A farmer wants to fence a rectangular habitat for goats. The length (y) of the habitat has to be at least 80 feet. The farmer currently has 310 feet of fencing available to use on the habitat. The system of inequalities below models this problem situation, where x represents the width of the habitat (in feet) and y represents the length of the habitat (in feet). y≥80
2x+2y≤310
Which of the following is a true statement?
a. If the farmer makes a rectangular habitat with a length of 60 feet, the width needs to be 80 feet.
b. The farmer can make a habitat that is 75 feet long and 60 feet wide.
c. The farmer does not have enough fencing to enclose a rectangular habitat that is 80 feet long.
d. The farmer can make a habitat that is 40 feet wide and 100 feet long.

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15

step-by-step explanation:

why? because i noticed a pattern. 60 120. those numbers without the zero, make the 6 times tables leaving your answer to be b since 6 times 4 is 24 and adding a zero making it 240.

b

step-by-step explanation:

write an equation for the line of best fit. then predict the number of milk cow operations in the year 2005.