Answer:
(1, 5)
Step-by-step explanation:
The solution to the system of equations is the point of intersection of the two lines. From inspection of the graph, the point of intersection is at (1, 5).
<u>Proof</u>
The solution to a system of equations is the point at which the two lines meet.
⇒ g(x) = f(x)
⇒ 3x + 2 = |x - 4| + 2
⇒ 3x = |x - 4|
⇒ 3x = x - 4 and 3x = -(x - 4)
⇒ 3x = x - 4
⇒ 2x = -4
⇒ x = -2
Inputting x = -2 into the 2 equations:
⇒ g(-2) = 3 · -2 + 2 = -4
⇒ f(-2) = |-2 - 4| + 2 = 8
Therefore, as the y-values are different, x = -2 is NOT a solution
⇒ 3x = -(x - 4)
⇒ 3x = 4 - x
⇒ 4x = 4
⇒ x = 1
Inputting x = 1 into the 2 equations:
⇒ g(1) = 3 · 1 + 2 = 5
⇒ f(1) = |1 - 4| + 2 = 5
Therefore, as the y-values are the same, x = 1 IS a solution
and the solution is (1, 5)
Answer:
x=1/3
Step-by-step explanation:
A function f is given as
in the interval [0,1]
This function f being an algebraic polynomial is continuous in the interval [0,1] and also f is differntiable in the open interval (0,1)
Hence mean value theorem applies for f in the given interval

The value

Find derivative for f

Equate this to -5 to check mean value theorem

We find that 1/3 lies inside the interval (0,1)
Answer:
It's A.
Step-by-step explanation:
I hope this answers your question correctly!
Answer:

Step-by-step explanation:
- this can be done by simple manipulation .
- in the given equation, A is the subject.
- so, by the above statement you can understand the meaning of making something as a subject.
- given equation: A = 1/2 bh
- multiply both the sides by 2,
2A = bh
- divide both the sides by h,

so, the required form is : 
Answer:
4082
Step-by-step explanation:
Given
The composite object
Required
The volume
The object is a mix of a cone and a hemisphere
Such that:
<u>Cone</u>
---- radius (r = 20/2)

<u>Hemisphere</u>

The volume of the cone is:



The volume of the hemisphere is:



So, the volume of the object is:





