The sum of three integers is 189. the first integer is 28 less than the second. the second integer is 21 less than the sum of the first and third integer. find the three integers

The first integer is 56

The second integer is 84

The third integer is 49

Step-by-step explanation:

Define the variables

Let

x ----> the first integer

y ----> the second integer

z ----> the third integer

we know that

----> equation A

----> ----> equation B

----> equation C

Equate equations B and C

subtract x both sides

Adds 21 both sides

substitute the value of z in equation A

-----> equation D

Solve the system of equations B and D

----> equation B

-----> equation D

substitute equation B in equation D and solve for x

Find the value of y

----->

therefore

The first integer is 56

The second integer is 84

The third integer is 49

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answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.