Find each missing length using pythagorean theorem.

a. x = 5

b. y ≈ 14.2

Step-by-step explanation:

Pythagorean theorem is:

c² = a² + b²

where c is the hypotenuse (the longest side, opposite of the right angle) and a and b are the legs.

a. c² = a² + b²

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = 5

b. c² = a² + b²

18² = y² + 11²

324 = y² + 121

203 = y²

y ≈ 14.2

x = 5

y = 14.25

Step-by-step explanation:

4a) The Pythagorean theorem is expressed as

Hypotenuse^2 = opposite side^ + adjacent side ^2

Looking at the triangle,

Hypotenuse = x

Opposite side = 3

Adjacent side = 4

Therefore,

x^2 = 3^2 + 4^2

x^2 = 9 + 16 = 25

x = √25 = 5

4b) Looking at the triangle,

Hypotenuse = 18

Opposite side = 11

Adjacent side = y

Therefore,

18^2 = 11^2 + y^2

y^2 = 18^2 - 11^2

y^2 = 324 - 121

y^2 = 203

y = 14.25

f(x) = y

f(-3) = -5

step-by-step explanation:

part a

x     y

0     8

1     7.5

2     7

3     6.5

4     6

5     5.5  

for every hour i deducted .5 inches from the length of the candle

part b

it is a function because for every x value there is only one y value

part   c

for every x value there is only one y value

x       y

0       8

1       7.6

2       7.2

3       6.8

step-by-step explanation: