1. 1.5x-10=3(2x-4)

2. 3(-3x+2)+4x=1/2(5x-30)-9

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1.   1.5x - 10 = 3 (2x - 4)

Step 1: Distribute 3 to the numbers in the parentheses

1.5x - 10 = (3 *2x) + (3* - 4)

1.5x - 10 = (6x) + (-12)

1.5x - 10 = 6x- 12

Step 2: Combine like terms (x's go with x's). Subtract 6x from both sides so that it is canceled out from the right side and brought to the left side.

(1.5x-6x) - 10 = - 12

-4.5x -10 = -12

Step 3: Continue combining like terms by adding 10 to both sides. This will cancel out -10 from the left side and move it to the right

-4.5x = -12 + 10

-4.5x = -2

Step 4: Divide -4.5 to both sides to isolate x

(-2/-4.5) = x

4/9 = x

2.  3 (-3x + 2) +4x = 1/2(5x - 30) - 9

Step 1: distribute 3 to the numbers in the parentheses.

(3*-3x) + (3*-2) +4x = 1/2 (5x - 30) -9

-9x + (-6) +4x = 1/2 (5x -30) -9

Step 2:

i can answer this question sweetie!

step-by-step explanation:

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

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part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

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part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).