Colin is painting figurines. he spends 20 minutes painting each figurine. after painting for 60 minutes, he still has more figurines left to paint.

the number of f of figurines left to paint is a function of t, the amount of time in minutes colin spends painting.

write the functions formula.

f=-1/20t+12
[hints]
the rate at which colin paints is constant, so we're dealing with a linear relationship.

we could write the desired formula in slope-intercept form: f=mt+b. in this form, m gives us the slope of the graph of the function and b gives us the y-intercept. our goal is to find the values of m and b and substitute them into this formula.

we know that the number of figurines left for colin to paint decreases by 1 every 20 minutes, so the slope m is -1/20, and our function looks like f=-1/20t+b.

we also know that colin has 9 figurines left to paint after painting for 60 minutes, which means that when t=60, f=9. we can substitute this into the formula of the function to find b:

-1/20×60+b=9

-3+b=9

b=12

this means colin initially had 12 figurines to paint.

since m=-1/20 and b=12, the desired formula is:

f=-1/20t+12

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step-by-step explanation:

this is not a question

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

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.