The sum of the interior angles of a triangle is always 180 degrees. The exterior angle is the angle between any side of a shape, and a line extended from the next side. The sum of an exterior angle and its adjacent interior angle is also 180 degrees.

6 0

3 years ago

Which would be the better value?<br> A) 12 pens for $2.70<br> B) 16 pens for $3.40

gregori [183]

Answer:

Step-by-step explanation:

8 0

3 years ago

A hyperbola is given by the equation x^2+2xy−y^2+x = 2. Use implicit differentiation

Mekhanik [1.2K]

$\bf x^2+2xy-y^2+x=2\qquad 
\begin{array}{llll}
(1&,&2)\\
x_1&&y_1
\end{array}\\\\
-------------------------------\\\\
2x+2\left( 1\cdot y+x\frac{dy}{dx} \right)-2y\frac{dy}{dx}+1=0
\\\\\\
2x+2y+2x\frac{dy}{dx}-2y\frac{dy}{dx}+1=0
\\\\\\
\cfrac{dy}{dx}(2x-2y)=-1-2x-2y\implies \cfrac{dy}{dx}=\cfrac{-1-2x-2y}{2x-2y}
\\\\\\
\left. \cfrac{dy}{dx}=\cfrac{2x+2y+1}{2y-2x} \right|_{1,2}\implies \cfrac{2+4+1}{4-2}\implies \cfrac{7}{2}\\\\
-------------------------------\\\\
$

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-2=\cfrac{7}{2}(x-1)\implies y-2=\cfrac{7}{2}x-\cfrac{7}{2}
\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
\boxed{y=\cfrac{7}{2}x-\cfrac{3}{2}}$

5 0

4 years ago

Help me if this is always true, sometimes true or never true pls<br> math

Angelina_Jolie [31]

23.
a. Sometimes true
b. Always true
c. Always true
d. Never true

Hope this helps. Good luck! :)

6 0

3 years ago