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4 years ago

. If ON = 4x – 6, LM = 3x + 5, NM = x – 4, and OL = 4y – 3, find the values of x and y for which LMNO must be a parallelogram.

1 answer:

5 0

In a parallelogram, opposite sides are congruent.

This means that
LM = ON
NM = OL

Using the equations, find x and y:
4x - 6 = 3x + 5
4x = 3x + 11
1x = 11
x = 11

x - 4 = 4y - 3
x - 1 = 4y
-1 = 3y
-1/3 = y

The values are:
x = 11
y = -1/3

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Answer:

option B

Step-by-step explanation:

Given :

$y = \frac{2}{3}x + 3\\\\y = \frac{5}{2}x + \frac{7}{2}\\\\$

Step 1 : simplify the equation :

$3y = 2x + 9\\\\2y = 5x + 7\\$

Step 2: Arrange the terms :

$2x - 3y = - 9\\\\5x -2 y = -7$

Step 3 : Solve for x and y :

2x - 3y = - 9 ------ ( 1 )

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_____________________

( 1 ) x 5 => 10x - 15y = - 45 ---------- (3 )

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$y = \frac{31}{11}$

Substitute y in ( 1 ) :

2x - 3y = - 9

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Therefore the solution to the sytem is $( - \frac{3}{11} , \frac{31}{11})$

The solution of the system of equation is a point which lies

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both the line.

Option B : True , says the solution is a point on the coordinate plane.

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3 years ago

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denis23 [38]

Answer: 0.345

Step-by-step explanation:

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Samples size : n=4

Let x be the random variable that represents the incomes of families in Newport Harbor.

The z-statistic :-

$z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

For x= $800,000

$z=\dfrac{800000-750000}{\dfrac{250000}{\sqrt{4}}}=0.4$

By using the standard normal distribution table , we have

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Hence, the probability that the average income of these 4 families exceeds $800,000 =0.345

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4 years ago

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3 years ago

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zvonat [6]

Answer:

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Steps:

4x+3y=-1

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First, multiply the top equations by -5, and the bottom by 4 to get :

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Then, you’re going to add the two equations with them being on top of each other so you can easily see what cancels out :

-20x-15y=5

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———————

0+1y=9

From this, you get :

y=9

Now that you have one variable, find x by substituting 9 for y in one of the equations, I choose :

4x+3y=-1

So :

4x+3(9)=-1

Then simplify by multiplying 3 and 9 :

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Then subtract 27 on each side :

4x=-28

Then, divide by 4 to get that :

x= -7

Hope this helps!!

7 0

3 years ago

Read 2 more answers