Answer:
21
Step-by-step explanation:
We have to create an identity
3x + 21 = 3x + k
if we substitute k with 21 we have
3x + 21 = 3x + 21
that is an identity so it’s true for every value of x
Answer:
375000 ft^2
Step-by-step explanation:
From the statement that we have that it would be 1 time the length and 2 times the width because one side is not necessary and also we must take into account that it would be divided by 3 equal enclosures therefore we will use 1000 feet (3000/3) so Therefore, the perimeter would be equal to:
1000 = l + 2 * w
we solve for w:
l = 1000 - 2 * w
Also the area is equal to:
A = w * l
replacing:
A = w * (1000 - 2 * w)
A = 1000 * w - 2 * w ^ 2
We derive:
A '= 1000 - 4 * w
Let's equal 0:
1000 - 4 * w = 0
w = 1000/4
w = 250
replacing and we calculate l:
l = 1000 - 2 * 250
l = 500
A = 250 * 500
A = 15,000 ft ^ 2
Which means that for each subdivision the maximum area would be 125000 square feet and the total would be:
125000 * 3 = 375000 ft ^ 2
For this you need to expand the brackets first:
3(2x+5)-4(2x-7) = 6x+15-8x-28
And then now you need to add and simplify:
6x+15-8x-28 —> 6x-8x= -2x
15-28= -13
So that leaves
-2x - 13
Answer:
yes
Step-by-step explanation:
yes of course.
This is a combination problem.
Given:
12 students
3 groups consisting of 4 students.
Mark can't be in the first group.
The combination formula that I used is: n! / r!(n-r)!
where: n = number of choices ; r = number of people to be chosen.
This is the formula I used because the order is not important and repetition is not allowed.
Since Mark can't be considered in the first group, the value of n would be 11 instead of 12. value of r is 4.
numerator: n! = 11! = 39,916,800
denominator: r!(n-r)! = 4!(11-4)! = 4!*7! = 120,960
Combination = 39,916,800 / 120,960 = 330
There are 330 ways that the instructor can choose 4 students for the first group
