Question

plz answer me fast .​

Answer 1

${\underline{\boxed{\bf{Question \; 1 :}}}}$

• What is the additive inverse of

$\bigstar{\underline{\boxed{\tt{ \dfrac{5}{-11} }}}}$

Solution:

We know that, when a fraction is in the form $\tt \dfrac{\; \; a}{- b}$ its additive inverse will be in the form $\tt \dfrac{a}{ b}$, So the additive inverse of 5/-11 will be,

$\dashrightarrow \tt \dfrac{5}{11}$

• Henceforth option c is correct

${\underline{\boxed{\bf{Question \; 2 :}}}}$

• The product of

$\bigstar{\underline{\boxed{\tt{ \dfrac{15}{19}\; and \dfrac{-19}{\;\;15} }}}}$

Solution:

$\dashrightarrow \tt \dfrac{15}{19} \times \dfrac{-19}{\;\;15}$

$\dashrightarrow \tt \dfrac{-285}{\;\;285}$

$\dashrightarrow {\underline{\boxed{\tt{ - 1}}}\star}$

• Henceforth option c is correct

${\underline{\boxed{\bf{Question \; 3 :}}}}$

• What is the absolute value of

$\bigstar{\underline{\boxed{\tt{| 20 \times ( - 10) | }}}}$

Solution:

$\dashrightarrow \tt | 20\times (-10)|$

$\dashrightarrow \tt | - 200 |$

$\dashrightarrow {\underline{\boxed{\tt{ 200}}}\star}$

• Henceforth option b is correct

${\underline{\boxed{\bf{Question \; 4 :}}}}$

• What is the reciprocal of

$\bigstar{\underline{\boxed{\tt{\bigg(\dfrac{-1}{\;\;9} \bigg)^4}}}}$

Solution:

The reciprocal of a fraction is the form a/b ^ n will be b/a ^ n, So the reciprocal of the fraction is

$\dashrightarrow \tt \bigg(\dfrac{\;\;9}{-1} \bigg)^4$

• henceforth option d is correct

${\underline{\boxed{\bf{Question \; 5 :}}}}$

• Solve the following

$\bigstar{\underline{\boxed{\tt{\Bigg(\bigg(\dfrac{6}{7} \bigg) ^2\Bigg)^4}}}}$

Solution:

Using the law of exponent which says( ( a/b) ^ n) ^ m is (a/b)^ n × n

$\dashrightarrow \tt \Bigg(\bigg(\dfrac{6}{7} \bigg) ^2\Bigg)^4$

$\dashrightarrow \tt \bigg( \dfrac{6}{7} \bigg)^{8}$

• Henceforth option b is correct

${\underline{\boxed{\bf{Question \; 6 :}}}}$

• Simplify

$\bigstar{\underline{\boxed{\tt{\bigg( 3^{-1}+ 4^{-1} \bigg)^{-1}}}}}$

Solution:

$\dashrightarrow \tt \bigg( 3 ^{-1} + 4\bigg)^1$

$\dashrightarrow \tt \bigg( - 3 + 4 \bigg)^1$

$\dashrightarrow\tt (1)^1$

$\dashrightarrow \tt {\underline{\boxed{\tt{ 1}}}}$

• Henceforth option b is correct

${\underline{\boxed{\bf{Question \; 7 :}}}}$

• Evaluate the following

$\bigstar{\underline{\boxed{\sf{\dfrac{91x^{2} y^3 z^4 }{13xyz^3\;\;\;} }}}}$

$\bigstar{\underline{\boxed{\tt{\dfrac{36\times 6x^{-2}}{6^{-2}\times 12x{-4}}}}}}$

Solution:

• Part - A

$\dashrightarrow \sf \dfrac{91x^{2} y^3 z^4 }{13xyz^3\;\;\;}$

$\dashrightarrow \sf \dfrac{7xy^2 z }{1}$

$\dashrightarrow \sf 7xy^2z$

• Part - B

$\dashrightarrow \sf \dfrac{36\times 6x ^{-2}}{6^{-2} \times 12x^{-4}}$

$\dashrightarrow \sf \dfrac{1}{2x^{-2}}$

$\dashrightarrow \sf 2x^{2}$

${\underline{\boxed{\bf{Question \; 8 :}}}}$

• find 3 rational numbers between

$\bigstar{\underline{\boxed{\tt{ \dfrac{1}{3}\; and \dfrac{1}{2} }}}}$

Solution:

$\dashrightarrow \tt \dfrac{9}{12}$

$\dashrightarrow \tt \dfrac{10}{12}$

$\dashrightarrow \tt \dfrac{11}{12}$

${\underline{\boxed{\bf{Question \; 9 :}}}}$

• Find the value of x

$\bigstar{\underline{\boxed{\tt{ 8^x = 512 }}}}$

$\bigstar{\underline{\boxed{\tt{ 3^{2x} \div 3^{-10} = 3^{24} }}}}$

Solution:

• Part - A

$\dashrightarrow \tt 8^x = 512$

$\dashrightarrow \tt 8^x = 8^3$

$\dashrightarrow \tt x = 3$

• Part - B

$\dashrightarrow \tt 3^{2x} = 3^{24} \times 3^{10}$

$\dashrightarrow \tt 3^{2x} = 3^{34}$

$\dashrightarrow \tt x = 34 \div 2$

$\dashrightarrow \tt x = 17$

${\underline{\boxed{\bf{Question \; 10 :}}}}$

• Write in scientific notation

Solution:

• Part - A

$\dashrightarrow \tt 45 \times 10^{-6}$

• Part - B

$\dashrightarrow \tt 727 \times 10^{4}$

${\underline{\boxed{\bf{Question \; 11 :}}}}$

• Let's find the sum of

$\dashrightarrow \tt \dfrac{6}{15} - \dfrac{9}{30}$

$\dashrightarrow \tt\dfrac{12}{30} - \dfrac{9}{30}$

$\dashrightarrow \tt \dfrac{3}{30}$

$\dashrightarrow \tt \dfrac{1}{10}$

• And then the sum of

$\dashrightarrow \tt \dfrac{3}{10} - \dfrac{5}{40}$

$\dashrightarrow \tt \dfrac{12}{40} - \dfrac{5}{40}$

$\dashrightarrow \tt \dfrac{7}{40}$

• Let's subtract them now

$\dashrightarrow \tt \dfrac{3}{10} - \dfrac{7}{40}$

$\dashrightarrow \tt \dfrac{12 - 7}{40}$

$\dashrightarrow \tt \dfrac{3}{40}$

${\underline{\boxed{\bf{Question \; 12 :}}}}$

• Write the following in usual form

$\bigstar{\underline{\boxed{\tt{15 \times 10^{-5}}}}}$

$\bigstar{\underline{\boxed{\tt{0.8875 \times 10^{-5}}}}}$

Solution:

• Part - A

$\dashrightarrow \tt 0.00015$

• Part - B

$\dashrightarrow \tt 88750$

• Hence solved.!!!