Karen has a red ribbon that is 18 feet long and the blue ribbon that is Sophie long she wants to cut both ribbons into pieces that are all the same length and she wants to have no ribbon left when she's done what is the greatest length in feet of a piece of ribbon that she can cut

6feet

Step-by-step explanation:

THIS IS THE COMPLETE QUESTION BELOW:

Karen has a red ribbon that is 18 feet long and a blue ribbon that is 12 feet long. She wants to cut both ribbons into pieces that are all the same length and she wants no ribbon leftover when she is done. What is the greatest length in feet, of each piece of ribbon that she can cut?

Here the question is only talking about the GREATEST COMMON FACTOR that exist between 12 and 18. Since we are told that She wants to cut both ribbons into pieces that are all the "THE SAME LENGHTH"

For the ribbon that of 18 feet long, it can only be cut into 3pieces of equal Lenght i.e(18/6)= 3 pieces

For the ribbon that of 12 feet long, it can only be cut into 2pieces of equal Lenght i.e(12/6)= 3 pieces

Therefore the greatest common factor which divide both 12 and 8 is 6. which means 6 is the greatest length in feet, of each piece of ribbon that she can cut

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have

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