A textbook is opened and the product of the page numbers of the pages is 6162. What are the numbers of the pages?
1 answer:
Answer:
The two page numbers are 78 and 79.
Step-by-step explanation:
Let's take the page numbers are x and x + 1 .
The produce of the page numbers is 6162
so, x(x + 1) = 6162
Here we have to use the quadratic formula to solve for x.
The quadratic formula, x =
Here a =1, b = 1 and c = -6162
Plugging in the value of a, b and c in the above formula, we get
x = [-1 ± 157] ÷ 2
Let's take the positive value alone since the page number cannot be negative.
x = [-1 + 157] ÷2
x = 78
The next page number x + 1 = 78 + 1 = 79
Therefore, the two page numbers are 78 and 79.
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Given:
M=(x1, y1)=(-2,-1),
N=(x2, y2)=(3,1),
M'=(x3, y3)= (0,2),
N'=(x4, y4)=(5, 4).
We can prove MN and M'N' have the same length by proving that the points form the vertices of a parallelogram.
For a parallelogram, opposite sides are equal
If we prove that the quadrilateral MNN'M' forms a parallellogram, then MN and M'N' will be the oppposite sides. So, we can prove that MN=M'N'.
To prove MNN'M' is a parallelogram, we have to first prove that two pairs of opposite sides are parallel,
Slope of MN= Slope of M'N'.
Slope of MM'=NN'.
Hence, slope of MN=Slope of M'N' and therefore, MN parallel to M'N'
Hence, slope of MM'=Slope of NN' nd therefore, MM' parallel to NN'.
Since both pairs of opposite sides of MNN'M' are parallel, MM'N'N is a parallelogram.
Since the opposite sides are of equal length in a parallelogram, it is proved that segments MN and M'N' have the same length.