HELP ASAP PLEASE 7a. Find the value of x. (Hint: How many sides does the shape have?)
5x
4x + 2
5x + 5 5
x-10
2x-2
2y - 1 3x+5
Your answer
!
This is a required question
7b. Find the value of y."
Your answer
This is a required question

x = 36

y = 34

Step-by-step explanation:

✔️Sum of the interior angles of an n-sided polygon = (n - 2) × 180

Thus, the figure given is a hexagon with 6 sides.

Therefore, the sum of its interior angles = (6 - 2) × 180

= 4 × 180 = 720.

This means:

(5x) + (4x + 2) + (5x + 5) + (2x - 2) + (3x + 5) + (x - 10) = 720

Solve for x

5x + 4x + 2 + 5x + 5 + 2x - 2 + 3x + 5 + x - 10 = 720

Add like terms

20x = 720

Divide both sides by 20

x = 36

✔️(2y - 1) + (3x + 5) = 180 (angles on a straight line)

Plug in the value of x

2y - 1 + 3(36) + 5 = 180

2y - 1 + 108 + 5 = 180

Add like terms

2y + 112 = 180

Subtract 118 from each side

2y = 180 - 112

2y = 68

Divide both sides by 2

y = 68/2

y = 34

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540

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).