen (0) Meason (2) gribnstalue (8) 10:30 in the conference room. is against this alternative proposal? (D) which m) boysin .GP .er Deda briced OS eldialval (A) 11. Tim is as as Linda. (A) more intelligent (B) intelligent (C) less intelligent (D) better intelligent for storage. (A) designated (B) detained (C) reciprocated (D) signified 12. According to the proposal, a large block of rooms in the east wing of the new building will be

26番の問題です。 答えはDなんですが、 穴が空いてるから返品するのになぜ急にサイズの話になるんでしょうか？ hisakoが残念と言っているから否定的なことが入るのは分かりますが、急に話が変わって変な感じがします…

Ⅲ 次の会話文の空所 1つ選べ。(20点) 25 A woman is at a department store. 31 Sales Clerk: Hi there, how can I help you? Hisako: Hello, I bought this outfit a couple of weeks ago but I found this hole the other day before I put it on. Sales Clerk: I see. Have you brought a receipt with you? Hisako: I can't find it anywhere, I've looked all over the house, in my bag, everywhere, but I can't find it. 25 Sales Clerk: Yes, if your item was damaged when you bought it. Hisako: Look, the tags are still on it. I haven't worn it at all. Sales Clerk: I see. Let me check. 26 Hisako: That's too bad. The outfit is really nice. Sales Clerk: There's nothing scheduled. something else, or 27 25 26 28 Would that be alright for you? Will you get any more in soon? You can choose I can give you a coupon for now. We can give you a call when we get more of these. Hisako: That would be fine. Sales Clerk: Because you don't have the receipt, I'll need to take some details. Hisako: Sure, no problem. Sales Clerk: Could you write down your name, phone number and email address on this form for me? Hisako : 29 Sales Clerk: Either is fine. Anywhere we can contact you in the day time Hisako: OK, I'll write my mobile number down. Sales Clerk: Thanks. Here's your voucher. You can use it for almost anything in the store. 31 food, drinks and sale items. A~Dのうちから A So, here it is. B Finally, I found it here. C Is it possible to exchange it without the receipt? D What is the store policy in this case? A When did you wear it? B We have a replacement outfit available for you. C Let me bring a new one for you now. D I'm afraid we don't have any more in that size. 30

穴埋め問題、並べ替え問題教えてください。

18 不定詞 to不定詞:〈to + 動詞の原形〉の形で,名詞・形容詞・副詞の働きをする。 ■原形不定詞:〈使役動詞・知覚動詞 ・ help + O+原形不定詞〉の形で用いられる。 < <be 動詞 + to不定詞〉:予定、義務命令, 可能, 運命などを表す。 Target 1 Not a cloud was to be seen in the sky. (空には雲1つ見えなかった) *可能の意味で使われるときには,否定文で受動態であることが多い。 (2) ●不定詞を用いた重要表現: 以下のように書きかえることができる。 ・too~ (for -) to... 2 SO ~ that can't ... (~すぎて･･･できない) enough (for -) to... ~ that-(can)... (十分~なので….できる)など SO ~ - Target 2 It's too cold to swim today. (今日は寒すぎて泳ぐことができない) = It's so cold that we can't swim today. 1 次の各組の文がほぼ同じ内容になるように, The ice is so thick that we can walk on it. The ice is thick I couldn't find my smartphone anywhere. My smartphone was nowhere に適する語を書きなさい。 (3) That computer is so expensive that I can't buy it. That computer is expensive 2 日本語の意味に合うように,( )内の語句を並べかえなさい。 (1)大統領は明日, テレビで演説することになっている。 (5点x3=15点,各完答) (2) 彼らはリサに、彼女の意志に反してバイオリンを弾かせた。 They (the / play / against/Lisa/violin/made/her will). They walk on. (on / a speech/is/the president / make / TV / to) tomorrow. found. (3) 父さんが呼んでいる。 居間へ来なさい。 Father is calling you.(living room/to/to/you/come/the / are). Father is calling you. me to buy. (5点x3=15点) tomorrow.

2の（1）から（4）の解説をお願いします🙇‍♀️

出石 2 次の(1)~(4) の下線部と同じ用法の 〈to+動詞の原形>を含む文を 出る 下から選び,記号で答えなさい。 (1) Bob visited Mai to help her. (2) I have something to tell Lisa. (3) Aya was surprised to see me there. (4) We liked to go fishing in the river. 7 London has many interesting places to visit. I got up early to make breakfast. 1 You need to wash your hands before dinner. I I'm very happy to be a member of this team. ( ( ( (

解いたのがあっているか教えて欲しいです。 G(１)、(3)とHが分からなかったので解説をお願いしたいです。

94 総合問題 次の各文の下線部のうち, 誤りがあるものを ① ~ ④ の中から1つ選んで記号で答えなさい。 (1) A feeding machine that designed to make life easier for older people 3 has won a top prize at an award ceremony. (2) Since this will be the last trip, you 3 may take 4whomever wants to go. (3) The girl has gone to Mexico City by herself 3 a couple of days ago to join her family. (4) Will you make a note of my phone number and get him 3 to call me when he will be back? (5) Ken changed his major Ofrom French to English, hoping 3 to find a job 4more easy. (6) The idea which one should know 3 one's immediate neighbors Ⓒhas died out in large cities, but still lingers in small towns. (7) Turned suddenly, with tears in her eyes, Mary ran out of the room without saying a word. (8) He wanted to help her out, but whenever he asked about 3 her past, she avoided to answer his questions. UNACHA E 次の文の中から文法または語法上誤っている英文をそれぞれ1つ選び記号で答えなさい。 (1) He must have become very sad at the news of his father's death. ? You had not better read such an obscene book. 3 We cannot be too careful in choosing our friends. 4 As a university student, I would often visit the museum. (2) They say that he is known to everybody. 2 He is said to have lost his fortune. 3 He is laughed by his friends. 4 Coffee is sold at that store.