Florence stands in her backyard and admires her flower gardens. First, she looks to her rose garden. Her rose garden is 80 feet away from her. She turns 63° and views where she has lilies planted. The lily garden is 140 feet away from her. How far apart are the rose garden and the lily garden?

The rose garden is 125.82 feet apart from the lily garden.

Step-by-step explanation:

See the attached diagram.

The position of Florence is A and the position of the rose garden and the lily garden forms a triangle Δ ARL.

Now, from the property of triangle, we can write

x² = 80² + 140² - 2 × 140 × 80 × Cos 63°

⇒ x² = 15830.61

⇒ x = 125.82 feet.

Therefore, the rose garden is 125.82 feet apart from the lily garden. (Answer)

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.

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)