asinus

\( The\ domain\ of\ the\ function\ is:\\ x\in \{\}\\ The\ range\ is\ complex\ for\ all\ x.\)

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What is the x-intercept of the line?

Hello tomtom!

\(m=2\\ b=2\\ y=mx+b\\ 2x+2=0\\ 2x=-2\\ \color{blue}x=-1\)

The x-intercept of the line is -1.

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Write the equation in the form $Ax + By = C.

Hello tomtom!

P(-8,2)

Q(1,7)

\(m=\frac{y_P-x_P}{y_Q-x_Q}=\frac{2-(-8)}{7-1}=\frac{5}{3}\\ y=m(x-x_Q)+y_Q\\ y=\frac{5}{3}(x-1)+7\\ y=\frac{5}{3}x-\frac{5}{3}+7\\ -\frac{5}{3}x+y=\frac{16}{3}\ |\ \cdot (-3)\\ \color{blue}5x-3y=-16\)

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What is BX?

Hello oventomato!

\(\overline {BX}\in \mathbb R>0\)

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primtime,vieleicht kann dir der Link ein wenig zu deinen Fragen helfen.

Gleichung lösen.

Hallo teez444!

\((2/3)*x^2+(4/5)*x=0\ |\ x\ ausklammern\\ x\cdot (2/3x+4/5)=0\ | \ Ist\ ein\ Produkt\ gleich\ 0, \\ kann\ jeder\ der Faktoren\ gleich\ 0\ sein.\ Also:\\ \color{blue}x=0\\ F\ddot uhre\ auf\ beiden\ Seiten\ der\ Gleichung\ aus,\\was\ hinter\ dem\ senkrechten\ Strich\ |steht.\\ \dfrac{2x}{3}+\dfrac{4}{5}=0\ |\ -\dfrac{4}{5}\\ \dfrac{2x}{3}=-\dfrac{4}{5}\ |\ \cdot 3\)

\(2x=-\dfrac{4\cdot 3}{5}\ |\ /2\\ x=-\dfrac{{\color{blue}4}\cdot 3}{5\cdot {\color{blue}2}}\ |\ k\ddot urzen\\ \color{blue}x=-\dfrac{6}{5}\\ \color{blue}x\in \{-\dfrac{6}{5};0\}\)

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Find the square of the largest real solution to the equation \((g(x))^2 - (f(x))^2 = 1.\)

Hello wiseowl!

\((g(x))^2 - (f(x))^2 = 1\\ \dfrac{1}{(x-\dfrac{1}{x})^2}-\dfrac{1}{(x+\dfrac{1}{x})^2}=1\)

\(\dfrac{1}{(\dfrac{x^2-1}{x})^2}-\dfrac{1}{(\dfrac{x^2+1}{x})^2}=1\)

\(\dfrac{x^2}{(x^2-1)^2}-\dfrac{x^2}{(x^2+1)^2}=1\\ \)

\(\dfrac{4x^4}{(x-1)^2(x+1)^2(x^2+1)^2}=1\)

Calculated by WolframAlpha.

\(x=-\sqrt{\sqrt{2}-1}\\ x=\sqrt{\sqrt{2}-1}\\ x=-\sqrt{1+\sqrt{2}}\\ x=\sqrt{1+\sqrt{2}}\\\)

\(\color{blue}x\in \{-1.55377,-0.64359,0.64359,1.55377\}\)

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What is a?

Hello Guest!

\((x-5^2)^2+(y-6)^2=4^2\\ y=3x-1\\ (x-5^2)^2+(3x-1-6)^2=4^2\\ x^2-10x+25+9x^2-42x+49-16=0\\ 10x^2-52x+58=0\\ x^2-5.2+5.8=0\\ x_{1,2}=2.6\pm\sqrt{2.6^2-5.8}\\ x\in \{1.620,\color{blue}3.580\}\)

\(y\in \{3.861,\color{blue}9.739\}\\ P_2\ (3.580,9.739)\\ P_1\ (0,5)\\ a= \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9.739-5}{3.58-0}\\a=1.324\)

\(\color{blue}a\ is\ 1.324\)

With P3 (1.620,3.861) the further a can be calculated.

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Equation to find the number of hours of labor spent repairing the car.

Hello Guest!

\(x\cdot 48\$ +265$=553$\ |\ -265$\\ x\cdot 48$=288$\ |\ /48$\\ \color{blue}x=6\)

The number of working hours is 6.

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Find the domain of the function \(f(x) = \sqrt{6-x-x^2-2x^2}\) .

Hello Guest!

\(f(x) = \sqrt{6-x-x^2-2x^2}\\ -3x^2-x+6=0\)

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\\ x = {1 \pm \sqrt{1+4\cdot 3\cdot 6} \over -2\cdot 3}\\ \color{blue}x\in \{-1.591,1.257\}\)

The domain of the function \(f(x) = \sqrt{6-x-x^2-2x^2}\)  goes from -1.591 to 1.257.

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