it has to be ummmm.........
Alright let's start by noting that due to it having a square bottom and top the Length is equal to the Width. They gave us the surface area, but what we need is the length/width of the square top/bottom. So let's take the surface area and make it equal to the equation for the surface area of a rectangular prism (our shape):
192cm^2 = 2(lw + lh + hw)
Let's replace all the "l's" with w's (we can do this due to the fact that the length (l) equals the width (w) (l = w))
192cm^2 = 2(w*w + wh + hw)
192cm^2 = 2(w^2 + 2wh)
We know what the height (h) is as it is given in the problem (5cm).
192cm^2 = 2(w^2 + 2*5w)
192cm^2 = 2(w^2 + 10w)
Divide 2 on both sides.
96cm^2 = w^2 + 10w
Subtract 96 on both sides.
0 = w^2 + 10w - 96
Factor it out.
0 = (w - __)(w + ___)
0 = (w - 6)(w+16)
We have two possible answers of:
w = 6
w = -16
The only answer which makes sense is the positive one, because a box in real life can't have negative length.
So,
w = 6 cm.
Answer:
2
(
n
+
2
)
(
n
+
1
2
)
Step-by-step explanation:
coefficient of the first term:
2
=
2
×
1
coefficient of the last term:
2
=
2
×
1
coefficient of the middle term (using only the factors above):
5
=
2
×
2
+
1
×
1
2
n
2
+
5
n
+
2
=
(
2
n
+
1
)
(
n
+
2
)
Alternative method:
Treat the given expression as a quadratic set equal to zero, with the form
a
n
2
+
b
n
+
c
and use the quadratic formula
−
b
±
√
b
2
−
4
a
c
2
a
This will given solutions
n
=
−
2 and n
=
−
1
2
for a factoring
2
(
n
+
2
)
(
n
+
1
2
)
Hope this helped
Answer:
Step-by-step explanation: