asinus

How much money do the two boys have in all?

Hello Ticon!

\(n-16\ $=d+16\ $\\ n=d+32\ $\\ (d-9\ $):(n+9\ $)=1:6\\ 6d-54\ $=n+9\ $\\ 6d-54\ $=d+32\ $+9\ $\\ 5d=95\ $\)

\(d=19\ $\\ n=51\ $\\ n+d=70\ $\)

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Die Gleichung sagt aus, dass 12^3  logarithmiert auf verschiedene Weise ausgedrückt werden kann.

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If m + 1/m = 8, what is the value of m^3 + 1/m^3?

Hello Guest!

\(m+\frac{1}{m}=8\\ m^2-8m+1=0\\ \color{blue}m\in \{4-\sqrt{15},4+\sqrt{15}\}\)

If  \(m\in \{4-\sqrt{15},4+\sqrt{15}\}\),  then  \(m^3+\dfrac{1}{m^3}=488\)

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If \(x^2 - x - 1 = 0\), what is the value of \(x^3 - 2x^2 \)?

Hello Guest!

\(x^2-x-1=0\\ \color{blue}x\in\{-0.618034,1.68034\}\)

\(If\ x\in\{-0.618034,1.68034\}, then\ \color{blue}x^3-2x^2=-1\)

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Find cos C.

Hello Guest!

If the sin B = 4/9 in a right triangle, then the ratio of the sides is

a: b: c = 9: 4: 3.

So is

cos C = 4/9

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Subtrahiere $0.\overline{01}$ von 0,02 und drücke das Ergebnis als Bruch aus.

Hello Guest!

\(0.02-0.\overline{01}=0.00\overline{98}\)

   \(0.009898\overline{98}\)  =    x

-  \(\underline{ 0.989898\overline{98}}\)  =  100x

\(-0.98\)               = - 49/50

\(x-100x=-\frac{49}{50}\\ -99x=-\frac{49}{50}\\ x=\dfrac{49}{99\cdot 50}=\dfrac{7^2}{3^2\cdot 11\cdot 5^2\cdot 2}\)

\(0.02-0.\overline{01}=\dfrac{49}{4950}\)

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\(What\ is\ 0.4\overline{8} + 0.3\overline{7}?\)

Hello Guest!

\(0.4\overline{8} + 0.3\overline{7}=0.8\overline 6\)

   \(0.86666\overline 6\)   =  x

 -\(\underline{0.66666\overline 6}\)    = 2/3

  \(0.2\)                = 1/5

\(x-\frac{2}{3}=\frac{1}{5}\\ x=\frac{1}{5}+\frac{2}{3}=\frac{3+2\cdot 5}{15}\\ x=\frac{13}{15}\)

\(0.4\overline{8} + 0.3\overline{7}=\dfrac{13}{15}\)

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Find a.

Hello Guest!

\(y=m(x-x_p)+y_p\\y=\frac{8-11}{4-1}\cdot (x-1)+11=-x+1+11=-x+12\\ x+y=12\)

\(\dfrac{x}{12}+\dfrac{y}{12}=1\\ \)

\(a=12\)

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Hello Guest!

(5x + 5 + 6x - 7x + 8x - 9x + 2x)(7x - 8x + 9x - 6x - 5x - 2x - 3x - 4x - x)

= - 13x(5x + 5)

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solve using elimination

Hello Guest!

\(-2x-5y=9\\ y=\frac{2x+9}{-5}=-0.4x-1.8\\ 3x+11y=4\\ y=\frac{-3x+4}{11}\)

\(-0.4x-1.8=\frac{-3x+4}{11}\\ -4.4x-19.8=-3x+4\\ -23.8=1.4x \)

\(x=-17\)

\(y=-0.4x-1.8\\ y=-0.4\cdot(-17)-1.8\)

\(y=5\)

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