Answer:
The graph not have x-intercepts
Step-by-step explanation:
we know that
The x-intercept is the value of x when the value of y is equal to zero
we have
This is the equation of an absolute value in vertex form open upward
The vertex is the point (2,12)
The y-coordinate of the vertex is above the x-axis and the graph open upward
That means ----> The graph do not intersect the x-axis
therefore
The graph not have x-intercepts
<u><em>Verify</em></u>
For y=0
substitute in the equation
----> is not true
The left side of the equation cannot be a negative number
so
The equation not have solution for y=0
therefore
The graph not have x-intercepts
see the attached figure to better understand the problem
It is the reflection across the y axis because if you move across the y axis it will make everything opposite because you are reflecting it
In a rectangle, opposite sides are congruent.
Let one side have length x.
The opposite side also has length x.
The lengths of these two sides add to 2x.
The lengths of all 4 sides add to 64, so the lengths of the other 2 sides
add up to 64 - 2x. Each side measures 32 - x.
The rectangle has sides of length x and 32 - x.
The area of the rectangle is
A = LW
A = x(32 - x)
A = 32x - x^2
y = 32x - x^2 is a parabola that opens downward.
The maximum value of the parabola is the vertex on top.
32x - x^2 = 0
(32 - x)x = 0
32 - x = 0 or x = 0
x = 32 or x = 0
Since the parabola is symmetric with respect to the vertical axis, the vertex has x-coordinate 16.
At x = 16, you get maximum area.
Two opposite sides measure 16 ft each.
32 - x = 32 - 16 = 16
The other two opposite sides also measure 16 ft.
Since all sides turned out to have length 16 ft, the rectangle is a square.
Answer: The maximum area is enclosed by a square with side 16 ft.
Answer:
Perimeter = a + b + sqrt ( (a^2/4) + b^2 ) + sqrt(3)a/2
Step-by-step explanation:
Givens
- ΔABC is equilateral
- AB = a
- The diagram is given below
- AM is a Median
- PB ⊥ AB
- PM = b
Find
Perimeter of ΔPBM
Formula
Perimeter of ABM = AB + PB + PM + AM
Solution
- AB = a Given
- PM = b Given
- PB = sqrt( (a/2)^2 + b^2)
- PB = sqrt( a^2/4 + b^2) PMB is a right angle Pythagoras applies.
- AM = sqrt( AB^2 - BM^2) AMB is a right angle Pythagoras applies.
- AM = sqrt(a^2 - (a/2)^2 ) = sqrt(3)a/2
Perimeter = a + b + sqrt ( (a^2/4) + b^2 ) + sqrt(3)a/2 Answer
The answer is 18. I hope it's right
