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2 years ago

What is the length of DE is the quadrilateral is a square ? Options A)3 B)10 C)5 D)1

Mathematics

1 answer:

maxonik [38]2 years ago

6 0

2x+3=5x

3=3x

x=1

2(1)+3=

2+3=

your answer is 5

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Which term is a word for an initial amount of money that is borrowed or invested?

ozzi

Answer:

principal is the correct answer

Step-by-step explanation:

principal is the correct answer

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2 years ago

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Jade had the following system of equations to help her with a physics problem, but she only needed to know what the sum of x and

pav-90 [236]

From the second:

2x-y=4

x=(4+y)/2 and applying this to first:

4+y+3y=12

4y+4=12

4y=8

y=2 and since x=(4+y)/2, x=3 so

x+y=2+3=5

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3 years ago

Find the absolute maximum and absolute minimum values of the function f(x, y) = x 2 + y 2 − x 2 y + 7 on the set d = {(x, y) : |

dsp73

Looks like $f(x,y)=x^2+y^2-x^2y+7$ .

$f_x=2x-2xy=0\implies2x(1-y)=0\implies x=0\text{ or }y=1$

$f_y=2y-x^2=0\implies2y=x^2$

If $x=0$ , then $y=0$ - critical point at (0, 0).
If $y=1$ , then $x=\pm\sqrt2$ - two critical points at $(-\sqrt2,1)$ and $(\sqrt2,1)$

The latter two critical points occur outside of $D$ since $|\pm\sqrt2|>1$ so we ignore those points.

The Hessian matrix for this function is

$H(x,y)=\begin{bmatrix}f_{xx}&f_{xy}\\f_{yx}&f_{yy}\end{bmatrix}=\begin{bmatrix}2-2y&-2x\\-2x&2\end{bmatrix}$

The value of its determinant at (0, 0) is $\det H(0,0)=4>0$ , which means a minimum occurs at the point, and we have $f(0,0)=7$ .

Now consider each boundary:

If $x=1$ , then

$f(1,y)=8-y+y^2=\left(y-\dfrac12\right)^2+\dfrac{31}4$

which has 3 extreme values over the interval $-1\le y\le1$ of 31/4 = 7.75 at the point (1, 1/2); 8 at (1, 1); and 10 at (1, -1).

If $x=-1$ , then

$f(-1,y)=8-y+y^2$

and we get the same extrema as in the previous case: 8 at (-1, 1), and 10 at (-1, -1).

If $y=1$ , then

$f(x,1)=8$

which doesn't tell us about anything we don't already know (namely that 8 is an extreme value).

If $y=-1$ , then

$f(x,-1)=2x^2+8$

which has 3 extreme values, but the previous cases already include them.

Hence $f(x,y)$ has absolute maxima of 10 at the points (1, -1) and (-1, -1) and an absolute minimum of 0 at (0, 0).

3 0

2 years ago

triangle ABC is reflected across the y-axis and then dilated by a factor of 1/2 centered at the origin. which statement correctl

Nadya [2.5K]

Answer:

Step-by-step explanation:

The reflection preserves the side lengths and angles of triangle ABC. The dilation preserves angles but not side lengths.

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2 years ago

Given the quadratic function

hjlf

The vertex is (-4,-3)

The axis of symmetry is x=-4

and the transformations are:

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2 years ago