During the cold winter months, a sheet of ice covers a lake near the arctic circle. at the beginning of spring, the ice starts to melt.
the variable
ss
s

models the ice sheet's thickness (in meters)
tt
t

weeks after the beginning of spring.
s=−0.25t+4s=-0.25t+4
s=−0.25t+4

by how much does the ice sheet's thickness decrease every
66
6

weeks

Decreased by 1.5 meters and is now at 2.5 meters.

Step-by-step explanation:

s=−0.25t+4 represents the thickness of the ice over t weeks. To find the thickness at 6 weeks, substitute t=6.

s = -0.25(6)+4 = 2.5 meters

It started at t= 0 at 4 meters. So it decreased by 1.5 meters.

The start of spring has 4 meters because when t= 0, s= -0.25(0)+4 = 4

y -5 = (-1/4)(x + 8)

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.