Based on the pattern of the drawings, which conjecture

Mathematics

2 answers:

anzhelika [568]3 years ago

8 0

Answer:

The most reasonable answer would likely be the first.

"When a pair of parallel lines is intersected by a third line, the alternate exterior angles are congruent."

Step-by-step explanation:

navik [9.2K]3 years ago

5 0

Answer:

<h2>When a pair of parallel lines is intersected by a third line, the alternate exterior angles are congruent.</h2>

Step-by-step explanation:

This is the reasonable conjecture, because it's what actually happens. To get the answer we must remember what are alternate exterior angles.

Alternate exterior angles are formed by the intersection of a pair of parallels and a lines that intersect them like the figure shows. From this intersection result 4 pair of angles that are related: alternate interior angles, alternate exterior angles, corresponding angles and interior angles on the same side of the transversal.

So, alternate exterior angles are those outside the parallels (that's why they are called exterior), and they are placed in different sides of the intersecting line, one on the left, one on the right.

Therefore, as you can see in the image, in each intersection, there are two angles outside the parallels and in different sides of the intersecting line, so they are alternate exterior angles, and they are the same, because the number shows it.

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Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa

Nataly_w [17]

Answer:

The first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

coefficient of $x^{2}$ in the expansion of $(2+x - x^{2})^{6}$ = (240 - 192) = 48

Step-by-step explanation:

$(2+x)^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})$

= $6_{C_{0}} \times x^{0} \times 2^{6} + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4}$ + terms involving higher powers of x