If the weight of a package is multiplied by 4/5 the result is 30 pounds. Find the weight of the package
1 answer:
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First, we are going to find the vertex of our quadratic. Remember that to find the vertex 
of a quadratic equation of the form 
, we use the vertex formula 
, and then, we evaluate our equation at 
to find 
.
We now from our quadratic that
and 
, so lets use our formula:
Now we can evaluate our quadratic at 8 to find:
So the vertex of our function is (8,-72)
Next, we are going to use the vertex to rewrite our quadratic equation:
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.
We can conclude that:
The rewritten equation is
The x-coordinate of the minimum is 8
We now from our quadratic that
Now we can evaluate our quadratic at 8 to find
So the vertex of our function is (8,-72)
Next, we are going to use the vertex to rewrite our quadratic equation:
The x-coordinate of the minimum will be the x-coordinate of the vertex; in other words: 8.
We can conclude that:
The rewritten equation is
The x-coordinate of the minimum is 8
Answer:
10.67
Explanation:
The given series is a geometric series:
8 , 2 , 0.5 , ...... etc
The general formula of the geometric sequence is:
a1 , a1*r , a1*r² , ......
Comparing the general form with the given, we would find that:
a1 = 8
a1 * r = 2
Therefore:
8*r = 2
r = 2/8 = 0.25
We can double check using another term as follows:
a1 = 8
a1*r² = 0.5
8r² = 0.5
r² = 0.5/8 = 0.0625
r = √0.0625 = 0.25
Now, we will get the sum of the sequence as follows:
S =
= 
= 32/3 = 10.67
Hope this helps :)
10.67
Explanation:
The given series is a geometric series:
8 , 2 , 0.5 , ...... etc
The general formula of the geometric sequence is:
a1 , a1*r , a1*r² , ......
Comparing the general form with the given, we would find that:
a1 = 8
a1 * r = 2
Therefore:
8*r = 2
r = 2/8 = 0.25
We can double check using another term as follows:
a1 = 8
a1*r² = 0.5
8r² = 0.5
r² = 0.5/8 = 0.0625
r = √0.0625 = 0.25
Now, we will get the sum of the sequence as follows:
S =
Hope this helps :)