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Nata [24]
3 years ago
6

Use technology to determine an appropriate model of the data. (-1,0), (1,-4), (2,-3), (4,5), (5,12)

Mathematics
1 answer:
Vinil7 [7]3 years ago
7 0
By graphing the points, The best mode of the data will be the quadratic function

There is 5 steps to find the quadratic function that models the data.

First step           ⇒ Plot the data pairs (x, y) in a coordinate plane.
                              which are the blue circles in the attached figure

Second step     ⇒ Draw the parabola you think best fits the data.
                             Which is the red function in the attached figure.

Third step         ⇒ Estimate the coordinates of three points on the
                             parabola, which are (-1, 0), (2, -3), and (5, 12).

Fourth step       ⇒ Substitute the coordinates of the points into the model
                            y = ax² + bx + c
                            to obtain a system of three linear equations.

                            a - b + c = 0           ---------(1)
                            4a + 2 b + c = -3    ---------(2)
                            25a + 5 b + c = 12 ---------(3)   

Fifth step   ⇒ Solve the linear system.
                      By using the calculator
                      a = 1 , b = -2 , c = -3

So, the quadratic model for the data is ⇒ y = x² - 2x - 3


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Two numbers are in the ratio 3:5. If one of them is greater than the other by 10,Find the smaller number.​
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Answer:

smaller number = 15

Step-by-step explanation:

Let the two numbers be 5x and 3x respectively.

According to the question —

5x — 3x = 10

2x = 10

x = 5

Thus the smaller number is 3 × 5 = 15

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3 years ago
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A pickup truck traveled a distance of 210 miles in 5 hours. If the pickup truck travels at the same speed, how many miles would
Zinaida [17]
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aleksandr82 [10.1K]

Step-by-step explanation:

Let A be the set of people who speak English.    

B be the set of people who speak French.  

A - B be the set of people who speak English and not French.  

B - A be the set of people who speak French and not English.  

A ∩ B be the set of people who speak both French and English.  

Given

n(A) = 72       n(B) = 43       n(A ∪ B) = 100  

Now, n(A ∩ B) = n(A) + n(B) - n(A ∪ B)  

 = 72 + 43 - 100  

= 72 + 43 - 100  

= 115 - 100  

= 15

Therefore, Number of persons who speak both French and English

= 15  

n(A) = n(A - B) + n(A ∩ B)  

⇒ n(A - B) = n(A) - n(A ∩ B)  

= 72 - 15  

= 57

and n(B - A) = n(B) - n(A ∩ B)  

 = 43 - 15 = 28  

Therefore, Number of people speaking English only = 57  

Number of people speaking French only = 28

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