A47-foot-long piece of pipe is to be cut into three pieces. the second piece is three times as long as the first piece, and the third piece is two feet more than five times the length of the first piece. what is the length of the longest piece? 5 feet 15 feet 27 feet 32 feet

The lenght of the longest piece is 27 ft.

Step-by-step explanation:

Hi, to solve this problem we have to write 3 equations, and combine them to calculate the value of the variables.

The pipe is 47 ft long and is going to be cut into three pieces (a,b, and c).

So:

1) a + b + c = 47

Then, the second piece is three times as long as the first piece.

2) b =3a

And finally, the third piece is two feet more than five times the length of the first piece.

3) c = 5a + 2

Now that we have the three equations, we combine equations 2) and 3) with 1).

1) a + 3a + 5a +2 = 47

Solving:

4a + 5a = 47 -2

9a =45

a = 45/9

a = 5 ft

With the value of "a", we can calculate the value of "b" and "c".

2) b= 3a

    b = 3 x 5 = 15 ft

3) c = 5a + 2

  c=     5x5 +2

   c = 25 +2

   c = 27 ft

In conclusion, the lenght of the longest piece is 27 ft.

a = 5ft  ; b= 15 ft ; c= 27ft

Feel free to ask for more if it´s necessary or if you did not understand something.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: