We can factor this by using grouping. Take the leading coefficient and multiply it by the constant. In this case we get 5*-7 = -35.
Now we need 2 numbers that add to 2 and multiply to be -35. The numbers are -5 and 7.
So split the 2r into these two terms and group.
(5r^2 - 5r) + (7r - 7)
Factor both groups.
5r(r-1) + 7(r-1)
The factors of (r-1) can be added together to get the answer.
(r-1)(5r+7)
Answer:
Widgets should be sold by $38.88 to maximize the profit.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:
It's vertex is the point 
In which
Where
If a<0, the vertex is a maximum point, that is, the maximum value happens at 
, and it's value is 
.
In this question:
The profit is given by:
Which is a quadratic function with 
The maximum profit happens at the x of the vertex. Thus
Widgets should be sold by $38.88 to maximize the profit.
Answer:
1. Total Trip Distance = 190 kilometers
2. To complete the trip, 38 more kilometers left
Step-by-step explanation:
1.
Let total trip be x kilometers.
So we can say
<em>"152 is 
of total" --- this into equation is:</em>
Total trip is 190 km.
2.
Since already driven 152, to complete 190, you have to drive 
kilometers more.
So, 38 more kilometers to complete the trip.
In mathematics, number sequencing of the same pattern are called progression. There are three types of progression: arithmetic, harmonic and geometric. The pattern in arithmetic is called common difference, while the pattern in geometric is called common ratio. Harmonic progression is just the reciprocal of the arithmetic sequence.
The common ratio is denoted as r. For values of r<1, the sum of the infinite series is equal to
S∞ = A₁/(1-r), where A1 is the first term of the sequence. Substituting A₁=65 and r=1/6:
S∞ = A₁/(1-r) = 65/(1-1/6)
S∞ = 78
Answer:
6 and 12 have the greatest common factor of 2
