C=chicken
p=pigs
c+p=13~p=13-c (plug in)
2c+4p=40
2c+4(13-c)=40
2c+52-4c=40
-2c=-12
c=6
6+p=13
p=7
6 chickens
7 pigs
<u>Answer:</u>
He will order 72 pairs of high tops
<u>Explanation:</u>
Given the store owner sells two pairs of running shoes for each pair of high tops
For every pair of high tops, he sells 2 pairs of running shoes
1 high top = 2 running shoes
He has planned to order 144 pairs of shoes
Therefore, 144 pair of running shoes = 144/2 = 72 pairs of high tops
Therefore, he will order 72 pairs of high tops
By the Pythagorean theorem,
Answer:
Solutions are 2, -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
or 2, -1 + 1.58 i and -1 - 1.58i
(where the last 2 are equal to nearest hundredth).
Step-by-step explanation:
The real solution is x = 2:-
x^3 - 8 = 0
x^3 = 8
x = cube root of 8 = 2
Note that a cubic equation must have a total of 3 roots ( real and complex in this case). We can find the 2 complex roots by using the following identity:-
a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Here a = x and b = 2 so we have
(x - 2)(x^2 + 2x + 4) = 0
To find the complex roots we solve x^2 + 2x + 4 = 0:-
Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2
= -1 +/- (sqrt( -10)) / 2
= -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
