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3 years ago

Y=1x+2 y=3x-4 use substtiution

Mathematics

2 answers:

postnew [5]3 years ago

7 0

Answer:

3Y - 4X - 4

Step-by-step explanation:

Brums [2.3K]3 years ago

3 0

The answer is X=2 and Y=-4

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A jar of marbles has five blue marbles, three red marbles, and four green marbles. What is the possibility of drawing a marble t

solniwko [45]

Answer:

5/36

Step-by-step explanation:

The chance of drawing a blue marble is 5/12. The chance of drawing a green marble is 4/12. You multiply the fractions to get the probability.

5/12 * 4/12 =20/144 = 5/36 simplified.

8 0

3 years ago

Read 2 more answers

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).

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3 years ago

Sergio is s years old. which expression shows how old he will be 7 years from now? question 5 options: 7s 7 – s s 7 7s 7

notsponge [240]

S+7. Tell your teacher never to use s as a variable ever again.

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3 years ago

At Jack’s birthday party, 23 of the kids had balloons. 14 of the balloons were red. What fraction of the kids at the party had r

Nonamiya [84]

14/23. You can’t simplify it anymore. It is also equivalent to about 61% (60.86% to be exact)

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3 years ago

Factorise 3c^2-c<br><br><br> Please help me quick

Dafna11 [192]

Answer:

c(3c - 1)

Step-by-step explanation:

3c² - c

Common factor = c

Factored:

c(3c - 1)

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3 years ago