The greatest common factor (GCF) of the expressions x² and x^9 is x². To determine this, we analyze each term: Factors of x² are x * x, while factors of x^9 are x multiplied by itself nine times. The common factors in both are x * x, which gives us the GCF as x².
For the first inequality, the solution is derived as follows:
4p > -8...... by subtracting 1
p > -2....... when divided by 4
This solution is represented on a graph as an open dot at -2, with the shading extending rightwards.
Since no inequality symbols incorporate "or equal to", all depicted dots remain open. The correct option is the first one:
a number line marked with open circles at -2 and 5, shaded in between.
2000 + 1500g ≤ 15000
1500g ≤ 15000 - 2000
1500g ≤ 13000
g ≤ 13000/1500
g ≤ 8 2/3
Thus, the crane is capable of safely lifting no more than 8 2/3 cubic meters of gravel.
