Robert Bosch Algebra Quiz 1

Explanation:

We have,

10^{0.48} = x, 10^{0.70} = y

\therefore x^{z} = y^{2}

Þ (10^{0.48})^{z} = (10^{0.70})^{z}

Þ 10^{0.48z} = 10^{1.4}

Þ 0.48z = 1.4

Þ z =  1.4/0.48 = 2.9

Explanation:

4A +\frac{7}{B}+ 2C + \frac{5}{D}+ 6E

= 47.2506

4A = 40 

Þ A = 10

Þ 7B = 7

 Þ B = 1

2 C = \frac{2}{10}

Þ C = 0.1

\frac{5}{D}=\frac{5}{100}

Þ D = 100

\frac{6}{E} =\frac{6}{10000}

Þ E = 0.0001

5A + 3B + 6C + D + 3E

= 5*10 + 3 * 1 + 6 * 0.1 + 100+ 3*0.0001

= 50 + 3 + 0.6 + 100 + 0.0003

= 153.6003

Explanation:

x * y = x^{2} + y^{2} – xy  (Given)

Þ 9 * 11 = 92 + 112 – 9 * 11

= 81 + 121 – 99

= 202 – 99 = 103

Explanation:

5^(5x +5) = 1

=>   5 ^(5 x +5) = 5^{ °}

=> 5x + 5 = 0 

=> x = –1

Explanation:

3 ^{x +3} + 7= 250

=> 3^{x+3} =  243

=> 3^{x+3} =  3^{5}

Þ x + 3 = 5 

Þ x = 2

Explanation:

x = 0.5 and y= 0.2 (Given)

\ sqrt{0 6} × (3y) ^{x}

\ sqrt{0 6} × (3*0.2) ^{0.5}

\ sqrt{0 6} × (0.6) ^{0.5}

\ sqrt{0 6*0.6} = 0.6

Explanation:

= a^{2} + b^{2} + c^{2} – ab – bc – ca

= \frac{1}{2} *[(a-b)^{2} + (b-c)^{2} + (c-a)^{2} ]

=\frac{1}{2} *[(7-5)^{2} + (5-3)^{2} + (3-7)^{2} ]

= \frac{1}{2} * (4 + 4 + 16)

= \frac{1}{2}1/ 2 *24 = 12

Explanation:

7^{x} = \frac{1}{343}

Þ 7^{x} = \frac{1}{7^{3}} = 7^{-3}

Þ x = –3

Explanation:

\frac{a}{2}= \frac{b}{3}= \frac{c}{5} =k   (Let)

a=2k,b=3k,c=4k

\frac{a+b+c}{c} =  \frac{2k+3k+5k}{5k}

= \frac{10k}{5k}= 2

Explanation:

0.13 ÷ p ^{2} = 13 

Þ \frac{0.13}{p^{2}}

Þ p ^{2} = \frac{0.13}{13} = \frac{1}{100}

Þ p = \frac{1}{10} = 0.1