The scatterplot shows the distance (in feet) that a person was from a motion sensor during an experiment in math class. use the labeled points to create a linear model. about what distance in feet (y) would a person be 8 seconds after the experiment begins?

a.) 21ft
b.) 27ft
c.) 30ft
d.) 57ft

B.) 27ft

Step-by-step explanation:

The labeled points given: (5,18) and (1.5, 7.5)

Slope = (18 - 7.5)/(5-1.5) = 10.5 / 3.5 = 3

A linear model:

y - 18 = 3(x - 5)

y - 18 = 3x - 15

y = 3x + 3

If x = 8 seconds then the distance in feet (y) would be: (plug in x = 8 into the equation y = 3x + 3)

y = 3(8) + 3

y = 24 + 3

y = 27 ft

B.) 27ft

answer: c is correct, a regular pentagon

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places