asinus

 A recipe calls for 1/2 cup of water for every 1/3 cup of milk. How many cups of water are needed per cup of milk?

Hello Guest!

\(\frac{1}{2}W:\frac{1}{3}M=x:1M\)

\(x\cdot\frac{1}{3}M=\frac{1}{2}W\cdot M\\ x=\frac{3\cdot W\cdot M}{2\cdot M}\)

\(x=\frac{3}{2}W\)

\(1\frac{1}{2}\ cups\ of\ water\ are\ needed\ per\ cup\ of\ milk. \)

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How far above the ground is Pierre's line of sight?

Hello Guest!

\(C=h\cdot tan(90-21)\\ DT=h\cdot tan(90-14)\\ DT-C=h\cdot tan(76^o)-h\cdot tan(69^o)=600feet\\ h\cdot (tan(76^o)- tan(69^o))=600feet\)

\(h=\frac{600ft}{tan(76^o)-tan(69^o)}\)

\(h\approx 426.8\ ft\)

\( Pierre's\ line\ of\ sight\ above\ the\ Ground\ is\ 426.8\ feet\ high.\)

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Wie hoch ist die Wahrscheinlichkeit, dass ich mit einem Becher mit 5 Würfeln beim ersten Wurf einen Pasch würfle?

Hallo Gast!

\(W=\frac{1}{6^{5-1}}=\frac{1}{1296}\approx 0,000716\)

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How to solve these algebraically? 

Hello Guest!

b)

\(\color{BrickRed}2,1x^{0,25}+5=7\\ x^{\frac{1}{4}}=\frac{2}{2,1}\\ x=(\frac{2}{2,1})^4 \)

\(x=(\frac{20}{21})^4=(\frac{2^2\cdot 5}{3\cdot 7})^4\)

\(x=\frac{2^8\cdot 5^4}{3^4\cdot7^4}=0,8227...\)

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How to solve these algebraically? 

Hello Guest!

a)

\(\color{BrickRed}-2+5z^{-\frac{3}{2}}=133\\ 5z^{-\frac{3}{2}}=135\\ z^{-\frac{3}{2}}=27\\ z^{-3}=27^2\\ z^3=\frac{1}{27^2}\\ z=\frac{1}{\sqrt[3]{(3^3)^2}}\)

\(z=\frac{1}{9}\)

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What is the slope-intercept form of the equation of the line that passes through the point (-6, 1) and is perpendicular to the graph of 2x + 3y = -5?

Was ist die Steigungsschnittform der Gleichung der Linie, die durch den Punkt (-6, 1) verläuft und senkrecht zum Graphen von 2x + 3y = -5 ist?

Hello Guest!

\(\color{BrickRed} 2x + 3y = -5\\ y=-\frac{2}{3}x-\frac{5}{3}\\ m_1=-\frac{2}{3}\\ \color{blue}m_2=\frac{3}{2}\)

\(y=m_2(x-x_1)+y_1\\ y=1.5(x+6)+1\)

The slope-intercept form of the equation  that passes through the point (-6, 1) is

\(y=1.5x+10\)

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is 1/5*30=6?

Hello Guest!

Yes, \(1/5*30= 1:5\cdot 30=6\).

The multiplication and division take place in succession from left to right.

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Miko and Freya saved the same amount of money. After Miko lent $32 to Freya, Freya had 5 times as much money as Miko. How much did Freya have in the end?

Miko und Freya haben den gleichen Geldbetrag gespart. Nachdem Miko Freya 32 Dollar geliehen hatte, hatte Freya fünfmal so viel Geld wie Miko. Wie viel hatte Freya am Ende?

Hello Guest!

The amount of money saved is x.

\(5(x-32)=x+32\\ 5x-160=x+32\\ 4x=192\)

\(x=48\)

\(Freya\ have\ in\ the\ end\ $48+$32=$80\)

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The hypotenuse of a right triangle measures 2√15 centimeters and its shorter leg measures 2√6  centimeters. What is the measure of the larger acute angle of the triangle? Round your answer to the nearest tenth of a degree.

Die Hypotenuse eines rechtwinkligen Dreiecks misst 2 \(\sqrt{15}\) Zentimeter und die kürzere Kathete 2 \(\sqrt{6}\)Zentimeter. Was ist das Maß für den größeren spitzen Winkel des Dreiecks? Runden Sie Ihre Antwort auf das nächste Zehntel eines Grades.

Hello valval2205!

A right triangle ABC

\(c=2\cdot \sqrt{15}\ cm\\ b=2\cdot \sqrt{6}\ cm\)

\(\alpha=arccos(\frac{b}{c})=arccos(\frac{\sqrt{6}}{\sqrt{15}})\)

\(\alpha=50.8^o\)

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Devi and Dave had the same amount of money x initially. After Devi donated $258 and Dave donated $196 to charity, Dave had 3 times as much as Devi. How much had Dave in the end?

Devi und Dave hatten anfangs den gleichen Geldbetrag x. Nachdem Devi 258 Dollar und Dave 196 Dollar für wohltätige Zwecke gespendet hatte, hatte Dave dreimal so viel wie Devi. Wie viel hatte Dave am Ende?

Hello Guest!

\(x-258+x-196=x-258+3(x-258)\)

   Devi            Dave           Devi           Dave

\(2x-454=x-258+3x-774\\ -2x=-578 \)      

\(x=289\)  

Dave ended up with $289 - $196 = $ 93

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