Expand 10w(5w – 3)

**solution**
= 10w(5w – 3)

= (10w x 5w) – (10w x 3)

= 50w

^{2}– 30w*answer*

**TRY THIS………..**
Expand 4y(9y+ 10)

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Expand 10w(5w – 3)

= 10w(5w – 3)

= (10w x 5w) – (10w x 3)

= 50w^{2} – 30w *answer*

Expand 4y(9y+ 10)

If
u = 20i + 2j and v = 3i + 10j find 5u + 3v

=
5u + 3v

=
5(20**i **+ 2**j**) + 3(3**i** + 10**j**)

= 100**i**
+ 10**j** + 9**i** + 30**j**

= (100**i**
+ 9**i**) + (10**j** + 30**j**)

= 109**i**
+ 40**j**

If
u = 4**i** + 3**j** and v = 2**i** + 4**j**; find 2**u** +
3**v**.

If F(x) = log_{2}x,
Find F(^{1}/ _{8192})

F(x) = log_{2}x

F(^{1}/8192) = log_{2}(^{1}/ _{8192})

F(^{1}/8192) = log_{2} 8192^{-1}

F(^{1}/8192) = log_{2}(2^{13})^{-1}

F(^{1}/8192) = log_{2}2^{(13} ^{x} ^{-1)}

F(^{1}/8192) = log_{2}2^{-13}

F(^{1}/8192) = -13log_{2}2

F(^{1}/8192) = -13 x 1

F(^{1}/8192) = -13

If F(x) = log_{5}x,
Find F(^{1}/_{3125})

A number is chosen at random
from 1 – 15 inclusive. Find the probability that it is a multiple of five or an
even number greater than 8.

Let n(S) represent sample
space

P(E) = probability of even
number greater than 8

P(M) = probability of a
multiple of 5

n(S) = {1, 2, 3, 4, 5, 6, 7,
8, 9,10, 11, 12, 13, 14, 15} = 15

n(E) = {10, 12, 14} = 3

n(M) = {5, 10, 15} = 3

But 10 appears on both
categories.

P(E) = ^{3}/15

P(M) = ^{3}/15

P(EnM) = ^{1}/15

………………………….

P(EuM) = P(E) + P(M) - P(EnM)

P(EuM) = ^{3}/15 + ^{3}/15
-^{1}/15

= ^{5}/15

= ^{1}/3 after simplification

∴ **P(EuM) = **^{1}/5

A number is chosen at random
from 17 – 30 inclusive. Find the probability that it is a multiple of 5 or an
even number.

Factorize 289x^{2 }- 169y^{2}

we use difference of two squares a^{2} – b^{2} = (a - b)(a + b)

289x^{2}- 169y^{2}
= 17^{2}x^{2}^{ }- 13^{2}y^{2}

=
(17x)^{2}^{ }- (13y)^{2}

=
(17x - 13y)( 17x + 13y)

factorize 121c^{2}- 49d^{2}

Multiply 2x - 4y by -5a

= -5a(2x - 4y)

= (-5a x 2x) - (-5a x 4y)

= (-10ax) - (-20ay) [since -5a **x** 4y = -20ay ]

= -**10ax + 20ay**

Multiply 40p - 3q by -4m

If 5^{2w}
(40^{w}) = 10^{w+40} ; Find w.

5^{2w}
(40^{w}) = 10^{w+40}

(5^{2})^{w}
(40^{w}) = 10^{w+40}

(25)^{w}
(40^{w}) = 10^{w+40}

(25 x 40)^{w}
= 10^{w+40}

(1000)^{w}
= 10^{w+40}

(10^{3})^{w}
= 10^{w+40}

3w = w+40

3w - w = 40

2w = 40

If 3^{2t}
(4^{t}) = 6^{t+10 }; Find t.

x is
directly proportional to y. x=12 while y=4. Find y when x is 69.

x ⍺ y

x = ky

12 = k x 4

4 4

k = 3

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 3, y= ?
x = 69.

69 = 3 x y

3 3

x is
directly proportional to y. x=20 while y=5. Find y when x is 68.

If log 2= 0.3010; find the value of log 400,000 without using
tables.

=log200,000

=log(4 x 100,000)

=log4 + log100,000

=log2^{2} + log10^{5}

=2log2 + 5log10

=2(0.3010) + (5 x 1) [since
log10=1 and Log3=0.3010]

=(0.6020) + 5

=5.6020

If log 2= 0.3010; find the value of log 4,000,000 without
using tables.

If 13w^{2}
= 325; find w

13w^{2} = 325

13 13

w^{2}
= 25

w = 5 Because the square root of 25 is 5.

If 14y^{2}
= 5600; find y.

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