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NISA [10]
4 years ago
8

I have a kit for constructing a chicken coop. The kit comes with 10-foot long beams. The instructions say to cut each beam into

two pieces such that one piece is 3 times the length of the other. How many feet long should the long piece be?
Mathematics
1 answer:
azamat4 years ago
8 0
<span>The long piece should measure 7.5 feet or 7'6" (7 foot 6 inches). If x is the length of the short piece then the length of the long piece must be 3x. The total length of the uncut beam is 10 foot. This can be represented by : x + 3x = 10 4x = 10 x = 2.5 As x = 2.5 = length of short piece, then the long piece measures 3x = 3(2.5) = 7.5 feet. There are 12 inches in a foot so 7.5 feet = 7'6"</span>
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The product of two whole numbers is<br> 416 and their sum is<br> 42. What are the two numbers?
olga55 [171]

Answer:

The two numbers are <em>16</em> and <em>26</em>.

Step-by-step explanation:

We can solve this question using 2 simultaneous equations based on the given information from the question.

Let number 1 = x

Let number 2 = y

xy = 416 -> ( 1 )

x + y = 42 -> ( 2 )

We can use either substitution or elimination to solve simultaneous equations. For this question, we will use substitution as it is the easier and shorter option.

Make y the subject in ( 2 ):

x + y = 42 -> ( 2 )

y = 42 - x -> ( 3 )

Substitute ( 3 ) into ( 1 ):

xy = 416 -> ( 1 )

x ( 42 - x ) = 416

42x - x^2 = 416

-x^2 + 42x - 416 = 0

- [ x^2 - 42x + 416 ] = 0

- [ x^2 - 16x - 26x + 416 ] = 0

- [ x ( x - 16 ) - 26 ( x - 16 ) ] = 0

- ( x - 16 ) ( x - 26 ) = 0

x = 16 -> ( 4 ) , x = 26 -> ( 5 )

Substitute ( 4 ) into ( 3 ):

y = 42 - x -> ( 3 )

y = 42 - ( 16 )

y = 26

Substitute ( 5 ) into ( 3 ):

y = 42 - x -> ( 3 )

y = 42 - ( 26 )

y = 16

Therefore:

x = 16 , y = 26

x = 26 , y = 16

The two numbers are 16 and 26.

7 0
4 years ago
Explain the differnce between a number that is a cube and a number that is a cube root
yawa3891 [41]

Answer:

https://www.mathsisfun.com/numbers/cube-root.html

Step-by-step explanation:

6 0
3 years ago
"la temperatura mas baja conocida en la tierra es de 273° bajo cero mientras que la temperatura promedio de la superficie de la
skelet666 [1.2K]

Answer:

Variación de temperatura: 310°C

Step-by-step explanation:

La variación de temperatura entre la temperatura más baja conocida en la tierra (-273°C = 273° bajo cero) y la temperatura promedio de la tierra (37°C) será el valor absoluto de la diferencia de estos dos valores, es decir:

Variación de temperatura: |-273°C - 37°C|

Variación de temperatura: |-310°C|

<em>Como el valor absoluto de un número negativo es su valor positivo (|-x| = x)</em>

<h3>Variación de temperatura: 310°C</h3>
4 0
3 years ago
Angela is taping 7 boxes for storage. She uses 1 1/2 feet of tape to close each box how much tape will Angela need to tape the b
Mrrafil [7]

Answer:

B. 10 1/2 feet

Step-by-step explanation:

We are told that she taped 7 boxes.

We are also told that she uses 1 1/2 feet of tape to close each box.

Therefore, the length of tape she will need to use for the 7 boxes will be the product of 7 boxes and 1 1/2 feet of tape per box:

L = 1 1/2 * 7 = 3/2 * 7 = 21/2 = 10 1/2 feet.

She will need to use 10 1/2 feet of tape.

5 0
3 years ago
Which conclusion is correct about the population of State A and State B?
Lapatulllka [165]
Could you post a Graph or the Question, please? 
Thank you.
8 0
4 years ago
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