Answer: 2
Step-by-step explanation:
The factors of 56: 1; 2; 4; 7; 8; 14; 28; 56
The factors of 84: 1; 2; 3; 4; 6; 14; 28; 42; 84
GCF(56; 84) = 28
Step-by-step explanation:
We need to use the binomial theorem/Pascal's triangle here.
(a+b)^5 = (5 choose 0)a^5 + (5 choose 1)a^4*b + (5 choose 2)a^3*b^2 + (5 choose 3)a^2*b^3 + (5 choose 4)a*b^4 + (5 choose 5)b^5.
5 choose 0 = 1
5 choose 1 = 5
5 choose 2 = 10
5 choose 3 = 10
5 choose 4 = 5
5 choose 5 = 1
And 1, 5, 10, 10, 5, 1, is the (5+1) = 6th row of pascal's triangle.
Therefore we get
g^5 + 5g^4*2 + 10g^3*2^2 + 10g^2*2^3 + 5g*2^4 + 2^5
which is
g^4 + 10g^4 + 40g^3 + 80g^2 + 80g + 32
Or, you could do the slow way, by just doing (g+2)(g+2)(g+2)(g+2)(g+2)
The complete question in the attached figure
Let
x-----------------> number of <span>paintbrushes----------- > $0.95 each
y---------------- > number of jar of paint-------------- > $0.99 each
we know that
0.95x+0.99y = </span><span>$4.87
</span><span>
using a graph tool
</span>the solution will be a pair of coordinates that are whole numbers -- > see the attached figure
<span>
the solution is the point (2,3)
x=2---------------------- > </span>number of paintbrushes
y=3---------------------- > number of jar of paint
the answer is
number of paintbrushes=2
number of jar of paint=3<span>
</span>