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3 years ago

The vertices of a parallelogram are A(x1,y1), B(x2,y2), C(x3,y3), D(x4,y4)

Mathematics

2 answers:

Bond [772]3 years ago

6 0

i just did this oneand option C. is correct

Tju [1.3M]3 years ago

3 0

<span>For a parallelogram to be proven to be a rectange, the opposide sides must be parallel and the two adjacent sides must be perpendicular. For two parallel sides, the slope of the two sides is equal. Thus, for the parallelogram to be a rectangle, AB is parallel to CD. The slope of AB = (y2 - y1)/(x2 - x1) while the slope of CD = (y4 - y3)/(x4 - x3) Also, BC is perpedicular to CD. For two perpendicular sides, the product of the slopes is -1. The slope of BC is given by (y3 - y2)/(x3 - x2). Therefore, for the parallelogram to be a rectangle. (y2 - y1)/(x2 - x1) = (y4 - y3)/(x4 - x3) and (y4 - y3)/(x4 - x3) x (y3 - y2)/(x3 - x2) = -1. The third option is the correct answer.</span>

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Suppose X, Y, and Z are random variables with the joint density function f(x, y, z) = Ce−(0.5x + 0.2y + 0.1z) if x ≥ 0, y ≥ 0, z

kompoz [17]

$f_{X,Y,Z}(x,y,z)=\begin{cases}Ce^{-(0.5x+0.2y+0.1z)}&\text{for }x\ge0,y\ge0,z\ge0\\0&\text{otherwise}\end{cases}$

is a proper joint density function if, over its support, $f$ is non-negative and the integral of $f$ is 1. The first condition is easily met as long as $C\ge0$ . To meet the second condition, we require

$\displaystyle\int_0^\infty\int_0^\infty\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=100C=1\implies \boxed{C=0.01}$

b. Find the marginal joint density of $X$ and $Y$ by integrating the joint density with respect to $z$ :

$f_{X,Y}(x,y)=\displaystyle\int_0^\infty f_{X,Y,Z}(x,y,z)\,\mathrm dz=0.01e^{-(0.5x+0.2y)}\int_0^\infty e^{-0.1z}\,\mathrm dz$

$\implies f_{X,Y}(x,y)=\begin{cases}0.1e^{-(0.5x+0.2y)}&\text{for }x\ge0,y\ge0\\0&\text{otherwise}\end{cases}$

Then

$\displaystyle P(X\le1.375,Y\le1.5)=\int_0^{1.5}\int_0^{1.375}f_{X,Y}(x,y)\,\mathrm dx\,\mathrm dy$

$\approx\boxed{0.12886}$

c. This probability can be found by simply integrating the joint density:

$\displaystyle P(X\le1.375,Y\le1.5,Z\le1)=\int_0^1\int_0^{1.5}\int_0^{1.375}f_{X,Y,Z}(x,y,z)\,\mathrm dx\,\mathrm dy\,\mathrm dz$

$\approx\boxed{0.012262}$

7 0

3 years ago

Solve the equation 4(x + 2)= 6x + 4

SIZIF [17.4K]

The answer is x=2

show you step-by-step

step 1:simplify both sides of the equation.

(4)(x)+(4)(2)=6x+4

4x+8=6x+4

step 2:subtract 6x from both sides.

4x+8-6x=6x+4-6x

-2x+8=4

step 3: subtract 8 from both sides

-2x+8-8=4-8

-2x=-4

step 4: divide both sides by -2

-2x/-2= -4/-2

x=2

that helps you

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3 years ago

1) What is additive inverse property?

mrs_skeptik [129]

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3 years ago

1. 18 is 30% off what number

marusya05 [52]

2 7.5
That’s all that I could do I hope it help

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2 years ago

Find variable values for two variables in an equation

never [62]

Simplifying

2x + 3y = 12

Solving

2x + 3y = 12

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3y' to each side of the equation.

2x + 3y + -3y = 12 + -3y

Combine like terms: 3y + -3y = 0

2x + 0 = 12 + -3y

2x = 12 + -3y

Divide each side by '2'.

x = 6 + -1.5y

Simplifying

x = 6 + -1.5y

5 0

3 years ago