Ten times the sum of half a number and 6 is 8

Mathematics

1 answer:

mixer [17]3 years ago

8 0

10(n/2 + 6 ) = 8

hope it helps

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Nataly [62]

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2 years ago

I’m confused on this one

tatyana61 [14]

$6\sqrt2$

Why?

We have the isosceles right triangle. The length of legs are 6. Use the Pythagorean theorem:

$h^2=6^2+6^2\\\\h^2=36+36\\\\h^2=36\cdot2\to h=\sqrt{36\cdot2}\\\\h=\sqrt{36}\cdot\sqrt2\\\\h=6\sqrt2$

In general, the formula for calculating the hypotenuse in an isosceles right triangle is $h=a\sqrt2$

a - a leg, h - a hypotenuse

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3 years ago

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strojnjashka [21]

Answer:

x = 0

Step-by-step explanation:

${2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {9}^{x } } \\ \\ {2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {( {3}^{2}) }^{x } } \\ \\ {2}^{x} - {3}^{x} = \sqrt{ {6}^{x} } - \sqrt{ {({3)}^{2x}}}\\ \\ {2}^{x} - \cancel{{3}^{x}} = \sqrt{ {6}^{x} } - \cancel{ {3}^{x} } \\ \\ {2}^{x} = \sqrt{ {6}^{x} } \\ squaring \: both \: sides \\ \\ {( {2}^{x} )}^{2} = {(\sqrt{ {6}^{x} })}^{2} \\ \\ {2}^{2x} = {6}^{x} \\ \\ {2}^{2x} = {(2 \times 3)}^{x} \\ \\ {2}^{2x} = {2 ^{x} \times 3}^{x} \\ \\ \frac{ {2}^{2x} }{ {2}^{x} } = 3^{x} \\ \\ {2}^{2x - x} = {3}^{x} \\ \\ {2}^{x} = {3}^{x} \\ \\ \frac{ {2}^{x} }{ {3}^{x} } = 1 \\ \\ \bigg( \frac{2}{3} \bigg)^{x} = 1 \\ \\ \implies \: x = 0 \\ \\ \because \: for \: x = 0 \\ \\ \bigg( \frac{2}{3} \bigg)^{0} = 1$