Identify the factors of x² - 4x - 12.

Mathematics

2 answers:

NNADVOKAT [17]2 years ago

8 0

Answer:

(x+2) (x-6)................

kogti [31]2 years ago

6 0

Answer:

Step-by-step explanation:

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Devon made a scale drawing of a triangle. He used a scale factor of 1/4 to draw the new triangle. How does each side of the new

Charra [1.4K]

The answer is Option A.
Scale Factors
If the Scale Factor IS 1, the polygon stays the SAME.
(If an equilateral triangle has a side length of 8 and the scale factor is 1, the sides will stay at 8)
If the Scale Factor is MORE THAN 1, the polygon's sides INCREASE depending on what the scale factor is.
(If a square has a side length of 3 and the scale factor is 4, the sides will increase to 12)
If the Scale Factor is LESS THAN 1, the polygon's sides DECREASE depending on what the scale factor is.
(If a square has a side length of 5 and the scale factor is 1/2, the side lengths will decrease down to 0.5)
Therefore each side length of the new triangle is 4 times shorter than the original (Option A)

7 0

3 years ago

Read 2 more answers

Find the volume of the ellipsoid x^2+y^2+9z^2=64

yuradex [85]

Parameterize the ellipsoid using the augmented spherical coordinates:

$\begin{cases}x=\frac18\rho\cos\theta\sin\varphi\\\\y=\frac18\rho\sin\theta\sin\varphi\\\\z=\frac38\rho\cos\varphi\end{cases}$

Then the Jacobian for the change of coordinates is

$\mathbf J=\dfrac{\partial(x,y,z)}{\partial(\rho,\theta,\varphi)}=\begin{bmatrix}\frac18\cos\theta\sin\varphi&-\frac18\rho\sin\theta\sin\varphi&\frac18\rho\cos\theta\cos\varphi\\\\\frac18\sin\theta\sin\varphi&\frac18\rho\cos\theta\sin\varphi&\frac18\rho\sin\theta\cos\varphi\\\frac38\cos\varphi&0&-\frac38\rho\sin\varphi\end{bmatrix}$

which has determinant

$\det\mathbf J=-\dfrac3{512}\rho^2\sin\varphi$

Then the volume of the ellipsoid is given by

$\displaystyle\iiint_E\mathrm dx\,\mathrm dy\,\mathrm dz=\iiint_E|\det\mathbf J|\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi$

where $E$ denotes the spaced contained by the ellipsoid. In particular, we have the definite integral and volume

$\displaystyle\frac3{512}\int_{\varphi=0}^{\varphi=\pi}\int_{\theta=0}^{\theta=2\pi}\int_{\rho=0}^{\rho=1}\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\dfrac\pi{128}$