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kherson [118]
2 years ago
7

If me.Arenth wants to put new carpeting in the room shown, how many square feet should he order

Mathematics
1 answer:
Liula [17]2 years ago
7 0

By definition, the area is given by:


A = w * l  


Where,


w: width


l: length


We have two expressions for the length:


L = 14\\L = 5 + 3c


Since the length is the same, we equate both expressions:


5 + 3c = 14  


From here, we clear the value of c:


3c = 14 - 5\\3c = 9  


c = \frac{9}{3}\\c = 3  


Then, we have that the width is given by:


W = 6c-8  


Substituting the value of c we have:


W = 6 (3) -8\\W = 18-8\\W = 10  


Finally, the area is given by:


A = w * l\\A = 10 * 14\\A = 140 ft ^ 2  


Answer:


he should order 140 square feet

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The product of two consecutive integers is 420 which quadratic equation can be used to find x the lesser number
Fynjy0 [20]

Answer:

Step-by-step explanation:

If the smallest number is 'x', then the other number = x +1

x*(x+1)= 420

Use distributive property

x*x + x*1 = 420

x² + x - 420 =0   ------> this is the required quadratic equation.

5 0
3 years ago
Revenue from Monorail Service, Las Vegas In 2005 the Las Vegas monorail charged $3 per ride and had an average ridership of abou
Karolina [17]

Answer:

A)The required linear demand equation ( q ) = -4500p + 41500

B) $4.61

   $95680.55

C) No it would not have been possible by charging a suitable price

Step-by-step explanation:

<u>A)  find the linear demand equation</u>

given two points ; ( 3, 28000 ) and ( 5, 19000 )

slope ( m ) = ( y2 - y1 ) / ( x2 - x1 )

                 = ( 19000 - 28000 ) / ( 5 - 3 )  = -4500

slope intercept is represented as ; y = mx + b

where y( 28000) = -4500(3) + b

  hence b = 41500  

hence ; y = -4500x + 41500

The required linear demand equation ( q ) = -4500p + 41500   ----- ( 1 )

p = price per ride

<u>B ) Determine the price the company should charge to maximize revenue from ridership  and corresponding daily revenue</u>

Total revenue ( R ) = qp

                               = p ( -4500p + 41500 )

  hence R = -4500p^2 + 41500p  ------ ( 2 )

To determine the price that should maximize revenue from ridership we will equate R = -4500p^2 + 41500p  to a quadratic equation R(p) = ap^2 + bp + c

where a = -4500 ,  b = 41500 , c = 0

hence p = -\frac{b}{2a}  = - \frac{41500}{2(-4500)} =  4.61

$4.61 is the price the company should charge to maximize revenue from ridership

corresponding daily revenue = R = -4500p^2 + 41500 p

where p = $4.61

hence R = -4500(4.61 )^2 + 41500(4.61) = $95680.55

C) No it would not have been possible by charging a suitable price

5 0
2 years ago
Consider this right triangle.<br> 21<br> 29<br> 20<br> Enter the ratio equivalent to s
AleksAgata [21]

Answer:

Part 1) sin(B)=\frac{21}{29}

Part 2) csc(A)=\frac{29}{20}

Part 3) cot(A)=\frac{21}{20}

Step-by-step explanation:

<u><em>The complete question is</em></u>

Consider this right triangle. 21 29 20 Write the ratio equivalent to: Sin B - CscA- Cot B

The picture of the question in the attached figure

Part 1) Write the ratio equivalent to: Sin B

we know that

In the right triangle ABC

sin(B)=\frac{AC}{AB} ----> by SOH (opposite side divided by the hypotenuse)

substitute the values

sin(B)=\frac{21}{29}

Part 2) Write the ratio equivalent to: Csc A

we know that

In the right triangle ABC

csc(A)=\frac{1}{sin(A)}

sin(A)=\frac{BC}{AB} -----> by SOH (opposite side divided by the hypotenuse)

substitute the values

sin(A)=\frac{20}{29}

therefore

csc(A)=\frac{29}{20}

Part 3) Write the ratio equivalent to: Cot A

we know that

In the right triangle ABC

cot(A)=\frac{1}{tan(A)}

tan(A)=\frac{BC}{AC} -----> by TOA (opposite side divided by the adjacent side)

substitute the values

tan(A)=\frac{20}{21}

therefore

cot(A)=\frac{21}{20}

4 0
3 years ago
Solve the following system of equations for all three variables.
nignag [31]
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 5x -  2y + 1z = 8
-9x + 2y + 2z = 5 ⇒ -9x + 2y + 2z = 5
-9z -  2y -  5z = 4 ⇒ -9x -  2y -  5z = 4
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     -4x + 3z = 13
    -18x - 3z =   9
           -22x = 22
            -22    -22
                x = -1
    -18x - 3z = 9
-18(-1) - 3z = 9
       18 - 3z = 9
     - 18       - 18
             -3z = -9
              -3     -3
                z = 3

    5x - 2y + z = 8
5(-1) - 2y + 3 = 8
     -5 - 2y + 3 = 8
     -2y - 5 + 3 = 8
           -2y - 2 = 8
                + 2 + 2
                -2y = 10
                 -2     -2
                   y = -5
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6 0
3 years ago
Please help as soon as possible PLEASE
pashok25 [27]

Area of the entire rectangle =x^2+10x+24

Solution:

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Area of the blue box =x^2

Area of the pink box =  length × width

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Area of the pink box =4x

Area of the green box = length × width

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Area of the green box =6x

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Total area of the rectangle =x^2+4x+6x+24

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Area of the entire rectangle =x^2+10x+24

4 0
3 years ago
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