Find two numbers a and b whose sum a+b is -4 and whose difference a−b is -4.

1 answer:

7 0

The answer is a = -4 and b = 0.

We can solve this by looking at a system of equations using what was given

a + b = -4
a - b = -4

Then add then two equations together.

2a = -8 ---> then divide by 2 for your a value
a = -4

You can then put that into the equation and solve for b.

-4 + b = -4 ---> add 4 to both sides
b = 0

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In △ABC, AD and BE are the angle bisectors of ∠A and ∠B and DE ║ AB . Find the length of DE if perimeter of ABDE is 30 cm and AB

-BARSIC- [3]

Answer:

DE = 6 cm

Step-by-step explanation:

Let DE = x cm.

Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)

As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.

Therefore, from (1) We get , m∠EAD = m∠ADE and m∠EBD = m∠BED.

So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.

So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then