In parallelogram abcd , be=7x−2 and de=x^2−10.segment ac intersects segment bd at point e. what is bd ? enter your answer in the box.

Length of BD = 108 units

Step-by-step explanation:

Given: In parallelogram ABCD , BE = 7x-2 and DE = .

Segment AC intersects segment BD at point E.

Properties of parallelograms:-

Opposite sides are congruent (AB=CD)Opposite angels are congruent (D=B). Also, consecutive angles are supplementary (A + D = 180°).Diagonals of a parallelogram bisect each other.Every diagonal of a parallelogram separates it into two congruent.

The diagonal BD;

BD = BE + ED

since, by properties of parallelogram;

BE = ED                     ......[1]

Substitute the given values of BE and DE in [1] to solve for x;

or

(x-8)(x+1) = 0

equate each factor equals to 0 we get;

x = 8 and x = -1

Since sides are always in positive,

⇒x =8

Then;

BE = 7x -2 = 7(8) -2 = 56-2 = 54 units.

To find the Length of BD:

As we know;

BD = BE + ED = BE + BE = 2BE              [Since, BE = ED]

BD = units

Therefore, the length of BD is 108 units.

What are the options for plato

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for