2
3
4
5
6
7
8
9
10
11
1 3
12
13
14
15
𝐿 = (2)(30)(3.14) = 1.884
(1.884)(10) = 18.84 16
4
2𝑐
2) − 3 𝑎5 𝑏 8 + 7𝑑4
4
2
−3 𝑦7
𝑐 𝑑4
17
2
− 11 (𝑥 3 𝑦 3 )4 5√𝑎7
4
− 3 𝑥 3 𝑦𝑧 2 4
1 2
1
𝑧=2
− 3 (−1)3 9 (2) 3
18
19
20
p p 1 100 2 4 p p p 1 100 2 4 p p p 1 100 1/ 2 1/ 4 pp
p p 2p 4p 1 100
pp
p p 1 100 1/ 2 1/ 4
21
22
a b
𝑎 𝑏
4
𝑐
= ,
= 2
𝑎: 𝑏 ∷ 𝑐: 𝑑
𝑑
12 6
,
9: 24 ∷ 18: 48
7
𝑥
=4 3 23
1 2
$ $
$
$
$
$
24
LECHE (gramos)
$
$
$
$ $
1600đ?‘”đ?‘&#x; $196.00 = 2200đ?‘”đ?‘&#x; đ?‘Ľ 25
𝑥=
(2200𝑔𝑟)($196.00) 1600𝑔𝑟 𝑥 = $269.50
$2300.00 100% = 𝑥 20% 𝑥=
($2,300.00)(20%) 100%
𝑥 = 460.00 $2,300.00 − $460.00 = $1840.00
1𝑐𝑚 5𝑘𝑚 = 13𝑐𝑚 𝑥 𝑥=
(13𝑐𝑚)(5𝑘𝑚) 1𝑐𝑚 𝑥 = 65𝑘𝑚
26
25 𝑎𝑙𝑢𝑚𝑛𝑜𝑠 → $300.00 20 𝑎𝑙𝑢𝑚𝑛𝑜𝑠
→
𝑥
20 𝑎𝑙𝑢𝑚𝑛𝑜𝑠 $300.00 = 25 𝑎𝑙𝑢𝑚𝑛𝑜𝑠 𝑥 𝑥=
(25 𝑎𝑙𝑢𝑚𝑛𝑜𝑠)($300.00) (20 𝑎𝑙𝑢𝑚𝑛𝑜𝑠) 𝑥 = $375.00
3 𝑓𝑢𝑔𝑎𝑠 → 4 𝑑í𝑎𝑠 → 4,000 𝑙𝑖𝑡𝑟𝑜𝑠 6 𝑓𝑢𝑔𝑎𝑠
→
5 𝑑í𝑎𝑠
→
𝑥
27
(
3 𝑓𝑢𝑔𝑎𝑠 4 𝑑í𝑎𝑠 4,000 𝑙𝑖𝑡𝑟𝑜𝑠 )( )= 6 𝑓𝑢𝑔𝑎𝑠 5 𝑑í𝑎𝑠 𝑥
12 4,000 𝑙𝑖𝑡𝑟𝑜𝑠 = 30 𝑥
𝑥 = 10,000 𝑙𝑖𝑡𝑜𝑠
(100)(200−160) 200
= 20
28
𝑚=
𝑦2 − 𝑦1 𝑥2 − 𝑥1
𝑚=
480 − 240 = 120 4−2
29
30
31
(3𝑥)(−𝑥 2 )
−3𝑥 3
(2𝑥)(3 − 𝑥 2 )
(2𝑥)(3) + (2𝑥)(−𝑥 2 ) 6𝑥 − 2𝑥 3
(5𝑥 − 𝑦)(3𝑦 − 𝑥)
(5𝑥)(3𝑦) + (5𝑥)(−𝑥) + (−𝑦)(3𝑦) + (−𝑦)(−𝑥)
15𝑥𝑦 − 5𝑥 2 − 3𝑦 2 + 𝑥𝑦
32
16𝑥𝑦 − 5𝑥 2 − 3𝑦 2
y x
y
x
a+4
a+1
𝑎2 +4𝑎+4 2 𝑎2 +5𝑎+8 2 𝑎2 +5𝑎+5 2 𝑎2 +5𝑎+4 2
33
34
35
36
3 6
1
=2
37
38
1 𝑎
1
(𝑎𝑥) = (−𝑏) 𝑎
𝑏
𝑥 = −𝑎
39
𝑥=
20 = −1 −20
40
𝑥=
96 = 32 3
𝑎≠0
41
𝑥=
±𝑏√𝑏 2 − 4𝑎𝑐 2𝑎
42
𝑥=
−7 ± √72 − 4(1)(10) −7 ± √49 − 40 −7 ± √9 −7 ± 3 = = = 2(1) 2 2 2
−7 + 3 −4 = = −2 2 2 −7 − 3 −10 𝑥2 = = = −5 2 2 𝑥1 =
43
⇒
44
⇒
45
{
ЁЭСе + ЁЭСж = 25 } ЁЭСеЁЭСж = 127
ЁЭСе 2 тИТ 25ЁЭСе + 144 = 0
ЁЭСе(25 тИТ ЁЭСе) = 144,
ЁЭСе1 = 9 ЁЭСж
ЁЭСе2= 16 46
o o o
o o o
47
r 2 (12 ) 2 90 º Asector 113 .04 360 360
48
4m
3.5 m 4.5 m 3m
24 √3 𝑚 24 √2 𝑚
𝑠𝑒𝑛 𝜃 =
𝐶𝑂 𝐻
∴
𝐻=
𝐶𝑂 12 12 = = = 24√3 𝑚 𝑠𝑒𝑛 𝜃 𝑠𝑒𝑛 60 √3 2 49
50
30% 20% 10% 0% 10 9
30%
8
7
6
30% 25% 20%
20%
15% 10%
10% 0% 10
9
8
7
6
10
9
8
7
6
10
9
8
7
6
30% 20% 10% 0%
30% 20% 10% 0%
51
ï‚·
52
5 9 7 18 11 18 4 9
27 23 50 5 + = = 90 90 90 9
53
54
55
(
Narrativos y novela)
Expositivos (divulgación científica e informativos)
Argumentativos (ensayos, artículos de opinión)
56
57
58
59
60
61
62
63
64
65
66
67
68
ï‚·
69

70
71
72
73
74
75
76
77
ï‚·
78
79
80
81
82
83
84
85
86
87
110 cm 110√3 110 √3
55
latas 88
661ЁЭСе тИТ 100ЁЭСе 2 + 4ЁЭСе 3 616 тИТ 100ЁЭСе + 4ЁЭСе 2 28ЁЭСе тИТ 4ЁЭСе 2 5 тИТ 12ЁЭСе тИТ 4ЁЭСе 2
89
𝐴 = 𝜋𝑟 2
154 m²
90
91
92
𝜋 2 4 3 3 2 3 4
𝜋 𝜋 𝜋
93
94
2ЁЭСе 2 + 5ЁЭСе тИТ 12 3ЁЭСе + 1 2ЁЭСе 2 тИТ 11ЁЭСе тИТ 12 6ЁЭСе + 2
95
𝜋 = 3.14
78.5 m2 80.5 m2 82.5 m2 84.5 m2
96
1 8
1 6 2 8 1 3
7 9 3 7
97
𝑦 = 3𝑥 + 7
𝒙
𝒚,
98
√29𝑚 2√29𝑚 29m 58m
99
𝜋=
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123