Answer:
Step-by-step explanation:
Given that:
Little Gull Island Lighthouse shines a light from a height of 91 feet above the sea level.
The angle of depression is unknown.
Distance of the point at sea surface from the base of lighthouse is 865 ft.
This situation can be modeled or can be represented as the figure attached in the answer area.
The situation can be represented by a right angled 
in which we are given the base and the height of the triangle.
And we have to find the value of 
(Because they are the internal vertically opposite angles).
Using tangent ratio:
Therefore, the angle of depression is:
Answer:
Step-by-step explanation:
A dime is worth 10 cents. Converting to dollars, it becomes 10/100 = $0.1
A quarter is worth 25 cents. Converting to dollars, it becomes 25/100 = $0.25
Let x represent the number of dimes that Jayden has.
Let y represent the number of quarters that Jayden has.
Jayden has some dimes and some quarters. He has at most 25 coins. It means that
x + y ≤ 25
The coins worth at least $4.60 combined. It means that
0.1x + 0.25y ≥ 4.6 - - - - - - - - - - 1
If Jayden has 7 dimes, then
7 + y ≤ 25
y ≤ 25 - 7
y ≤ 18
Substituting x = 7 into equation 1, it becomes
0.1 × 7 + 0.25y ≥ 4.6
0.7 + 0.25y ≥ 4.6
0.25y ≥ 4.6 - 0.7
0.25y ≥ 3.9
y ≥ 3.9/0.25
y ≥ 15.6
All possible values for the number of quarters that he could have would be
15.6 ≤ y ≤ 18
Answer:
(D)The midpoint of both diagonals is (4 and one-half, 5 and one-half), the slope of RP is 7, and the slope of SQ is Negative one-sevenths.
Step-by-step explanation:
- Point P is at (4, 2),
- Point Q is at (8, 5),
- Point R is at (5, 9), and
- Point S is at (1, 6)
Midpoint of SQ 
Midpoint of PR 
Now, we have established that the midpoints (point of bisection) are at the same point.
Two lines are perpendicular if the slope of one is the negative reciprocal of the other.
In option D
- Slope of SQ
Therefore, lines RP and SQ are perpendicular.
Option D is the correct option.
Answer:
9 feet
Step-by-step explanation:
Given:
The border of the garden is a right angled triangle.
Two lengths are given as 12 ft and 15 ft.
Let the length of the shortest timber be 'x' feet.
Now, in a right angled triangle, the longest length is called the hypotenuse.
As 15 feet is the largest length, it is the hypotenuse of the triangle. Now, applying Pythagoras theorem, we get:
The negative value is neglected as length can never be negative.
Therefore, the length of the shortest timber is 9 feet.
