In NOP, the measure of p=90 the measure of n=59 and PN=7.4 feet. Find the length of OP to the nearest tenth of a foot

12.3 feet

Step-by-step explanation:

Given

<P = 90 degrees

<N = 59 degrees

PN = 7.4 feet

Required

OP

NO = hypotenuse

OP = adjacent

PN = opposite = 7.4

Using SoH CAH TOA identity

tan <O =PN/OP

tan (180-149) = 7.4/OP

tan 31 = 7.4/OP

OP = 7.4/tan 31

OP = 7.4/0.600

OP = 12.3 feet (to the nearest tenth)

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)