Answer:
((2 x + 1) (4 x^2 - 2 x + 1))/8
Step-by-step explanation:
Factor the following:
x^3 + 1/8
Put each term in x^3 + 1/8 over the common denominator 8: x^3 + 1/8 = (8 x^3)/8 + 1/8:
(8 x^3)/8 + 1/8
(8 x^3)/8 + 1/8 = (8 x^3 + 1)/8:
(8 x^3 + 1)/8
8 x^3 + 1 = (2 x)^3 + 1^3:
((2 x)^3 + 1^3)/8
Factor the sum of two cubes. (2 x)^3 + 1^3 = (2 x + 1) ((2 x)^2 - 2 x + 1^2):
((2 x + 1) ((2 x)^2 - 2 x + 1^2))/8
1^2 = 1:
((2 x + 1) ((2 x)^2 - 2 x + 1))/8
Multiply each exponent in 2 x by 2:
((2 x + 1) (2^2 x^2 - 2 x + 1))/8
2^2 = 4:
Answer: ((2 x + 1) (4 x^2 - 2 x + 1))/8
Equation 1. N+D=500
equation 2 5N+10D=3000
This is for equation 1
N=500-d
Substitute into equations 2 and solve for D
5N+10D=3000
5(500-D)+10D=3000
2500-5D+10D=3000
5D=500
D=100
Lets go back the equation 1
N=500-D
N=500-100
N=400
there are 400 Nickles and 100 Dimes
Harry can rake the leaves in the yard 8 hours faster than his little brother Jimmy can.
<span>If they join to work together they can complete the job in 3 hours. </span>
<span>1/x + 1/(x - 8) = 1/3 </span>
<span>3(x - 8) + 3x = x(x - 8) </span>
<span>x^2 - 14x + 24 = 0 </span>
<span>(x - 12)(x - 2) = 0 </span>
<span>Solutions: </span>
<span>x = 2 </span>
<span>x = 12 </span>
<span>Jimmy can complete the job on his own in 12 hours.</span>
Answer:
Step-by-step explanation:
By geometric mean property:
By Pythagoras Theorem:
