✅
Step-by-step explanation:


Answer: 5/2
Step-by-step explanation:
Using slope formula m = rise/run
It is true that t<span>he more surface area an ice cube has, the more quickly it melts to cool a beverage. By making the length of the prism shorter by 1 and the height longer by 2, the resulting prism will look like a 2D object floating on the beverage. Thus, it will cool it faster.
The correct answer is: </span>1 by 2 by 4 or 1 x 2 x 4
Maybe it’s 3 but it actually depends on the equation . . .
4.)
n^2+4n=<span>32
--------------------------
Subtract 32 from each side
</span><span><span>n^2+<span>4n-</span></span>32</span>=<span>32-32
</span>n^2+4n-32=<span>0
</span>--------------------------
Factor left side of equation
(n-4)(n+8)=<span>0
</span>--------------------------
Now set the factors to equal 0
n-4=<span>0
</span>or/and
n+8=<span>0
</span>--------------------------
n=4 and/or n=-<span>8
</span>====================================================================
5.)
t^2-26t=56
Subtract 56 from each side
<span><span>t^2-<span>26t-</span></span>56</span>=<span>56-56
</span>t^2-26t-56=<span>0
</span>----------------------------
Factor left side
(t+2)(t-28)=<span>0
</span>--------------------------
Set factors equal to 0
<span>t+2=<span><span><span>0
or/and
</span>t-</span>28</span></span>=<span>0
</span>t = -2 and/or t = 28
===================================================================
As you may have noticed you need to subtract to get 0 on the right side, then you factor the left side and then switch the symbols from the numbers. Negative to Positive and Positive to Negative. I'll keep provided the work for the next 3 or 4 questions
===================================================================
6.)
z^2-14z=<span>72
</span>----------------
Subtract 72 from each side
<span><span>z^2-<span>14z-</span></span>72</span>=<span>72-72
</span>z^2-14z-72=<span>0
</span>----------------
Factor left side
(z+4)(z-18)=<span>0
</span>----------------
Set factors equal to 0
z+4=0 or z-18=<span>0
</span>Invert
z = -4 and z = 18
===================================================================
7.)
80+a^2=<span>18<span>a
-------------------------
</span></span>Simplify
a^2+80=<span>18<span>a
</span></span>------------------------
Subtract 18a from each side
<span><span>a^2+80-</span>18a</span>=<span><span>18a-</span><span>18a
</span></span>a^2-18a+80=<span>0
</span>------------------------
Factor left side
(a-8)(a-10)=<span>0
</span>-----------------------
Set factors to equal 0
a-8=0 or a-10=<span>0
</span>Invert
a = 8 and a = 10
===================================================================
8.)
u^2=<span>16u+<span>36
--------------------------
</span></span><span>Subtract 16u+36 from both sides.
</span><span><span>u^2-</span><span>(<span>16u+36</span>)</span></span>=<span><span>16u+36-</span><span>(<span>16u+36</span>)
</span></span>u^2-16u-36=<span>0
</span>--------------------------
Factor left side
(u+2)(u-18)=0
--------------------------
Set factors to 0
u+2=0 or u-18=<span>0
</span>Invert
u = -2 and u = 18
====================================================================
9.)
3h^2+6h=<span>105
</span>--------------------------
Subtract 105 from each side
<span><span>3h^2+<span>6h-</span></span>105</span>=<span>105-105
</span>3h^2+6h-105=<span>0
</span>--------------------------
Factor left side
3(h-5)(h+7)=<span>0
</span>--------------------------
Set factors to equal 0
h-5=0 or h+7=<span>0
</span>h = 5 and h = -7
===================================================================
10.)
a^2+14a=-<span>45
</span>---------------------------
Subtract -45 from each side
<span><span>a^2+<span>14a-</span></span><span>(-45)</span></span>=-<span><span>45-</span><span>(-45)
</span></span>a^2+14a+45=<span>0
</span>--------------------------
Factor left side
(a+5)(a+9)=<span>0
</span>-------------------------
Set factors to equal 0
<span>a+5=<span>0 or a+9</span></span>=<span>0
</span>Invert
a = -5 and a = -9
===================================================================
12.)
<span>w=<span>5 and w</span></span>=<span>6
</span>===================================================================
13.)
<span>k=<span><span>6 and </span>k</span></span>=-<span>9
</span>===================================================================
14.)
<span>h=<span><span>5 and </span>h</span></span>=<span>12</span>