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Use expressions for odd integers to confirm the conjecture that the product for two odd integers is an odd integer.

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k, n - integers

2k+1 - an odd integer

2n+1 - another odd integer

The product of them:

(2k + 1)(2n + 1) =

= 4kn + 2k + 2n + 1 =

= 2(2kn + k + n) + 1

The product of integers (2kn) is integer

and the sum of them (2kn+k+n) also is integer

So (2k + 1)(2n + 1) = 2(2kn + k + n) + 1 is an odd integer

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LK is tangent to circle J at point K. Circle J is shown. Line segment J K is a radius. Line segment K L is a tangent that inters

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Answer:

$(B)r=\dfrac{85}{12}$

Step-by-step explanation:

Given a circle centre J

Let the radius of the circle =r

LK is tangent to circle J at point K

From the diagram attached

LX=6
Radius, XJ=JK=r
LK=11

Theorem: The angle between a tangent and a radius is 90 degrees.

By the theorem above, Triangle JLK forms a right triangle with LJ as the hypotenuse.

Using Pythagoras Theorem:

$(6+r)^2=r^2+11^2\\(6+r)(6+r)=r^2+121\\36+6r+6r+r^2=r^2+121\\12r=121-36\\12r=85\\r=\dfrac{85}{12}$

The length of the radius, $r=\dfrac{85}{12}$

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The same amount of principal is invested in different accounts earning the same interest rate. Which of the following

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Suppose that the amount of algae in a pond doubles every 4 hours. If the pond initially contains 90 pounds of algae, how much al

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