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Quy luật: Hiệu của số lớn hơn trừ cho số nhỏ hơn trong mổi ô chính là kết quả của ô màu vàng đối diện
17-13=4
15-6=9
14-8=6
19-12=7
23-15=8
27-25=2
23-18=5
Suy ra: 12-x=3
=> x=12-3=9
Đáp án C
Giải thích: Mỗi số trong hình tam giác màu vàng bằng số lớn hơn của hình bình hành đối diện trừ đi số bé hơn ở hình bình hành đối diện.
=> ? - 12 = 3 hoặc 12 - ? = 3
=> Đáp án là 15 hoặc 9
Đáp án: c
Bổ sung: Đáp án cũng có thể là 15

Ta có các quy luật sau:
\(\left(1+3\right)-2=2\)
\(\left(2+2\right)-3=1\)
\(\left(5+5\right)-6=4\)
Vậy dòng cuối là:
\(\left(5+9\right)-5=9\)
Số điền vào là 9
(Quy luật: lấy 2 số phía dưới cộng với nhau rồi trừ cho số phía trên sẽ ra được số ở giữa)

1: \(1026-\left\lbrack\left(3^4+1\right):41\right\rbrack\)
\(=1026-82:41\)
=1026-2
=1024
\(2^{11}:\left\lbrace1026-\left\lbrack\left(3^4+1\right):41\right\rbrack\right\rbrace\)
\(=2^{11}:2^{10}=2\)
2: \(250:\left\lbrace1500:\left\lbrack4\cdot5^3-2^3\cdot25\right\rbrack\right\rbrace\)
\(=250:\left\lbrace1500:\left\lbrack4\cdot125-8\cdot25\right\rbrack\right\rbrace\)
\(=250:\left\lbrace1500:\left\lbrack500-200\right\rbrack\right\rbrace=250:\frac{1500}{3}=250:500=0,5\)
3: \(12+3\cdot\left\lbrace90:\left\lbrack39-\left(2^3-5\right)^2\right\rbrack\right\rbrace\)
\(=12+3\cdot\left\lbrace90:\left\lbrack39-\left(8-5\right)^2\right\rbrack\right\rbrace\)
\(=12+3\cdot\left\lbrace90:\left\lbrack39-3^2\right\rbrack\right\rbrace\)
\(=12+3\cdot\left\lbrace90:\left\lbrack39-9\right\rbrack\right\rbrace\)
\(=12+3\cdot\left\lbrace90:30\right\rbrace=12+3\cdot3=21\)
4: \(24:\left\lbrace390:\left\lbrack500-\left(5^3+49\cdot5\right)\right\rbrack\right\rbrace\)
\(=24:\left\lbrace390:\left\lbrack500-\left(125+245\right)\right\rbrack\right\rbrace\)
\(=24:\left\lbrace390:\left\lbrack500-125-245\right\rbrack\right\rbrace\)
\(=24:\left\lbrace390:\left\lbrack375-245\right\rbrack\right\rbrace\)
\(=24:\left\lbrace390:130\right\rbrace=\frac{24}{3}=8\)
5: \(117:\left\lbrace\left\lbrack79-3\cdot\left(3^3-17\right)\right\rbrack:7+2\right\rbrace\)
\(=117:\left\lbrace\left\lbrack79-3\cdot\left(27-17\right)\right\rbrack:7+2\right\rbrace\)
\(=117:\left\lbrace\left\lbrack79-3\cdot10\right\rbrack:7+2\right\rbrace\)
\(=117:\left\lbrace49:7+2\right\rbrace=\frac{117}{9}=13\)
6: \(514-4\cdot\left\lbrace\left\lbrack40+8\left(6-3\right)^2\right\rbrack-12\right\rbrace\)
\(=514-4\cdot\left\lbrace\left\lbrack40+8\cdot3^2\right\rbrack-12\right\rbrace\)
\(=514-4\cdot\left\lbrace\left\lbrack40+8\cdot9\right\rbrack-12\right\rbrace\)
\(=514-4\cdot\left\lbrace112-12\right\rbrace\)
\(=514-4\cdot100=514-400=114\)
7: \(25\cdot\left\lbrace32:\left\lbrack\left(12-4\right)+4\cdot\left(16:2^3\right)\right\rbrack\right\rbrace\)
\(=25\cdot\left\lbrace32:\left\lbrack8+4\cdot2\right\rbrack\right\rbrace\)
\(=25\cdot\left\lbrace32:16\right\rbrace=25\cdot2=50\)
8: \(30:\left\lbrace175:\left\lbrack355-\left(135+37\cdot5\right)\right\rbrack\right\rbrace\)
\(=30:\left\lbrace175:\left\lbrack355-\left(135+185\right)\right\rbrack\right\rbrace\)
\(=30:\left\lbrace175:\left\lbrack355-320\right\rbrack\right\rbrace=30:\left\lbrace175:35\right\rbrace=\frac{30}{5}=6\)
9: \(32:\left\lbrace160:\left\lbrack300-\left(175+21\cdot5\right)\right\rbrack\right\rbrace\)
\(=32:\left\lbrace160:\left\lbrack300-\left(175+105\right)\right\rbrack\right\rbrace\)
\(=32:\left\lbrace160:\left\lbrack300-280\right\rbrack\right\rbrace\)
\(=32:\left\lbrace160:20\right\rbrace=\frac{32}{8}=4\)
10: \(750:\left\lbrace130-\left\lbrack\left(5\cdot14-65\right)^3+3\right\rbrack\right\rbrace\)
\(=750:\left\lbrace130-\left\lbrack\left(70-65\right)^3+3\right\rbrack\right\rbrace\)
\(=750:\left\lbrace130-\left\lbrack5^3+3\right\rbrack\right\rbrace\)
\(=750:\left\lbrace130-128\right\rbrace=750:2=375\)

