Answer:
a) P = 362880 ways
b) P = 2880 ways
Step-by-step explanation:
a) We have four boys and five girls, they are going to sit together in a row of 9 theater seats, without restrictions
We have a permutation of 9 elements
P = 9!
P = 9*8*7*6*5*4*3*2*1
P = 362880 ways
b) Boys must seat together, we have two groups of people
4 boys they can seat in 4! different ways
P₁ = 4!
P₁ = 4*3*2*1
P₁ = 24
And girls can seat in 5! dfferent ways
P₂ = 5!
P₂ = 5*4*3*2*1
P₂ = 120
To get total ways in the above mentioned condition, we have to multiply P₁*P₂
P = 24*120
P = 2880 ways
This is the product of the square of a binomial expression. Therefore, it will have two factors.
Square of a binomial: a² + 2ab + b² = (a+b)²
The process:
9x² + 24x + 16
= (3x)² +2(3x)(4) + (4)²
= (3x + 4)² or (3x+4)(3x+4)
I hope this helps :)
The solution to the systems of equations is (7, 3)
Given the systems of equations expressed as:
-x + 4y = 5 ....................1
x - 5y = -2 ...................... 2
Add both equations to have:
-x+x + 4y - 5y = 5 - 2
4y-5y = -3
-y = -3
y = 3
Substitute y = 3 into equation 1:
-x + 4(3) = 5
-x + 12 = 5
-x = 5 - 12
-x = -7
x = 7
Hence the solution to the systems of equations is (7, 3)
Learn more on simultaneous equations here: brainly.com/question/148035
The approximate solution to the given system of equations, considering the graph, is given as follows:
D. 
.
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
On a graph, the solution of a system of equations is given by the intersection between the curves. In this graph, the intersection of the two curves happen close to x = -3.25, y = 2.5, hence the solution is approximated by:
D.
More can be learned about a system of equations at brainly.com/question/24342899
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