Answer:
3(3x + 5)
Step-by-step explanation:
x + 8x + 15 Combine liked terms
9x + 15
GCF: 3
3(3x +5) Factor
Let 
represent the depth of the miner and equipments elevator, respectively. We know that equipment elevator descends with a velocity of 
feet per second, and the miners one descends with a velocity of 
feet per second.
If we start counting time (
) when the equipment elevator begins to descend, after 
seconds its depth will be
On the other hand, the miner elevator follows the same rule, but we have to use its velocity, and remember that it starts with a delay of thirty seconds:
Now, we have to wait the 30 seconds of delay, and then another 14 seconds. This means that we want to know the positions of both elevators when 
. Let's plug this value into the two equations:
So, the equipment elevator is 176 feet deep, and the miner elevator is 210 feet deep, and thus this is the deeper one.
Answer:
Let's suppose that each person works at an hourly rate R.
Then if 4 people working 8 hours per day, a total of 15 days to complete the task, we can write this as:
4*R*(15*8 hours) = 1 task.
Whit this we can find the value of R.
R = 1 task/(4*15*8 h) = (1/480) task/hour.
a) Now suppose that we have 5 workers, and each one of them works 6 hours per day for a total of D days to complete the task, then we have the equation:
5*( (1/480) task/hour)*(D*6 hours) = 1 task.
We only need to isolate D, that is the number of days that will take the 5 workers to complete the task:
D = (1 task)/(5*6h*1/480 task/hour) = (1 task)/(30/480 taks) = 480/30 = 16
D = 16
Then the 5 workers working 6 hours per day, need 16 days to complete the job.
b) The assumption is that all workers work at the same rate R. If this was not the case (and each one worked at a different rate) we couldn't find the rate at which each worker completes the task (because we had not enough information), and then we would be incapable of completing the question.
Answer:
a = 4 cm
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
a² + 3² = 5²
a² + 9 = 25 ( subtract 9 from both sides )
a² = 16 ( take the square root of both sides )
a = 
= 4
Given:
The quadratic equation is
To find:
The vertex of the given quadratic equation.
Solution:
If a quadratic function is 
, then
We have,
It can be written as
...(i)
Here, 
.
Putting 
in (i), we get
On further simplification, we get
So, the vertex of the given quadratic equation is 
.
Therefore, the correct option is A.
