Toán

Độ dài cạnh hình thoi con diều là:

[6,8 - (1,2 + 1,8)] : 4 = 0,75 (m)

\(\dfrac{\sqrt{a}+\sqrt{ab}}{a-b}-\dfrac{\sqrt{b}}{\sqrt{a}-\sqrt{b}}\left(a,b\ge0;a\ne b\right)\)

\(=\dfrac{\sqrt{a}+\sqrt{ab}}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}-\dfrac{\sqrt{b}\left(\sqrt{a}+\sqrt{b}\right)}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\)

\(=\dfrac{\sqrt{a}+\sqrt{ab}-\sqrt{ab}-b}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\)

\(=\dfrac{\sqrt{a}-b}{\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)}\)

\(=\dfrac{\sqrt{a}-b}{a-b}\) 

102 - (35 + x) = 40

35 + x = 102 - 40

35 + x = 62

x = 62 - 35

x = 27

\(102-\left(35+x\right)=40\\ 35+x=102-40\\ 35+x=62\\ x=62-35\\ x=27\)

102 - (35 + x) = 40

=> 35 + x = 62

=> x = 27 

48/41 + 45/27 + 34/28 + 37/23 - 18/27 - 6/28 - 7/41 - 14/23

= (48/41 - 7/41) + (45/27 - 18/27) + (34/28 - 6/28) + (37/23 - 14/23)

= 1 + 1 + 1 + 1

= 4

Bài 2

1) -11/8 - 1 4/11 + 1 3/8 + 0,5 - 5/41

= -11/8 - 15/11 + 11/8 + 1/2 - 5/41

= -15/11 + 1/2 - 5/41

= -19/22 - 5/41

= -889/902

2) -(3/7 + 3/8) - (-3/8 + 4/7)

= -3/7 - 3/8 + 3/8 -4/7

= (-3/7 - 4/7) + (-3/8 + 3/8)

= -1

3) -5/17 . 31/33 + (-5/17).2/33 + 2 5/17

= -5/17.(31/33 + 2/33) + 39/17

= -5/17 + 39/17

= 2

4) 12/17 . 5/7 + (-12/17).2/17 - 4/17

= 12/17.(5/17 - 2/17) - 4/17

= 12/17 . 3/17 - 4/17

= 36/17 - 4/17

= 32/17

5) 3/8 . 23/14 - 3/8 . 9/14 + (3/8)⁰

= 3/8 . (23/14 - 9/14) + 1

= 3/8 + 1

= 11/8

6) -3/11 . 5/7 + 5/7 . (-8/11) + 2 5/7

= 5/7 . (-3/11 - 8/11) + 19/7

= 5/7 . (-1) + 19/7

= -5/7 + 19/7

= 1

7) 35 1/6 : (-4/5) - 45 1/6 : (-4/5)

= 211/6 . (-5/4) - 271/6 . (-5/4)

= -5/4 . (211/6 - 271/6)

= -5/4 . 10

= -25/2

8) (-6/7 + 6/19 - 6/31)/(9/7 - 9/19 + 9/31)

= (-3030/4123)/(5196/4123)

= -505/866

9) (0,125)¹⁰⁰ . 8¹⁰¹

= 1/8¹⁰⁰ . 8¹⁰¹

= 8

10) -3,75 . (-7,2) + 2,8 . 3,75

= 3,75.(7,2 + 2,8)

= 3,75 . 10

= 37,5

87561 - x - 12345 = 10234

75216 - x = 10234

x = 75216 - 10234

x = 64982

a: \(\dfrac{13}{25}-\dfrac{31}{41}+\dfrac{12}{25}-\dfrac{10}{41}-0,5\)

\(=\left(\dfrac{13}{25}+\dfrac{12}{25}\right)-\left(\dfrac{31}{41}+\dfrac{10}{41}\right)-\dfrac{1}{2}\)

\(=1-1-\dfrac{1}{2}=-\dfrac{1}{2}\)

b: \(\left(-2\right)^3-\left(-\dfrac{1}{2}\right)^2:\dfrac{-1}{16}-2023^0\)

\(=-8-\dfrac{1}{4}\cdot\dfrac{-16}{1}-1\)

=-8+4-1

=-4-1

=-5

c: \(\left(-\dfrac{1}{3}\right)^2+\dfrac{4}{3}:2-0,6\)

\(=\dfrac{1}{9}+\dfrac{4}{3}\cdot\dfrac{1}{2}-\dfrac{3}{5}\)

\(=\dfrac{1}{9}+\dfrac{2}{3}-\dfrac{3}{5}\)

\(=\dfrac{10}{90}+\dfrac{60}{90}-\dfrac{54}{90}=\dfrac{16}{90}=\dfrac{8}{45}\)

d: \(\dfrac{2}{9}\cdot\dfrac{7}{5}+\dfrac{2}{9}\cdot\dfrac{-11}{5}+\dfrac{4}{5}\cdot\dfrac{2}{9}\)

\(=\dfrac{2}{9}\left(\dfrac{7}{5}-\dfrac{11}{5}+\dfrac{4}{5}\right)\)

\(=\dfrac{2}{9}\cdot0=0\)

a: \(18\cdot7+65:13\)

=126+5

=131

b: \(785-\dfrac{323+148}{3}+2781\)

\(=785+2781-\dfrac{471}{3}\)

=3566-157

=3409

c: \(703-\dfrac{140}{42+28}-17^6\cdot17^9:17^{13}\)

\(=703-\dfrac{140}{70}-17^2\)

\(=703-289-2\)

=703-291

=412

e: \(\left(2^3\cdot9^4+9^3\cdot45\right):\left(9^2\cdot10-9^2\right)\)

\(=\dfrac{9^3\left(2^3\cdot9+45\right)}{9^2\cdot\left(10-1\right)}=\dfrac{9^3}{9^3}\cdot\left(8\cdot9+45\right)\)

=72+45

=117

a) Diện tích cần quét sơn:

(9 + 6).2.4 + 9.6 - 11,25 = 172,75 (m²)

b) Số tiền phải trả:

172,75 . 100000 = 17250000 (đồng)

a) Cạnh của mảnh sân:

√169 = 13 (m)

b) Diện tích viên gạch:

50 . 50 = 2500 (cm²) = 0,25 (m²)

Số viên gạch cần dùng:

169 : 0,25 = 676 (viên)

a: Cạnh của mảnh sân là: \(\sqrt{169}=13\left(m\right)\)

b:

50cm=0,5m

Diện tích 1 viên gạch là: \(0,5^2=0,25\left(m^2\right)\)

Số viên gạch cần dùng tới là:

\(169:0,25=676\left(viên\right)\)