A38-inch piece of steel is cut into 3 pieces so that the second piece is twice as long as the first, and the third piece is three inches more than four times the length of the first piece. what is the length of the second piece?

66/7

Step-by-step explanation:

There are three pieces. Lets call the 1st piece A, the 2nd B and the 3rd C. As all of them sum 38:

A + B + C = 36 (eq 1)

As the second is twice as long as the first:

2A = B  (eq. 2) the first multiplied by 2 is equal to the second

As  the third is three inches more than the length of four times the 1st:

C = 3 + 4A (eq. 3) The 3rd is equal to four times the first plus 3 inches

Now we can replace eqs. 2 and 3 in eq. 1:

A + B + C = A + 2A + 3 + 4A = 36

7A + 3 = 36

Subtracting 3 in both sides:

7A = 33

Dividing by 7:

A = 33/7

Now, we can replace A in the 2nd eq. to get B:

2A = B

2 * (33/7) = B

66/ 7 = B

We can verify the results by finding C:

C = 3 + 4A = 3 + 4(33/7) = 3 + 132/7 = 21/7 + 132/7 = 153/7

Then:

A+B+C = 33/7 + 66/7 + 153/7 = 252/7 = 36 --> Verifies!!

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

a. 32 degrees

step-by-step explanation:

here we have to use the rule.

m∠e = 1/2 (major arc - minor arc)

m∠e = 1/2 (212 - 148)

m∠e = 1/2 (64)

m∠e = 32 degrees

answer: a. 32 degrees

you