In parallelogram abcd , diagonals ac⎯⎯⎯⎯⎯ and bd⎯⎯⎯⎯⎯ intersect at point e, ae=x2−16 , and ce=6x . what is ac ?

Step-by-step explanation:

We are given a parallelogram ABCD with diagonals AC and BD intersect at point E.

, and CE=6x .

Note: The diagonals of a parallelogram intersects at mid-point.

Therefore, AE = EC.

Plugging expressions for AE and EC, we get

Subtracting 6x from both sides, we get

Factoriong quadratic by product sum rule.

We need to find the factors of -16 that add upto -6.

-16 has factors -8 and +2 that add upto -6.

Therefore, factor of quadratic is (x-8)(x+2)=0

Setting each factor equal to 0 and solve for x.

x-8=0  => x=8

x+2=0  => x=-2.

We can't take x=-2 as it's a negative number.

Therefore, plugging x=8 in EC =6x, we get

EC = 6(8) = 48.

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8