aragorn44aragorn
Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Determine any data values that are missing from the table, assuming that the data represent a linear function.

a. Missing x:13 Missing y:20
b. Missing x:13 Missing y:19
c. Missing x:11 Missing y:20
d. Missing x:11 Missing y:19​

Determine Any Data Values That Are Missing From The Table Assuming That The Data Represent A Linear Functiona Missing X13 Missing Y20 B Missing X13 Missing Y19 class=

Sagot :

mhanifa

Answer:

  • d. Missing x:11 Missing y:19​

Step-by-step explanation:

It can be determined that the function is:

  • y = 0.5x + 12.5

So missing x is:

  • 18 = 0.5x + 12.5 ⇒ 0.5x = 5.5 ⇒ x = 11

Missing y is:

  • y = 13*0.5 + 12.5 = 19

Missing numbers are:

  • x= 11 and y = 19

Correct choice is d.

absor201

                                           FIRST METHOD

Answer:

  • Missing x = 11
  • Missing y = 19          

Step-by-step explanation:

Given the table

x                                         y

7                                        16

9                                        17

Missing x                          18

13                                        Missing y

From the table, it is clear that y-values are incremented by 1 unit and the x-values are incremented by 2 units.

i.e.

y = 17-16 = 1

y = 18-17 = 1

as 19-18 = 1

Thus,

Thus, the value of Missing y = 19

also the x-values increment by 2.

i.e.

x  = 9-7 = 2

as x = 11 - 9 = 2

Thus, Missing x = 11

Therefore,

  • Missing x = 11
  • Missing y = 19        

                                                2ND METHOD

Given that the table represents a  linear function, so the function is a straight line.

Taking two points

  • (7, 16)
  • (9, 17)

Finding the slope between (7, 16) and (9, 17)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(7,\:16\right),\:\left(x_2,\:y_2\right)=\left(9,\:17\right)[/tex]

[tex]m=\frac{17-16}{9-7}[/tex]

[tex]m=\frac{1}{2}[/tex]

Using the point-slope form to determine the linear equation

[tex]y-y_1=m\left(x-x_1\right)[/tex]

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 1/2 and the point (7, 16)

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-16=\frac{1}{2}\left(x-7\right)[/tex]

Add 16 to both sides

[tex]y-16+16=\frac{1}{2}\left(x-7\right)+16[/tex]

[tex]y=\frac{1}{2}x+\frac{25}{2}[/tex]

Thus, the equation of the linear equation is:

[tex]y=\frac{1}{2}x+\frac{25}{2}[/tex]

Now substituting y = 18 in the equation

[tex]18=\frac{1}{2}x+\frac{25}{2}[/tex]

Switch sides

[tex]\frac{1}{2}x+\frac{25}{2}=18[/tex]

subtract 25/2 from both sides

[tex]\frac{1}{2}x+\frac{25}{2}-\frac{25}{2}=18-\frac{25}{2}[/tex]

[tex]\frac{1}{2}x=\frac{11}{2}[/tex]

[tex]x=11[/tex]

Thus, the value of missing x = 11 when y = 18

Now substituting x = 13 in the equation

[tex]y=\frac{1}{2}\left(13\right)+\frac{25}{2}[/tex]

[tex]y=\frac{13}{2}+\frac{25}{2}[/tex]

[tex]y=\frac{13+25}{2}[/tex]

[tex]y=\frac{38}{2}[/tex]

[tex]y = 19[/tex]

Thus, the value of missing y = 19 when x = 13

Hence, we conclude that:

  • The value of missing x = 11
  • The value of missing y = 19

Hence, option D is true.

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.