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3 years ago

Complete the square to make a perfect square trinomial. Then, write the result as a binomial squared. n^2+5/2n

Mathematics

1 answer:

Sergeeva-Olga [200]3 years ago

5 0

Answer: $\bigg(n+\dfrac{5}{4}\bigg)^2$

Step-by-step explanation:

$n^2+\dfrac{5}{2}n+\underline{\qquad}\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{2\cdot 2}\bigg)^2\\\\\\n^2+\dfrac{5}{2}n+\bigg(\dfrac{5}{4}\bigg)^2\\\\\\=\bigg(n+\dfrac{5}{4}\bigg)^2$

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ruslelena [56]

Let's try to render the first part of the proof a bit more legibly.

Point F is a midpoint of Line segment AB

Point E is a midpoint of Line segment AC

Draw Line segment BE

Draw Line segment FC by Construction

Point G is the point of intersection between Line segment BE and Line segment FC Intersecting Lines Postulate

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Point D is the point of intersection between Line segment AG and Line segment BC Intersecting Lines Postulate

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OK, now we continue. We need to prove some parallel lines; statement 4 lets us do so.

IV Line segment FG is parallel to line segment BH and Line segment GE is parallel to line segment HC -------- Midsegment Theorem

Now that we've shown some segments parallel we extend that to collinear segments.

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We have enough parallel lines to prove a parallelogram

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Now we draw conclusions from that.

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3 years ago

Solve for x.......................

AURORKA [14]

Answer:

D) x = 40.5

Step-by-step explanation:

When parallel lines create a smaller triangle inside a larger triangle, the triangles are similar. Triangle similarity means that side lengths are proportional, meaning to find x we must use dimensions of the smaller triangle to create a proportion.

The left side of the larger triangle is 12 + 15, so it is 27.

The left side of the smaller triangle is 12.

So, part of the proportion will be $\frac{27}{12}$