Zina solves a system of linear equations by elimination and finds a solution of (2, 2). one of the equations is a + b = 4. what is the other equation?
a. a + 3b = 4
b. 2a + 2b = 2
c. 4a + 4b = 8
d. a + 3b = 8

D. a + 3b = 8

Step-by-step explanation:

We have that one of the equation of the system is a + b = 4 and the solution is given by ( a,b ) = ( 2,2 ).

Now, since the solution is ( a,b ) = ( 2,2 ), then it must satisfy the equations in the options.

So, substituting ( 2,2 ) in the options, we get:

A. a + 3b = 4 → a + 3b = 4 → 2 + 3 × 2 = 4 → 2 + 6 = 4 → 8 = 4, which is not true.

B. 2a + 2b = 2 → a + b = 1 → 2 + 2 = 1 → 4 = 1, which is not true.

C. 4a + 4b = 8 → a + b = 2 → 2 + 2 = 2 → 4 = 2, which is not true.

D. a + 3b = 8 → 2 + 3 × 2 = 8 → 2 + 6 = 8 → 8 = 8, which is correct.

So, we get that the other equation of this system is a + 3b = 8.

We can also check using elimination method that these equations give the result ( a,b ) = ( 2,2 ).

a + b = 4

a + 3b = 8

Subtracting both equation gives us,

- 2b = -4 i.e. b = 2

So, a + b = 4 → a = 4 - b → a = 4 - 2 → a = 2.

Thus solution is ( 2,2 ).

Hence, option D is correct.

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).

( - 4 , -7 )

all the lines must parallel  

step-by-step explanation:

coordinates of c = ( - 1 , 2 )

3 units left = ( -4 , 2 )

9 units down = ( - 4 , 11 )