K^2-5k-50
(k-10)(k+5)
This is because k*k=k^2 (your first term), 5k-10k=-5k (your second term) and -10*5=-50 (your last term).
Distribute to check.
Answer: width = 42, length = 74
Step-by-step explanation: 42 + 32 = 74
42 + 42 + 74 + 74 = 232
Answer: Let's assume that the pig pens need to be fenced in the way shown in the diagram above.
Then, the perimeter is given by
4
x
+
3
y
=
160
.
4
x
=
160
−
3
y
x
=
40
−
3
4
y
The area of a rectangle is given by
A
=
L
×
W
, however here we have two rectangles put together, so the total area will be given by
A
=
2
×
L
×
W
.
A
=
2
(
40
−
3
4
y
)
y
A
=
80
y
−
3
2
y
2
Now, let's differentiate this function, with respect to y, to find any critical points on the graph.
A
'
(
y
)
=
80
−
3
y
Setting to 0:
0
=
80
−
3
y
−
80
=
−
3
y
80
3
=
y
x
=
40
−
3
4
×
80
3
x
=
40
−
20
x
=
20
Hence, the dimensions that will give the maximum area are
20
by
26
2
3
feet.
A graphical check of the initial function shows that the vertex is at
(
26
2
3
,
1066
2
3
)
, which represents one of the dimensions that will give the maximum area and the maximum area, respectively.
Hopefully this helps!
Step-by-step explanation: hope this helps
Interval notation uses parenthesis ( or ) for points that are not included in the function (open circle) and brackets [ or ] for points that are included in the function (filled in circle).
Remember that the domain for a function is the range of x-values in a function.
Interval notation includes the numbers at the each end of a continuous function. For function F, the leftmost x-value is 0. The rightmost x-value is 8. Both points at x = 0 and x = 8 are included in the function (filled in circles), so you would use the brackets. The entire function is continuous between those two points.
That means the interval notation for the domain of F is:
[0, 8]
------
Answer: [0, 8]
Answer:
VW = 1
Step-by-step explanation:
Tan 45 = 4/VW
VW = 4/Tan 45 = 1
