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Ghella [55]
2 years ago
10

Model the following problem with a quadratic equation. Then solve. Find the length of a side of a square with an area of 75 ft2.

Model the problem with a quadratic equation. Let x be the length of a side of the square.
Mathematics
1 answer:
Vaselesa [24]2 years ago
5 0

Answer:

x = 8.6603 m

Step-by-step explanation:

If x is the length of a side of the square, the area of the square will be x^2.

So, if the area of the square is 75 ft2, we can formulate the quadratic equation:

x^2 = 75

Now, solving the equation, we just need to make the square root of 75:

x = sqrt(75) = ±8.6603

x1 = 8.6603

x2 = -8.6603

Now, as x represents the length of a side of the square, and measurements can't be negative, we take only the positive value, so:

x = 8.6603 m

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<h3>Given Equation:</h3>

\huge \purple {\rm { {x}^{2}  + kx - 12 = 0}}

<h3>Value:</h3>

\huge \purple {\rm {x = 4}}

<h3>To Find:</h3>

\huge \purple {\rm {The \: value \: of \: k.}}

<h3>Solution:</h3>

\huge \purple {\rm { {(4)}^{2}  + k(4) - 12 = 0}}

\huge \purple {\rm {or, \: 16 + 4 k - 12 = 0}}

\huge \purple {\rm {or, \: 4k =  - 4}}

\huge \purple {\rm {or, \: k =  \frac{ - 4}{4}  =  - 1}}

<h2>Answer:</h2>

\huge \purple {\sf {The \: value \: of \: k \: is \: -1}}

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