asinus

Compute the domain of the real-valued function \( f(x) = \sqrt{1 + \sqrt{2 - \sqrt{x}}}.\)

Hello Guest!

\(\mathbb D = \mathbb R|\ 0\ge x\ge4\)

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Line m has the equation y = 3x + 5. Line n has the equation y = kx - 7. Lines m and n intersect at the point (-4, -7). What is the value of k?

Hello Guest!

\(kx-7=3x+5\\ x=-4\\ -4k-7=3\cdot (-4)+5\\ -k=\frac{-12+5+7}{4}\)

\(\color{blue}k=0\)

Line m has the equation y = 3x + 5. Line n has the equation y =  - 7. Lines m and n intersect at the point (-4, -7).

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Kumi is 3/4 the height of Zac.

Sue is 2/3 the height of Zac.

Kumi is 15 cm taller than Sue.

How tall is Zac in centimetres?

Hello Guest!

\(k=\frac{3}{4}z\\ s=\frac{2}{3}z\\ k=s+15cm\\ \frac{3}{4}z=s+15cm\\ \frac{2}{3}z=\frac{3}{4}z-15cm\)

\((\frac{3}{4}-\frac{2}{3})z=15cm\\ \frac{9-8}{12}\cdot z=15cm\\ z=\frac{15\cdot 12}{9-8}\cdot cm\\ \color{blue}z=180cm\)

\(k=\frac{3}{4}z=\frac{3}{4}\cdot 180cm\\ \color{blue}k=135cm\\ s=\frac{2}{3}z=\frac{2}{3}\cdot 180cm\\ \color{blue}s=120cm\)

Zac is 180 centimeters tall.

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The age of a tortoise is 52 years more than the combined age of two elephants. In 10 years, the tortoise will be twice as old as the two elephants combined. How old is the tortoise now?

Hello Guest

\(t-e=52\\ t=52+e\\ t+10=2(e+10)\\ 52+e+10=2e+20\\ \color{blue}e=42\)

\(t=52+42\\ \color{blue}t=94\)

The tortois is now 94 years old.

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In meiner Antwort ist H die Höhe des Dreiecks zwischen der Seite c und der Ecke C.

\({\color{blue} H}=4,8cm\cdot sin\ (90°-38^°)=\color{blue}3,782cm\)

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Gegeben ist: gamma = 90grad, alpha = 38grad, Seite a = 4,8 cm. 

Hallo matheog!

Dreieck ABC

\(c=\dfrac{4,8cm}{sin\ 38°}=7,796cm\\ b=\dfrac{4,8cm}{tan\ 38°}=6,144cm\\ H=4,8cm\cdot sin\ (90°-38^°)=3,782cm\)

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Find the value of B - A if the graph of Ax + By = 3 passes through the point (-7,2),

and is parallel to the graph of x + 3y = -5.

Hello VoidAsks​!

\(x + 3y = -5\\ y=-\frac{1}{3}x-\frac{5}{3}\\ \color{blue}m=-\frac{1}{3}\)

\(\color{blue}y=m(x-x_p)+y_p\\ y=-\frac{1}{3}(x-(-7))+2\\ y=-\frac{1}{3}x-\frac{7}{3}+\frac{6}{3}\\ \color{blue}y=-\frac{1}{3}x-\frac{1}{3}\)

\(Ax + By = 3\\ \frac{1}{3}x+y=-\frac{1}{3}\ |\ \cdot -9\\ \color{blue}-3x-9y=3\\ A-B=-3-(-9)\)

\(\color{blue}A-B=6\)

Because of the language barrier,

OK. VoidAsks, so 

\(\color{blue}B-A =-6\)

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Wie schreibt man negative Potenzen?

Hallo Gast!

Eine negative Potenz ist eine Potenz aus Basis a und einem negativen Exponenten - b.

a^(-b)= \(a^{-b}=\dfrac{1}{a^b}\)

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Immerhin nennt er dich Kollege.