Robert Bosch Algebra Quiz 4

Explanation:

a \times* b  = 2a – 3b + ab

=>  3\times 5 = 2 \times 3 – 3 \times 5 + 3 \times 5 = 6 

5 \times 3 = 2 \times 5 – 3 \times 3 + 3 \times 5 

= 10 – 9 + 15 = 16

Therefore, 3 \times 5 + 5 \times 3  

= 6 + 16 = 22

Explanation:

 

  p \times q= p +q + \frac{p}{q}  

\therefore  8 \times 2 = 8 + 2 + \frac{8}{2}  

 

 =10 + 4 = 14

Explanation:

(x + y) = 3 (x – y) = 3x – 3y

=> 3y + y = 3x – x

=> 2x = 4y

=> x = 2y

=> \frac{x}{y} = \frac{2}{1}

\therefore x = 2, y = 1

\frac{3xy}{2(x^{2} -y^{2}) }

= \frac{3*2*1}{2x *(4-1) }

= \frac{6}{6} =1

Explanation:

 

= (1 + \frac{1}{x})(1 + \frac{1}{(x+1)})(1 + \frac{1}{(x+2)})(1 + \frac{1}{(x+3)})

 

=  x+\frac{1}{x}* x+\frac{2}{x+1} * x+\frac{3}{x+2} * x+\frac{4}{x+3}

= x+\frac{4}{x}

Explanation:

a * b = 2 (a + b)

\therefore 5 * 2 = 2 (5 + 2)

= 2 *7 = 14

Explanation:

2a +\frac{b}{a} +4b =3

Þ 2a + b = 3a + 12b

Þ 3a – 2a = b – 12 b

Þ a = – 11b

Then, \frac{a+b}{a+2b} = -11b + \frac{b}{-11b} +2b

=  \frac{10b}{9b} = \frac{10}{9}

 

Explanation:

Given a * b = a + b + ab

\therefore 3 * 4 – 2 * 3

= (3 + 4 + 3 * 4) – (2 + 3 + 2* 3)

= (7 + 12) – (5 + 6) = 19 – 11 = 8

Explanation:

x\times y = 3x + 2y

2 \times 3 + 3 \times4

= 3 \times 2 + 2\times 3 + 3\times 3 + 2\times 4

= 6 + 6 + 9 + 8 = 29

 

Explanation:

\frac{a}{3}=\frac{b}{4}=\frac{c}{7} = k (Let)

a = 3k, b = 4k, c = 7k

\frac{a+b+c}{c}= \frac{3k+4k+7k}{7k}

= \frac{14k}{7k}= 2

Explanation:

\frac{144}{0.144} = \frac{14.4}{x}

144*x= 144*0.144

x=\frac{144*0.144}{144}

\frac{144*144 }{144*10000} = 0.0144