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Firlakuza [10]
2 years ago
7

Gary needs 24 screws for every 2 chairs he builds.

Mathematics
2 answers:
erastovalidia [21]2 years ago
8 0

Answer:

\begin{array}{cc}\text{Nimber of chairs}&\text{Number of screws}\\ \\2&24\\6&72\\9&108\end{array}

Step-by-step explanation:

Gary needs 24 screws for every 2 chairs he builds.

Equivalent unit rate:

Gary needs 12 screws for each chair he builds.

Using this unit rate, we can state that

  • Gary needs 72 screws for every 6 chairs he builds;
  • Gary needs 108 screws for every 9 chairs he builds.

So, the table is

\begin{array}{cc}\text{Nimber of chairs}&\text{Number of screws}\\ \\2&24\\6&72\\9&108\end{array}

Liula [17]2 years ago
4 0

Answer:

72 screws are required to make 6 chairs.

108 screws are required to make 9 chairs.

Step-by-step explanation:

We are given the following in the question:

Gary needs 24 screws for every 2 chairs he builds.

We calculate the equivalent ratio to calculate number of screws required.

Ration of chairs to screws can be calculated as:

\displaystyle\frac{\text{Number of chairs}}{\text{Number of screws}} = \frac{2}{24} = \frac{1}{12} = 1:12

This can be interpreted hat 1 chair needs 12 screw.

We have to find number of screws required to make:

1. 6 chairs

Let x be the number of screws required to make 6 chairs, the we can write,

\displaystyle\frac{6}{x} = \frac{1}{12}\\\\x = 6\times 12 = 72

72 screws are required to make 6 chairs.

2. 9 chairs

Let y be the number of screws required to make 9 chairs, the we can write,

\displaystyle\frac{9}{y} = \frac{1}{12}\\\\y = 9\times 12 = 108

108 screws are required to make 9 chairs.

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Write y = x2 + 24x + 144 as a square of binomial.
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Answer:

y=(x+12)^2\\

Step-by-step explanation:

To write a quadratic equation into binomial form we can compare the equation into the completing square form of a quadratic equation like this ,

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now since,

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we can equate both the equations from left hand side to right hand side like this,

x^2+24x+144=a(x-h)^2+k\\

now we solve,

x^2+24x+144=a(x-h)^2+k\\x^2+24x+144=a((x)^2-2(x)(h)+(h)^2)+k\\x^2+24x+144=a(x^2-2hx+h^2)+k\\x^2+24x+144=ax^2-2ahx+ah^2+k\\

now we compare the coefficients of x^2:

1 = a\\

now we compare the coefficients of x :

24=-2ah\\24=-2(1)h\\24=-2h\\\frac{24}{-2}=h\\-12=h\\

now we compare the constants , (constants are the letters which are not associated with any variable in this case the variable is x)

144 = ah^2+k\\144=(1)(-12)^2+k\\144=(1)(144)+k\\144=144+k\\144-144=k\\0=k\\

so now the value we got all the values for the completing square form we plug those in , a = 1 , h = -12 , k = 0 ,

y=a(x-h)^2+k\\y=1(x-(-12))^2+0\\y=(x+12)^2\\

this is the square of a binomial, if you want to verify if we expands this formula by the formula of (a + b)^2 we would get the same result. Thus this is the correct answer.

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