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Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans plants 29 daisies, how many snapdragons will he plant?

The equation_____models the scenario.

Hans will plant______snapdragons.

Hans is planting a garden with snapdragons and daisies. The table shows some possible combinations of the two plants. If Hans plants 29 daisies, how many snapdr class=

Verified Answer :

JeanaShupp

Answer: The equation \(x+y=45\) models the scenario.

Hans will plant 16 snapdragons.

Step-by-step explanation:

From the given table, it can be seen that there is constant change in y with respect to x.

i.e. for every one increment of x, there is decrease in y by one quantity.

Thus, the given equation must be linear.

The linear equation is given by :-

\(y=mx+c\), where m, is the rate of change of y w.r.t. x.

Now, the rate of change of function will be :-

\(m=\dfrac{\text{change in y}}{\text{change in x}}=\dfrac{33-34}{12-1}=-1\)

Put m=-1, x=11 and y = 34, we get

\(34=-11+c\\\\\Rightarrow\ c=34+11=45\)

Thus the equation models the scenario:

\(y=-x+45\\\\\Rightarrow\ x+y=45\)

Now, to find the number of snapdragons by planting 29 daisies, put y=29 in the above equation,

\(29=-x+45\\\\\Rightarrow\ x=45-29=16\)

  • The linear equation \(y = -x + 45\) models the scenario.
  • Solving the linear equation, it is found that Hans will paint 16 snapdragons.

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Since the rate of change is always the same, this question is modeled by a linear equation.

Linear equation:

Has the following format:

\(y = mx + b\)

In which m is the slope and b is the y-intercept.

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  • To find the slope, we have to get two points (x,y), and the slope is given by change in y divided by the change in x.
  • Points: (11,34) and (12,33).
  • Change in y: 33 - 34 = -1
  • Change in x: 12 - 11 = 1.
  • Slope: \(m = -\frac{1}{1} = -1\)

Thus, the equation of the line is:

\(y = -x + b\)

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  • Replacing one of the points, the y-intercept can be found.
  • Point (11,34) means that when \(x = 11, y = 34\). Thus:

\(y = -x + b\)

\(34 = -11 + b\)

\(b = 45\)

Thus:

The equation \(y = -x + 45\) models the scenario.

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29 daisies means that \(y = 29\), thus, we have to find x for which y = 29.

\(y = -x + 45\)

\(29 = -x + 45\)

\(x = 45 - 29 = 16\)

Thus, Hans will plant 16 snapdragons.

A similar problem is given at https://brainly.com/question/24141057

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