Busca dos números consecutivos de manera que la diferencia de sus cuadrados sea 19

1 answer:

4 0

The numbers are 9 and 10.

Let x be the first number. Since they are consecutive, this means (x+1) represents the second number.

The square of x is x². The square of (x+1) is
(x+1)²=(x+1)(x+1)=x²+1x+1x+1=x²+2x+1

The difference of these squares would be given by
x²+2x+1 - x²

Setting this equal to 19,
x²+2x+1 - x² = 19

Combining like terms,
2x+1=19

Subtract 1 from each side:
2x+1-1=19-1
2x=18

Divide both sides by 2:
2x/2 = 18/2
x = 9

The first number, x, is 9. This means the second number, x+1, is 9+1=10.

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Find the angle measures. Justify your responses. Given: a||b, m1=71º Find m5, m8

Natalka [10]

Answer:

The measure of angle MNP is

m ∠ MNP = (x - y)/2

Explanation:

The image attached shows the figure corresponding to this question.

The angle MNP, which is also the angle LNP, is formed by the intersection of a secant and a tangent to a circle.

Then, you can use the theorem:

the angle formed by a secant and a tangent to a circle that intersect outside the circle is half the difference of the major arc minus the minor arc.

The major arc formed is identified with the letter x and the minor arc is identified with the letter y. Thus, the measure of the angle MNP is half the difference x - y:

m ∠ MNP = (x - y)/2

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