We know that
<span>When two chords intersect each other inside a circle, the products of their segments are equal (</span>Intersecting Chord Theorem)<span>
</span>so
in this problem
AE*EB=DE*EF----> EB=DE*EF/AE
AE=4 in
DE=12 in
EF=8 in
EB=?
EB=DE*EF/AE-----> EB=12*8/4----> EB=24 in
the answer is
EB=24 in
The common ratio of the given geometric sequence is the number that is multiplied to the first term in order to get the second term. Consequently, this is also the number multiplied to the second term to get the third term. This cycle goes on and on until a certain term is acquired. In this item, the common ratio r is,
r = t⁵/t⁸ = t²/t⁵
The answer, r = t⁻³.
The next three terms are,
n₄ = (t²)(t⁻³) = t⁻¹
n₅ = (t⁻¹)(t⁻³) = t⁻⁴
n₆ = (t⁻⁴)(t⁻³) = t⁻⁷
The answers for the next three terms are as reflected above as n₄, n₅, and n₆, respectively.
The factors include 1,2,4,5,8,10,20,40.
To solve problems like this you can either graph or solve mathematically. To do the ladder we need to solve for one variable at a time. So lets cancel one variable out.
Multiply equation 1 by 2
This will give 4x-2y=14
Now we can get rid of y by subtracting 2 from 1
This will give x=9
Plug back in to either equation, i will use equation 2
3(9)-2y=5 simplify
-2y=-22 solve
Y=11
I know of two ways to solve quadratic equations. The first is through factoring. Let us take the example (x^2)+2x+1=0. We can factor this equation out and the factors would be (x+1)(x+1)=0. To solve for the roots, we equate each factor to 0, that is
x+1=0; x+1=0
In this case, the factors are the same so the root of the equation is
x=1.
The other way is to use the quadratic formula. The quadratic formula is given as [-b(+-)sqrt(b^2-4ac)]/2a where, using our sample equation above, a=1, b=2 and c=1. Substitute these to the formula, and you will get the same answer as the method above.
