|x+5|=x Solve these equations

Mathematics

1 answer:

natka813 [3]3 years ago

8 0

Answer:

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Step-by-step explanation:

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Which of the following is equal to the square root of the cube root of 6?

stiks02 [169]

The correct answer is: [A]: " 6 to the power of (1 over 6) " .

Explanation:

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√ [(∛6)] = √ [6⁽¹/³⁾ ] = [6⁽¹/²⁾ ] ⁽¹/³⁾ = 6^ ( ⁽¹/²⁾ * ⁽¹/³⁾ ) = ???? ;

<u>Note</u>: $\frac{1}{2} *\frac{1}{3} = \frac{(1*1)}{(2*3)} = \frac{1}{6}$ ;

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→ 6^ ( ⁽¹/²⁾ * ⁽¹/³⁾ ) ;

= 6^ ( ⁽¹/⁶⁾ ) ;

→ which is: Answer choice: [A]: " 6 to the power of (1 over 6) " .

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Find the values of x and y if 5 ˣ⁻³ x 3²ʸ⁻⁸ =225

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x = 5, y = 5

Step-by-step explanation:

${5}^{x - 3} \times {3}^{2y - 8} = 225 \\ {5}^{x - 3} \times {3}^{2y - 8} = 25 \times 9 \\ {5}^{x - 3} \times {3}^{2y - 8} = {5}^{2} \times {3}^{2} \\ equating \: like \: power \: terms \: from \: both \:\\ sides \\ {5}^{x - 3} = {5}^{2} \\ x - 3 = 2 (Bases\: are\: equal, \: so\: exponents \: \\will\: also\: be\: equal) \\ x = 3 + 2 \\ \huge \red{ \boxed{ x = 5}} \\ \\ {3}^{2y - 8} = {3}^{2} \\ 2y - 8 = 2(Bases\: are\: equal, \: so\: exponents \: \\will\: also\: be\: equal) \\ 2y = 2 + 8 \\ 2y = 10 \\ y = \frac{10}{2} \\ \huge \purple{ \boxed{y = 5}}$