Answer:
Step-by-step explanation:
GIVEN: A farmer has 
of fencing to construct a rectangular pen up against the straight side of a barn, using the barn for one side of the pen. The length of the barn is 
.
TO FIND: Determine the dimensions of the rectangle of maximum area that can be enclosed under these conditions.
SOLUTION:
Let the length of rectangle be 
and 
perimeter of rectangular pen 
area of rectangular pen 
putting value of
to maximize 
but the dimensions must be lesser or equal to than that of barn.
therefore maximum length rectangular pen 
width of rectangular pen 
Maximum area of rectangular pen 
Hence maximum area of rectangular pen is 
and dimensions are
Answer: 75%
We know that 1/4 of 24 (25%) is 6, 6 fits into 18 three times and 25 times 3 is 75. So the answer is 75%
X/5 = 24/8
(because the triangles are similar)
x/5 = 3
x = 5*3 = 15 Answer
a/27 = 8/24 = 1/3
a = 9 Answer
add the two equations together
5a+5b=25
-5a+5b=35
------------------
0 + 10b =60
divide by 10
b=6
5a + 5b = 25
5a +5(6) = 25
5a +30 =25
subtract 30 from each side
5a =-5
divide by 5
a = -1
Answer (-1,6)
or a=-1 b=6
To find the vertex of the parabola, we need to write it in a vertex form.
y=x² - 8x +12
1) complete the square
y=
x² - 8x +12
y =
x² -2*4x + 4² - 4² +12
y=
(x-4)² -16 +12
2) calculate and write a vertex
y=
(x-4)² -16 +12
y=
(x-4)² - 4
(x-4) ----- x- coordinate of the vertex x=4
y=(x-4)²
- 4 -------y- coordinate of the vertex y = - 4 Vertex is (4, -4).
Answer is (4, -4). No correct answer is given in choices.
