Answer:
k = 12
Step-by-step explanation:
Given:
The equation 
To find:
Value of 
for which the given equation has one distinct real solution.
Solution:
The given equation is a quadratic equation.
There are always two solutions of a quadratic equation.
For the equation: 
to have one distinct solution:
Here,
a = 2,
b = -k and
c = 18
Putting the values, we get:
The equation becomes:
And the one root is:
The correct answer of 1/3 is the decimal form of it which is 0.3 repeated (you can put a line on top of the 3). If not just leave it as 1/3 it is simplified as a fraction.
This question is referred to two similar triangles.
One triangle has sides x and x - 2.
The other triangle has the respective sides x + x + 5 and x - 2 + x + 1
Then you can state a proportionality relation between the sides>
[x + x + 5] / x = [x - 2 + x + 1] / [x - 2]
=> [2x + 5] / x = [2x - 1] / [x - 2]
=> (2x + 5)(x - 2) = (2x - 1)x
=> 2x^2 - 4x + 5x - 10 = 2x^2 - x
=> x - 10 = - x
=> 2x = 10
=> x = 10 / 2
=> x = 5
Answer: x = 5
Answer:
Area_lawn = 393.75 π ft^2
Step-by-step explanation:
Maximum radius : 30 feet
Minimum radius: 30 feet - 0.25*(30feet) = 22.5 feet
(25 percent reduction)
To find the area of lawn that can be watered, we just need to calculate the area for the maximum radius and the minimum radius, and then subtract them.
Since the sprinklers have a circular area:
Area = π*radius^2
Max area = π*(30 ft)^2 = 900π ft^2
Min area = π*(22.5 ft)^2 = 506.25π ft^2
Maximum area of lawn that can be watered by the sprinkler:
Area_lawn = Max area - Min area = 900π ft^2 -506.25π ft^2
Area_lawn = 393.75 π ft^2
