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Oduvanchick [21]
1 year ago
5

Quadrilateral a'b'c'd' is the result of dilating quadrilateral abcd about point p by a scale factor of

Mathematics
1 answer:
Karolina [17]1 year ago
4 0

The two statements about the dilated quadrilateral a'b'c'd' are false.

bc and bc' are on the same line ( False)

The length of the cd and c'd' are the same. (False)

<h3 />

The complete question is attached with the answer below.

<h3>What is dilation?</h3>

Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

Here the quadrilateral abcd is dilated by the scale factor 5 / 2.So the new quadrilateral is a'b'c'd'.

The given two statements are false:-

bc and bc' are on the same line ( False)

The length of the cd and c'd' are the same. (False)

<h3 />

To know more about dilation follow

brainly.com/question/3457976

#SPJ1

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Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.
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The Lagrangian for this function and the given constraints is

L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-4)+\lambda_2(x-y-8)

which has partial derivatives (set equal to 0) satisfying

\begin{cases}L_x=2x+\lambda_1+\lambda_2=0\\L_y=2y+2\lambda_1-\lambda_2=0\\L_z=2z+\lambda_1=0\\L_{\lambda_1}=x+2y+z-4=0\\L_{\lambda_2}=x-y-8=0\end{cases}

This is a fairly standard linear system. Solving yields Lagrange multipliers of \lambda_1=-\dfrac{32}{11} and \lambda_2=-\dfrac{104}{11}, and at the same time we find only one critical point at (x,y,z)=\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right).

Check the Hessian for f(x,y,z), given by

\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}

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3 years ago
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Because x = y + 6, 330 = y + 6 + y, which simplifies to 330 = 2y + 6.

Now all we need to do is simplify the equation.  First, we subtract 6 from both sides:

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<span>C) y = (x + a)2 - b </span>is the answer
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