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Veseljchak [2.6K]
2 years ago
5

Kim and Danielle each improved their yards by planting hostas and ivy. They bought their supplies from the same store. Kim spent

$62 on 5 hostas and 4 pots of ivy. Danielle spent $144 on 8 hostas and 12 pots of ivy. What is the cost of one hosta?
Mathematics
1 answer:
svetlana [45]2 years ago
8 0

Answer:

The cost of one hosta is $6

Step-by-step explanation:

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, the variables are:

  • x = price of a hosta .
  • y = price of a pot of ivy.

If Kim spent $62 on 5 hostas and 4 pots of ivy, t his is represented by the equation: 5*x +4*y= 62

If Danielle spent $144 on 8 hostas and 12 pots of ivy, t his is represented by the equation: 8*x +12*y=144

So, the system of equations to solve is:

\left \{ {{5*x+4*y=62} \atop {8*x+12*y=144}} \right.

One way to solve a system of equations is through the substitution method, which consists of solving or isolating one of the unknowns (for example, x) and substituting its expression in the other equation. In this way, you obtain an equation of the first degree with the other unknown, and. Once solved, you calculate the value of x by substituting the already known value of y.

Isolating y from the first equation:

y=\frac{62-5*x}{4}

and replacing this expression in the second equation you get:

8*x +12*\frac{62-5*x}{4}=144

Solving:

8*x +\frac{12}{4}*(62-5*x)=144

8*x + 3*(62-5*x)=144

8*x + 3*62 - 3*5*x=144

8*x + 186 - 15*x=144

8*x  - 15*x=144 -186

(-7)*x= -42

x= (-42)÷ (-7)

x= 6

<u><em>The cost of one hosta is $6</em></u>

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The quadratic regression equation that best fits the data set is y = 32.86x² - 379.14x  + 1369.14

<h3>The data points </h3>

The following table of values represents the data points that would be used to solve this question:

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Where:

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<h3>The function of the dataset</h3>

The table of values illustrates a quadratic function.

The function would be calculated using a graphing calculator

From the graphing calculator, we have:

a = 32.86; b = -379.14 and c = 1369.14

A quadratic regression equation is represented as:

y = ax² + bx + c

So, we have:

y = 32.86x² - 379.14x  + 1369.14

Hence, the quadratic regression equation that best fits the data set is y = 32.86x² - 379.14x  + 1369.14

<h3>Why the function type was chosen?</h3>

From the table of values in (a), we can see that as x increases; the value of y decreases and then increases after it reaches a minimum.

This illustrates the behavior of a quadratic regression function

See attachment for the scatter plot

Read more about quadratic regression equation at:

brainly.com/question/14786188

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5 0
2 years ago
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LekaFEV [45]

Answer:

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Step-by-step explanation:

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2 years ago
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5 0
2 years ago
Replace * with a monomial in such a way, that the trinomial becomes a perfect square. *+12x+1
Mrrafil [7]

Answer: * = 36x^2

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Step-by-step explanation:

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2 years ago
A bill from a plumber was $306 The plumber charged $150 for parts and $52 per hour for labor. How long did ths plumber work at h
ludmilkaskok [199]
We can make an equation from this.
Our intial value is 150 for parts, and he works for 52 dollars an hour.
We can define <em /><em>h</em> for hours and <em /><em>c</em> for total cost.
Therefore, we have:
c = 150 + 52h.
We can set this equal to 306 dollars, as that's the given total cost:
306 = 150 + 52h
Subtract 150 from both sides:
52h = 156
Divide both sides by 2:
h = 3
He worked 3 hours.
hope this helped!

6 0
3 years ago
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