It is 8 sq in his because if u use the formula bh1/2 u get 4 x 4 x 1/2 which is equal to 8
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>
Answer:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis
