I would really appreciate anyone who can answer this, Thanks!
1 answer:
You might be interested in
Answer:
Step-by-step explanation:
24 + 4y = 12y
- 4y - 4y
__________
I am joyous to assist you anytime.
Answer:
The students can group themselves in 360360 ways
Step-by-step explanation:
For this exercise we need to use the following equation:
This equation give us the number of assignation of n elements in k cell, where n1, n2, ..nk are the element that are in every cell
In this case we have 15 student that need to be assign in three vehicles with an specific capacity. This vehicles would be the equivalent to cells, so we can write the equation as:
Because the first vehicle have 7 seating, the second vehicle have 5 seating and the third vehicle have 3 seating.
Solving the equation we get 360360 ways to organized 15 students in three vehicles with capacity of 7, 5 and 3 seating.
Part A:
Given that the <span>straight line p(x) joins the ordered pairs (0, 2) and (1, -5), thus the equation of the line joining ordered pairs (0, 2) and (1, -5) is given by
Thus, p(x) = -7x + 2
</span>Given that the <span>straight line f(x) joins the ordered pairs (4, 1) and (2, -3), thus the equation of the line joining ordered pairs (4, 1) and (2, -3) is given by
Thus, f(x) = 2x - 7
</span>
The solution to the pair of equations represented by p(x) and f(x) is given by
p(x) = f(x)
⇒ -7x + 2 = 2x - 7
⇒ -7x - 2x = -7 - 2
⇒ -9x = -9
⇒ x = -9 / -9 = 1
Substituting for x into p(x), we have
p(1) = -7(1) + 2 = -7 + 2 = -5
Therefore, the solution to the pair of equations represented by p(x) and f(x) is (1, -5)
Part B:
From part A, we have that f(x) = 2x - 7
when x = -8
f(-8) = 2(-8) - 7 = -23
Thus, (-8, -23) is a solution to f(x).
When x = -10
f(-10) = 2(-10) - 7 = -27
Thus, (-10, -27) is a solution to f(x).
Therefore, two solutions of f(x) are (-8, -23) and (-10, -27).
Part C:
From part A, we have that p(x) = -7x + 2, given that
From the graphs of p(x) and g(x), we can see that the two graphs intersected at the point (0, 2).
Therefore, the solution to the equation p(x) = g(x) is (0, 2).
Given that the <span>straight line p(x) joins the ordered pairs (0, 2) and (1, -5), thus the equation of the line joining ordered pairs (0, 2) and (1, -5) is given by
Thus, p(x) = -7x + 2
</span>Given that the <span>straight line f(x) joins the ordered pairs (4, 1) and (2, -3), thus the equation of the line joining ordered pairs (4, 1) and (2, -3) is given by
Thus, f(x) = 2x - 7
</span>
The solution to the pair of equations represented by p(x) and f(x) is given by
p(x) = f(x)
⇒ -7x + 2 = 2x - 7
⇒ -7x - 2x = -7 - 2
⇒ -9x = -9
⇒ x = -9 / -9 = 1
Substituting for x into p(x), we have
p(1) = -7(1) + 2 = -7 + 2 = -5
Therefore, the solution to the pair of equations represented by p(x) and f(x) is (1, -5)
Part B:
From part A, we have that f(x) = 2x - 7
when x = -8
f(-8) = 2(-8) - 7 = -23
Thus, (-8, -23) is a solution to f(x).
When x = -10
f(-10) = 2(-10) - 7 = -27
Thus, (-10, -27) is a solution to f(x).
Therefore, two solutions of f(x) are (-8, -23) and (-10, -27).
Part C:
From part A, we have that p(x) = -7x + 2, given that
From the graphs of p(x) and g(x), we can see that the two graphs intersected at the point (0, 2).
Therefore, the solution to the equation p(x) = g(x) is (0, 2).