Question

please solve this question​

Answer 1

Answer:

Step-by-step explanation:

1                    -12 x -5 = 60 x 12 = 720

2                  11/16  -  7/12 = by cross multipliction and after substraction we get

                               132-112 /192  = 20/192

3       4/11  - (- 6/11)  = 4/11 + 6/11 = 10/11

   4     -0.131687243

5  x = 9/2

Answer 2

Questions

(i) Find the product -: (-12) × (-5) × 12

(ii) Find difference -: $\dfrac{11}{16} - \dfrac{7}{12}$

(iii) Subtract -: $\dfrac{-6}{11}$ from $\dfrac{4}{11}$

(iv) Express $\dfrac{-32}{243}$ in the exponential form.

(v) Solve -: 2x - 3 = 6

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Answers

(i) We will first multiply the negative terms. We know that when we multiply two negative numbers we get the product as a positive number.

⇒ (-12) × (-5) × 12

⇒ 60 × 12

⇒ 720

∴ (-12) × (-5) × 12 = 720

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(ii) $\dfrac{11}{16} - \dfrac{7}{12}$

Step 1: Find the LCM of the denominators.

$\begin{array}{c|c} \tt 2 & \sf{ 16,12} \\ \cline{1-2} \tt 2 & \sf {8,6} \\ \cline{1-2} \tt 2 & \sf{ 4,3} \\ \cline{1-2} \tt 2 & \sf{ 2,3} \\ \cline{1-2} \tt 3 & \sf{1,3 }\\ \cline{1-2} \tt & \sf{ 1 , 1 }\\ \end{array}}$

LCM of 16 and 12 = 2×2×2×2×3 = 48

Step 2: Using the LCM make the denominators equal.

⇒ $\dfrac{11\times 3 }{16\times 3 } - \dfrac{7\times 4 }{12\times 4 }$

⇒ $\dfrac{33 }{48} - \dfrac{28 }{48 }$

⇒ $\dfrac{5}{48}$

$\bf \therefore \dfrac{11}{16} - \dfrac{7}{12} = \dfrac{5}{48}$

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(iii) $\dfrac{4}{11} - \dfrac{-6}{11}$

⇒ $\dfrac{4--6}{11}$

⇒ $\dfrac{4+6}{11}$

⇒ $\dfrac{10}{11}$

$\bf \therefore \dfrac{4}{11} - \dfrac{-6}{11} = \dfrac{10}{11}$

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(iv) Let's prime factorize the numerator and denominator.

$\begin{array}{c|c} \tt 2 & \sf{ 32} \\ \cline{1-2} \tt 2 & \sf {16} \\ \cline{1-2} \tt 2 & \sf{ 8} \\ \cline{1-2} \tt 2 & \sf{ 4} \\ \cline{1-2} \tt 2& \sf{2 }\\ \cline{1-2} \tt & \sf{ 1 }\\ \end{array}}$

32 ⇒ 2 × 2 × 2 × 2 × 2

(-32) ⇒ -2 × -2 × -2 × -2 × -2

(-32) ⇒ (-2)⁵

$\begin{array}{c|c} \tt 3 & \sf{ 243} \\ \cline{1-2} \tt 3 & \sf {81} \\ \cline{1-2} \tt 3 & \sf{ 27} \\ \cline{1-2} \tt 3 & \sf{ 9} \\ \cline{1-2} \tt 3& \sf{3}\\ \cline{1-2} \tt & \sf{ 1 }\\ \end{array}}$

243 ⇒ 3 × 3 × 3 × 3 × 3

243 ⇒ 3⁵

$\bf \therefore \dfrac{-32}{243} \ in \ exponential \ form \ is \rightarrow \dfrac{(-2)^{5}}{3^{5}}$

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(v) Let's solve your equation step-by-step.

2x - 3 = 6

Step 1: Add 3 to both sides of the equation.

⇒ 2x - 3 + 3 = 6 + 3

⇒ 2x = 9

Step 2: Divide 2 from both sides of the equation.

⇒ 2x ÷ 2 = 9 ÷ 2

⇒ x = 4.5

∴ x = 4.5 in the equation → 2x - 3 = 6

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