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vlabodo [156]
3 years ago
5

If O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6 , find the values of x and y for which LMNO must be a paralle

logram. The diagram is not drawn to scale.

Mathematics
1 answer:
posledela3 years ago
7 0

Answer:

x=12\\y=\frac{13}{3}


Step-by-step explanation:

For it to be a parallelogram, opposite sides have to be of same length.

  • OL = NM, and
  • ON = LM

Using the expressions given, we can make 2 equations:

<u>Equation 1:</u>

OL=NM\\3y-6=x-5\\-x+3y=1


<u>Equation 2:</u>

ON=LM\\8x-8=7x+4\\


<em>Solving equation 2, we have x:</em>

8x-8=7x+4\\8x-7x=4+8\\x=12

<em>Plugging this value of x into equation 1, we can solve for y:</em>

-x+3y=1\\-(12)+3y=1\\-12+3y=1\\3y=13\\y=\frac{13}{3}

So,

x=12\\y=\frac{13}{3}



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Point S is on line segment RT. Given RT=4x, ST = 5x-10, and RS = 6 determine the numerical length of ST.
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Answer:

ST=10

Step-by-step explanation:

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3 years ago
An investor plans to invest $500 a year and expects to get a 10.5% return. If the investor makes these contributions at the end
taurus [48]

The present value of the investment is $6000.

According to the statement

Principal amount = $500

and Return amount = 10.5%

Time period = 20 years.

Now we find the present value of money then

By the formula

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PV = 500[1-(1+0.10)^20]/0.10

PV = 6000

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1 year ago
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uysha [10]
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Number 4 is 3

And number 6 is 9

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4 0
3 years ago
The following is the recipe to make one dozen muffins: 1 cups flour; 2 cups sugar; 2 tsps. Baking powder; 1 egg; 1 cup Crisco; 1
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Starbucks reports net income for 2015 of $2,634.4 million. Its stockholders' equity is $5,605 million and $6,151 million for 201
ExtremeBDS [4]

Answer:

A. 44.82%

B.

Option b. Return On Equity usually increases since the repurchase of shares reduces the denominator (avg. stockholders' equity)

C.

Option b. The Companies would tend to repurchase their own stock if they feel the stock is been undervalued by the market

Step-by-step explanation:

a. Computation for return on equity for 2015

Using this formula

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Let plug in the formula

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Return on equity=2,634.4/(11,756/2)

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Therefore the repurchase increase Starbucks’ Return On Equity.

c. In a situation where Starbucks had not repurchased common stock in the year 2015, what their Return On Equity would have been is that they will repurchase their own stock if they feel the stock is been undervalued by the market

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