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:
3/16 or 0.1875
Step-by-step explanation:
3/4 - ((3/8)/2/3))
= 3/4 - 3/8 * 3/2
= 3/4 - 9/16
= 12/16 - 9/16
= 3/16 or 0.1875
Hope this help you :3
Answer: Volume = 796.6 cm³
Step-by-step explanation:
We would apply the formula for determining the volume of a cone which is expressed as
Volume = 1/3 × πr²h
Where
r represents the radius of the cone.
h represents the vertical height of the cone.
π is a constant whose value is 3.14
From the information given,
Diameter of cone = 18.6 cm
Radius = diameter/2
Radius = 18.6/2 = 9.3 cm
Height = 8.8cm
Therefore,
Volume = 1/3 × 3.14 × 9.3² × 8.8
Volume = 1/3 × 3.14 × 86.49 × 8.8
Volume = 796.6 cm³
Answer:
The sequence is a function since,
- It maps to a number from each of the numbers or points in it's domain set which is the set of positive integers
- It maps to only one point from each point in it's domain set.
Step-by-step explanation:
This sequence is a function whose domain is the set of positive integers.
The function is given by,
f(x) = 10 + (x -2) when x is even
= (x- 1) when x is odd
The sequence is a function since,
- It maps to a number from each of the numbers or points in it's domain set which is the set of positive integers
- It maps to only one point from each point in it's domain set.
