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irga5000 [103]
3 years ago
15

A farmer plants corn and wheat on a 180-acre farm. the farmer wants to plant three times as many acres of corn as wheat. write a

system of linear equations that represents this situation. use xx to represent the number of aces of corn planted and yy to represent the number of acres of wheat planted. how many acres of each crop should the farmer plant?
Mathematics
1 answer:
Anna [14]3 years ago
7 0
Let the number of corn acres be xx and the number of wheat acres be yy.
We are given that:
1- The total number of acres is 180, this means that:
xx + yy = 180 ..............> equation I
2- The number of corn acres is 3 times that of wheat. This means that:
xx = 3yy .........> equation II

Substitute with equation II in equation I to get the value of yy as follows:
xx + yy = 180
3yy + yy = 180
4yy = 180
yy = 45 acres

Now substitute with yy in equation II to get xx as follows:
xx = 3yy
xx = 3*45
xx = 135 acres

Based on the above calculations:
acres of corn = xx = 135 acres
acres of wheat = yy = 45 acres
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Answer:

6 units

Step-by-step explanation:

(-4 , -10) ; (-4 , -4)

Distance = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}

               = \sqrt{(-4-[-4])^{2}+(-4-[-10])^{2}}\\\\= \sqrt{(-4+4)^{2}+(-4+10)^{2}}\\\\=\sqrt{0+(6)^{2}}\\\\= \sqrt{36}\\\\= 6

4 0
2 years ago
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Can someone help me?
geniusboy [140]

Step-by-step explanation:

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3 years ago
Evaluate the following limit:
Makovka662 [10]

If we evaluate the function at infinity, we can immediately see that:

        \large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle L = \lim_{x \to \infty}{\frac{(x^2 + 1)^2 - 3x^2 + 3}{x^3 - 5}} = \frac{\infty}{\infty}} \end{gathered}$}

Therefore, we must perform an algebraic manipulation in order to get rid of the indeterminacy.

We can solve this limit in two ways.

<h3>Way 1:</h3>

By comparison of infinities:

We first expand the binomial squared, so we get

                         \large\displaystyle\text{$\begin{gathered}\sf \displaystyle L = \lim_{x \to \infty}{\frac{x^4 - x^2 + 4}{x^3 - 5}} = \infty \end{gathered}$}

Note that in the numerator we get x⁴ while in the denominator we get x³ as the highest degree terms. Therefore, the degree of the numerator is greater and the limit will be \infty. Recall that when the degree of the numerator is greater, then the limit is \infty if the terms of greater degree have the same sign.

<h3>Way 2</h3>

Dividing numerator and denominator by the term of highest degree:

                            \large\displaystyle\text{$\begin{gathered}\sf L  = \lim_{x \to \infty}\frac{x^{4}-x^{2} +4  }{x^{3}-5  }  \end{gathered}$}\\

                                \ \  = \lim_{x \to \infty\frac{\frac{x^{4}  }{x^{4} }-\frac{x^{2} }{x^{4}}+\frac{4}{x^{4} }    }{\frac{x^{3} }{x^{4}}-\frac{5}{x^{4}}   }  }

                                \large\displaystyle\text{$\begin{gathered}\sf \bf{=\lim_{x \to \infty}\frac{1-\frac{1}{x^{2} } +\frac{4}{x^{4} }  }{\frac{1}{x}-\frac{5}{x^{4} }  }  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{0}=\infty } \end{gathered}$}

Note that, in general, 1/0 is an indeterminate form. However, we are computing a limit when x →∞, and both the numerator and denominator are positive as x grows, so we can conclude that the limit will be ∞.

5 0
2 years ago
Which value for y makes the sentence true? 8 - y = 6 - 1 A. 4 B. 5 C. 1 D. 3
Oksi-84 [34.3K]

Answer:

4

Step-by-step explanation:

3 0
3 years ago
I need help!! What is he answer??
IgorC [24]
2 is the answer i think
7 0
3 years ago
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