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Dominik [7]
3 years ago
5

Solve by using elimination. Express your answer as an Ordered pair (-x +2y=3 3x-2y=7

Mathematics
1 answer:
MAVERICK [17]3 years ago
4 0

Answer:

(5,4)

Step-by-step explanation:

-x+2y=3

3x-2y=7

Add the like terms( 2y and -2y)(-x and 3x)(3 and 7) together. Do this vertically. 2y and -2y cancel eachother out.

  • 2x=10

Divide both sides by 2

  • <u>x=5</u>

To find y, substitute x in for y in one of the equations

  • -5+2y=3

add 5 to both sides

  • 2y=8

Divide both sides by 2

  • <u>y=4</u>

Check:

  • -5+2(4)=3
  • 3=3
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3 years ago
Right triangle ABC and its image, triangle A'B'C' are shown in the image attached.
AlladinOne [14]

Answer:

See explanation

Step-by-step explanation:

Triangle ABC ha vertices at: A(-3,6), B(0,-4) and (2,6).

Let us apply 90 degrees clockwise about the origin twice to obtain 180 degrees clockwise rotation.

We apply the 90 degrees clockwise rotation rule.

(x,y)\to (y,-x)

\implies A(-3,6)\to (6,3)

\implies B(0,4)\to (4,0)

\implies C(2,6)\to (6,-2)

We apply the 90 degrees clockwise rotation rule again on the resulting points:

\implies (6,3)\to A''(3,-6)

\implies (4,0)\to B''(0,-4)

\implies (6,-2)\to C''(-2,-6)

Let us now apply 90 degrees counterclockwise  rotation about the origin twice to obtain 180 degrees counterclockwise rotation.

We apply the 90 degrees counterclockwise rotation rule.

(x,y)\to (-y,x)

\implies A(-3,6)\to (-6,-3)

\implies B(0,4)\to (-4,0)

\implies C(2,6)\to (-6,2)

We apply the 90 degrees counterclockwise rotation rule again on the resulting points:

\implies (-6,-3)\to A''(3,-6)

\implies (-4,0)\to B''(0,-4)

\implies (-6,2)\to C''(-2,-6)

We can see that A''(3,-6), B''(0,-4) and C''(-2,-6) is the same for both the 180 degrees clockwise and counterclockwise rotations.

7 0
3 years ago
Let Y1 and Y2 be independent exponentially distributed random variables, each with mean 7. Find P(Y1 &gt; Y2 | Y1 &lt; 2Y2). (En
ArbitrLikvidat [17]

<em>Y</em>₁ and <em>Y</em>₂ are independent, so their joint density is

f_{Y_1,Y_2}(y_1,y_2)=f_{Y_1}(y_1)f_{Y_2}(y_2)=\begin{cases}\frac1{49}e^{-\frac{y_1+y_2}7}&\text{for }y_1\ge0,y_2\ge0\\0&\text{otherwise}\end{cases}

By definition of conditional probability,

P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = P((<em>Y</em>₁ > <em>Y</em>₂) and (<em>Y</em>₁ < 2 <em>Y</em>₂)) / P(<em>Y</em>₁ < 2 <em>Y</em>₂)

Use the joint density to compute the component probabilities:

• numerator:

P((Y_1>Y_2)\text{ and }(Y_1

=\displaystyle\frac1{49}\int_0^\infty\int_{\frac{y_1}2}^{y_1}e^{-\frac{y_1+y_2}7}\,\mathrm dy_2\,\mathrm dy_1

=\displaystyle-\frac17\int_0^\infty\int_{-\frac{3y_1}{14}}^{-\frac{2y_1}7}e^u\,\mathrm du\,\mathrm dy_1

=\displaystyle-\frac17\int_0^\infty\left(e^{-\frac{2y_1}7} - e^{-\frac{3y_1}{14}}\right)\,\mathrm dy_1

=\displaystyle-\frac17\left(-\frac72e^{-\frac{2y_1}7} + \frac{14}3 e^{-\frac{3y_1}{14}}\right)\bigg|_0^\infty

=\displaystyle-\frac17\left(\frac72 - \frac{14}3\right)=\frac16

• denominator:

P(Y_1

(I leave the details of the second integral to you)

Then you should end up with

P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = (1/6) / (2/3) = 1/4

5 0
2 years ago
Find the sum of (x+5) and (2x+3)
telo118 [61]
X+5+2x+3
=3x+8

hope that was helpful! 
5 0
3 years ago
Read 2 more answers
Problem
PolarNik [594]

Answer:

The equation of this line would be y = -8

Step-by-step explanation:

Since y = 9 is a horizontal line, the parallel line must also be horizontal. All horizontal lines can be written as y = (a number). That number can be found as the y-coordinate in the ordered pair, which is -8.

y = -8

8 0
3 years ago
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