john is placing cement tiles for a patio in a rectangle surrounding a rectangular fire pit. The fire pit has a width of x ft and a length that is 5 times the width. The entire patio is 6ft wider and 19 ft longer than the fire pit. What is the area that he will need to buy tiles for?

Answers

Answer 1

Answer:

49x + 114

Step-by-step explanation:

[   [ fireplace ] x   = area of 5[tex]x^{2}[/tex]                   ]  x + 6

     5x

   patio               = area of 5[tex]x^{2}[/tex] + 49x + 114

5x + 19

 

(5x + 19) ( x + 6) = 5[tex]x^{2}[/tex] + 19x + 30x + 114

(5[tex]x^{2}[/tex] + 49x + 114)                     -   (5[tex]x^{2}[/tex] )                         =           49x + 114

(area of patio and fireplace) - (area of fireplace)     =       (area of patio only)


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what is the x-intercept of the graph 4x-6y=12

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So the x-intercept is 3. Also, the y-intercept can also be obtained by putting x=0 in the equation to get y=12/(-6)=-2

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If y varies inversely with x and y = 8 when x = 10, then what is the constant of variation?

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Answer:

Constant Variation = 80

Step-by-step explanation:

Here,

Said that x and y vary inversely ,

So,

Then an increase in x causes corresponding decrease in y and vice-versa then to find the constant k will be:

xy = k

Hence,

Here y = 8 and x = 10

So their constant will be,

x × y = k

=> k = 8 × 10

=> k = 80

Therefore, the required constant is 80 (Ans)

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Step-by-step explanation:

see attached. hope it's helps

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3

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67. There are 15 clarinet players, 12 flute
players, and 7 saxophone players in a
marching band. How many ways can the
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one clarinet player, one flute player, and
one saxophone player?
A. 34 ways
B. 187 ways
C. 1,260 ways
D. 1,500 ways

Answers

Answer:

A

Step-by-step explanation: add 15+12+7

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The band director can create a trio in 1,260 different ways.

Hence, option C is correct.

Use the concept of permutations,

The formula for permutations is,

⇒  [tex]^{n}P_{r}[/tex] = n! / (n - r)!

Where n is the total number of items and r is the number of items we are selecting.

So in this case, we have,

⇒  n = 15 clarinet players

⇒ n = 12 flute players

⇒ n = 7 saxophone players

⇒ r = 1 clarinet player,

1 flute player, and 1 saxophone player

To find the number of ways we can create a trio with one player from each instrument, we need to calculate,

⇒ ([tex]^{15}P_{1}[/tex]) x ([tex]^{12}P_{1}[/tex]) x ([tex]^{7}P_{1}[/tex])

⇒  ([tex]^{15}P_{1}[/tex])   = 15! / (15 - 1)!

                = 15! / 14!

                = 15  

This represents the number of ways we can choose one clarinet player out of 15.  

([tex]^{12}P_{1}[/tex]) ) = 12! / (12 - 1)!

           = 12! / 11!

           = 12  

This represents the number of ways we can choose one flute player out of 12.

[tex]^{7}P_{1}[/tex] = 7! / (7 - 1)!

     = 7! / 6!

     = 7

This represents the number of ways we can choose one saxophone player out of 7.

So the total number of ways we can create a trio consisting of one clarinet player, one flute player, and one saxophone player is,

⇒ 15 x 12 x 7 = 1,260

Therefore,

The band director can create a trio in 1,260 different ways.

To learn more about permutations visit:

https://brainly.com/question/14368656

#SPJ2

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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the square of a negative number increased by 6 times the number is 72. Find the number.

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Answer:

y = 6

Step-by-step explanation:

(y + 6) × y = 72

y = negative number²

When negative numbers are squared they become positive.

y = 6

Check

(6 + 6) × 6 = 72

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A rectangle has an area of 24 cm2. Function f gives the length of the rectangle, in centimeters, when the width is w cm.



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3

Answers

Answer:

Input is the value of w and the function f = 24/w as length x breadth = area of rectangle

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LMNP is rotated 180* clockwise around the origin.

Answers

Answer:

D

Step-by-step explanation:

If a shape is rotated 180* clockwise around the origin, then it is basically being flipped around which means that the current coordinates would be the opposite of what they currently are. So (3,4) would be (-3, -4).

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Answers

Answer:

= 868.1ft^3

Step-by-step explanation:

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Volume of the pyramid = 868.1ft^3

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Step-by-step explanation:

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The figure is a parallelogram so the facing sides have equal size which means :

DE = GF & DG = EF

-------------------------------------------------------------

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subtract sides minus 2x

==》- 2x + 3x - 1 = - 2x + 2x + 11

collect like terms

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add sides 1

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-------------------------------------------------------------

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Step-by-step explanation:

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