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3 years ago

Show that 1/ 1+ √2 + 1 /√2+√3 = -1 + √3

Mathematics

2 answers:

laila [671]3 years ago

6 0

Answer:

See below.

Step-by-step explanation:

1/( 1+√2) + 1 /(√2+√3)

Multiply both fractions by the conjugate of the denominators:

= (1 -√2) / (1 +√2)(1 - √2) + (√2 - √3) / (√2 + √3)(√2 - √3)

= (1 - √2) / -1 + (√2 - √3) / -1

= -1 + √2 - √2 + √3

= -1 + √3 as required.

m_a_m_a [10]3 years ago

4 0

Answer:

here is your answer...

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Feliz [49]

Answer:

6) x = 40.5

8) x = 16.5

Step-by-step explanation:

6) 45/x = 20/18

simplify and cross-multiply to get:

45/x = 10/9

10x = 405

x = 40.5

8) 22/8 = x/6

11/4 = x/6

4x = 66

x = 33/2

x = 16.5

8 0

3 years ago

Plz help me with this math and also explain

jasenka [17]

Step-by-step explanation:

SI = $250
Rate (R) = 12 $\sf \dfrac{1}{2}$ %
Time (t) = 4 years

$\longrightarrow \tt { SI = \dfrac{PRT}{100} } \\$

$\longrightarrow \tt { 250 = \dfrac{P \times 12\cfrac{1}{2} \times 4}{100} } \\$

$\longrightarrow \tt { 250 = \dfrac{P \times \cfrac{25}{2} \times 4}{100} } \\$

$\longrightarrow \tt { 250 = \dfrac{P \times 25 \times 2}{100} } \\$

$\longrightarrow \tt { 250 = \dfrac{P \times 50}{100} } \\$

$\longrightarrow \tt { 250 \times 100 = P \times 50} \\$

$\longrightarrow \tt { 25000 = P \times 50} \\$

$\longrightarrow \tt { \dfrac{25000}{50} = P } \\$

$\longrightarrow \underline{\boxed{ \green{ \tt { \$ \; 500 = P }}}} \\$

Therefore principal is $500.

2/7 of the balls are red.
3/5 of the balls are blue.
Rest are yellow.
Number of yellow balls = 36

Let the total number of balls be x.

→ Red balls + Blue balls + Yellow balls = Total number of balls

$\longrightarrow \tt{ \dfrac{2}{7}x + \dfrac{3}{5}x + 36 = x} \\$

$\longrightarrow \tt{ \dfrac{10x + 21x + 1260}{35} = x} \\$

$\longrightarrow \tt{ \dfrac{31x + 1260}{35} = x} \\$

$\longrightarrow \tt{ 31x + 1260= 35x} \\$

$\longrightarrow \tt{ 1260= 35x-31x} \\$

$\longrightarrow \tt{ 1260= 4x} \\$

$\longrightarrow \tt{ \dfrac{1260 }{4}= x} \\$

$\longrightarrow \underline{\boxed{ \tt { 315 = x }}} \\$

Total number of balls is 315.

A/Q,

3/5 of the balls are blue.

$\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}x} \\$

$\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}(315)} \\$

$\longrightarrow \tt{ Balls_{(Blue)} = 3(63)} \\$

$\longrightarrow \underline{\boxed{ \green {\tt { Balls_{(Blue)} = 189 }}}} \\$

8 0

3 years ago

15% of amount = 112.79

Mazyrski [523]

To find the original amount, you divide the product by the percentage.

112.79 / 0.15 ≈ 751.933 (the 3's repeat infinitely).

To check your answer, multiply 751.933 by 0.15.
751.933 * 0.15 = 112.78995 ≈ 112.79

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3 years ago

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How do you solve this (5/6)(5/6)

Vikentia [17]

Answer:

25/36

Step-by-step explanation:

Use the top top, bottom bottom method.

5*5 = 25

6*6 = 36

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3 years ago

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vfiekz [6]

Answer:

No solution

Step-by-step explanation:

In pic

<u><em>(Credits: Symbolab) </em></u>

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3 years ago

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