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3 years ago

X - 2y = 5 3х - 5y = 8

2 answers:

8 0

For elimination you multiply both sides by the common factor for substitution we need at Sam’s isolate each variable and get it once and and plug in! Hope this helps :))

natali 33 [55]3 years ago

6 0

Answer:

Ax: x=2y+5

Ay: y= 1/2 x+ -5/2

Bx: x=5/3+8/3

By: y=3/5x+-8/5

Step-by-step explanation:

if you're asking for the intersect solution: (-9,-7)

I hope one of those answers can help you :3

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3. Find the volume of the figure. Simplify.<br> Cube<br> x + 4

Oliga [24]

Answer:

[see below]

Step-by-step explanation:

V = s^3

V = (x+4)^3

V = x^3 + 3x^2 * 4 + 3x * 4^2 + 4^3

V = x^3 + 12x^2 + 48x + 64

Hope this helps.

6 0

3 years ago

Which of the following is true about equations?

Setler [38]

Issbns ubskagsgjzajs

4 0

3 years ago

Read 2 more answers

Use the method of Lagrange multipliers to find the dimensions of the rectangle of greatest area that can be inscribed in the ell

Tanzania [10]

Answer:

Length (parallel to the x-axis): $2 \sqrt{2}$ ;

Height (parallel to the y-axis): $4\sqrt{2}$ .

Step-by-step explanation:

Let the top-right vertice of this rectangle $(x,y)$ . $x, y >0$ . The opposite vertice will be at $(-x, -y)$ . The length the rectangle will be $2x$ while its height will be $2y$ .

Function that needs to be maximized: $f(x, y) = (2x)(2y) = 4xy$ .

The rectangle is inscribed in the ellipse. As a result, all its vertices shall be on the ellipse. In other words, they should satisfy the equation for the ellipse. Hence that equation will be the equation for the constraint on x and y.

For Lagrange's Multipliers to work, the constraint shall be in the form: $g(x, y) =k$ . In this case

$\displaystyle g(x, y) = \frac{x^{2}}{4} + \frac{y^{2}}{16}$ .

Start by finding the first derivatives of $f(x, y)$ and $g(x, y)$ with respect to x and y, respectively:

$f_x = y$ ,
$f_y = x$ .

$\displaystyle g_x = \frac{x}{2}$ ,
$\displaystyle g_y = \frac{y}{8}$ .

This method asks for a non-zero constant, $\lambda$ , to satisfy the equations:

$f_x = \lambda g_x$ , and

$f_y = \lambda g_y$ .

(Note that this method still applies even if there are more than two variables.)

That's two equations for three variables. Don't panic. The constraint itself acts as the third equation of this system:

$g(x, y) = k$ .

$\displaystyle \left\{ \begin{aligned} &y = \frac{\lambda x}{2} && (a)\\ &x = \frac{\lambda y}{8} && (b)\\ & \frac{x^{2}}{4} + \frac{y^{2}}{16} = 1 && (c)\end{aligned}\right.$ .

Replace the $y$ in equation $(b)$ with the right-hand side of equation $(b)$ .

$\displaystyle x = \lambda \frac{\lambda \cdot \dfrac{x}{2}}{8} = \frac{\lambda^{2} x}{16}$ .

Before dividing both sides by $x$ , make sure whether $x = 0$ .

If $x = 0$ , the area of the rectangle will equal to zero. That's likely not a solution.

If $x \neq 0$ , divide both sides by $x$ , $\lambda = \pm 4$ . Hence by equation $(b)$ , $y = 2x$ . Replace the $y$ in equation $(c)$ with this expression to obtain (given that $x, y >0$ ) $x = \sqrt{2}$ . Hence $y = 2x = 2\sqrt{2}$ . The length of the rectangle will be $2x = 2\sqrt{2}$ while the height will be $2y = 4\sqrt{2}$ . If there's more than one possible solutions, evaluate the function that needs to be maximized at each point. Choose the point that gives the maximum value.

7 0

3 years ago

Based on the graph, which statement could describe janelle’s trip home from school

RoseWind [281]

Answer: Janelle rode the bus to the bus stop, talked with a friend, and then walked home,

Step-by-step explanation: I literally just put it and it’s correct

3 0

4 years ago

Read 2 more answers

If eight cars are entered in a race and three finishing places are considered, how many finishing orders can they finish? Assume

Sladkaya [172]

Answer:

a) 336

b)6

c)6

Step-by-step explanation:

a) In the 1st place fit 8 cars, in the 2nd only fit 7 cars, because one is already in the first place and 3th fit 6 cars, so all the possibilities are 8*7*6.

b) in the 1st place fit 3 cars, 2nd 2 cars and 3th 1 car, so all the possibilities are 3*2*1

c) every shirt can be matched with 1 pair of pants, there are 2 shirts and 3 pants, so all the the possibilities are 6+6.

3 0

4 years ago