c: \(\left(x-1\right)^3=\left(-9\right)^3\)
=>x-1=-9
=>x=-9+1=-8
f: \(3x-2^3=7+\left(-9\right)\)
=>3x-8=7-9=-2
=>3x=-2+8=6
=>x=2

1: \(3^2\cdot5^3+9^2\)
\(=9\cdot125+81\)
=1125+81
=1206
2: \(55+45:3^2\)
\(=55+45:9\)
=55+5
=60
3: \(8^3:4^2-5^2=64:16-25=4-25=-21\)
4: \(5\cdot3^2-32:2^2=5\cdot9-32:4=45-8=37\)
5: \(16:2^3+5^2\cdot4=16:8+25\cdot4\)
=2+100
=102
6: \(5\cdot2^2-18:3^2\)
\(=5\cdot4-18:9\)
=20-2
=18
7: \(3\cdot5^2-15\cdot2^2=3\cdot25-15\cdot4=75-60=15\)
8: \(2^3\cdot6-72:3^2=8\cdot6-72:9=48-8=40\)
9: \(5\cdot2^2-27:3^2\)
\(=5\cdot4-27:9\)
=20-3
=17
10: \(3\cdot2^4+81:3^2=3\cdot16+81:9=48+9=57\)
11: \(4\cdot5^3-32:2^5=4\cdot125-32:32=500-1=499\)
12: \(6\cdot5^2-32:2^4=6\cdot25-32:16=150-2=148\)
a) \(4\dfrac{7}{10}=\dfrac{47}{10};6\dfrac{7}{10}=\dfrac{67}{10}\)
vì \(\dfrac{47}{10}< \dfrac{67}{10}\) nên \(4\dfrac{7}{10}< 6\dfrac{7}{10}\)
b) \(3\dfrac{4}{15}=\dfrac{49}{15};3\dfrac{11}{15}=\dfrac{56}{15}\)
vì \(\dfrac{49}{15}< \dfrac{56}{15}\) nên \(3\dfrac{4}{15}< 3\dfrac{11}{15}\)
c) \(5\dfrac{1}{9}=\dfrac{46}{9};2\dfrac{2}{5}=\dfrac{12}{5}\)
MSC: 45
Quy đồng: \(\dfrac{46}{9}=\dfrac{230}{45};\dfrac{12}{5}=\dfrac{108}{45}\)
mà \(230>108\) nên \(\dfrac{46}{9}>\dfrac{12}{5}\Rightarrow5\dfrac{1}{9}>2\dfrac{2}{5}\)
d) Rút gọn: \(2\dfrac{10}{15}=2\dfrac{2}{3}\) nên \(2\dfrac{2}{3}=2\dfrac{10}{15}\)
13:
a: 4<6
=>4+7/10<6+7/10
=>\(4\dfrac{7}{10}< 6\dfrac{7}{10}\)
b: 4/15<11/15
=>3+4/15<3+11/15
=>\(3\dfrac{4}{15}< 3\dfrac{11}{15}\)
c: 5+1/9=46/9=230/45
2+2/5=7/5=63/45
mà 230>63
nên \(5\dfrac{1}{9}>2\dfrac{2}{5}\)
d: \(2+\dfrac{2}{3}=\dfrac{8}{3};2+\dfrac{10}{15}=2+\dfrac{2}{3}=\dfrac{8}{3}\)
=>\(2\dfrac{2}{3}=2\dfrac{10}{15}\)