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laila [671]
3 years ago
7

The rectangle below has an area of 81-x^2 square meters and a width of 9-x meters. What expression represents the length of the

rectangle?
Mathematics
1 answer:
oksian1 [2.3K]3 years ago
3 0

For this case we have that by definition, the area of a rectangle is given by:

A = w * l

Where:

w: Is the width of the rectangle

l: is the length of the rectangle

According to the data of the statement we have:

A = 81-x ^ 2\\w = 9-x

So, the length is given by:

l = \frac {A} {w}\\l = \frac {81-x ^ 2} {9-x}

We factor the numerator:

l = \frac {(9 + x) (9-x)} {9-x}

We simplify:

l = 9 + x

So, the length is 9 + x

Answer:

9 + x

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Answer:

Therefore the of blue in the second urn is 4.

Step-by-step explanation:

Let second urn contain x number of blue ball .

Urn            Red Ball          Blue Ball         Total Ball

1                       4                       6                      10

2                      16                       x                    16+x

Getting a red ball from first urn is P(R_1)=\frac{\textrm {Number of red ball}}{\textrm {Total ball}}    =\frac{4}{10}

Getting a blue ball from first urn is P(B_1)=\frac{\textrm {Number of blue ball}}{\textrm {Total ball}} =\frac {6}{10}

Getting a red ball from second urn is P(R_2)=\frac{\textrm {Number of red ball}}{\textrm {Total ball}}    =\frac{16}{16+x}

Getting a blue ball from second urn is P(B_2)=\frac{\textrm {Number of blue ball}}{\textrm {Total ball}} =\frac {x}{16+x}

Getting two red balls from first and second urn is =\frac{4}{10}\times \frac{16}{16+x}

                                                                                  =\frac{32}{5(16+x)}

Getting two blue balls from first and second urn is =\frac{6}{10}\times \frac{x}{16+x}

                                                                                  =\frac{3x}{5(16+x)}

The probability that both balls are the same in color is =\frac{32}{5(16+x)}+\frac{3x}{5(16+x)}

Given that the probability that both balls are the same in color is 0.44.

According to the problem,

\frac{32}{5(16+x)}+\frac{3x}{5(16+x)}=0.44

\Rightarrow \frac{32+3x}{5(16+x)} =0.44

\Rightarrow \frac {32+3x}{(80+5x)} =0.44

\Rightarrow 32+3x =0.44(80+5x)

\Rightarrow 32+3x =35.2 +2.2x

\Rightarrow 3x -2.2 x= 35.2 -32

\Rightarrow 0.8x= 3.2

\Rightarrow x = 4

Therefore the of blue in the second urn is 4.

               

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