Answer:
15 feet
Step-by-step explanation:
The question talks about;
- A rectangular flower bed whose dimensions are 12 ft by 9 ft
We are required to determine the length of the diagonal
To answer the question, we need to know the following;
- All the angles in a rectangle are right angles
- A diagonal divides a rectangle into two right-angled triangles
- The dimensions of the rectangle acts as the legs of right angled triangle.
Therefore;
Using Pythagoras theorem;
a² + b² = c²
Where, c is the hypotenuse (in this case the diagonal)
a and b are the shorter sides of the right-angled triangle
Therefore;
c² = 12² + 9²
c² = 144 + 81
= 225
c = √225
= 15
Therefore, the length of the diagonal is 15 feet
Answer:
The rate is 0.9 gallon per minute
Step-by-step explanation:
Here, we have 4.5 gallons drained in 5 minutes but we are interested in calculating the rate per minute
Let the amount drained per minute be x
4.5 gallons = 5 minutes
x gallon = 1 minute
Let’s cross multiply;
x * 5 = 4.5 * 1
5x = 4.5
x = 4.5/5
x = 0.9 gallons
Answer:
4.33 : 6.49
Step-by-step explanation:
Given endpoints as A(-7,-2) and (2,4) find the length of the segment
d=√ (x₂-x₁) + (y₂-y₁)²
d=√ (2--7)² + (4--2)²
d=√ 9² + 6²
d= √ 81 +36
d=√117 =10.82
The partition is at (-3.4,0.4)
The length from A to the partition will be
A(-7,-2) (-3.4,0.4)
√ (-3.4--7)² + (0.4--2)²
√ 3.6²+2.4²
√18.72 = 4.33
Length of segment from partition to end point B
(-3.4,0.4) , B(2,4)
√(2--3.4)²+(4-0.4)²
√ 5.4² + 3.6²
√42.12
=6.49
The ration that results from the partition of the segment is;
4.33 : 6.49
In this problem, given the focus at (2,4) and directrix at y = 8. then it is implied that the parabola is facing downwards. The vertex hence is at the middle of the focus and the directrix, hence at (2, 6). The general formula of the parabola is y-k = -4a ( x-h)^2. Substituting, y -6 = -1/8 *(x-2)^2. Answer is A.
