How do i find the length of side AB?
1 answer:
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Step-by-step explanation:
In the attached images we can see the rigid transformation of the function
1. The basic graph
2. The reflected graph
3. The displaced graph
Reflection: In the expression , the sign - before the parenthesis indicates that the function is reflected in the x axis, for this case the function is even, this means that -f(x) = f(-x)
, then the reflection on the x axis is equal to the reflection on the y axis.
Displacement: We observe the term (x-4) of the function and analyze the value -4, where, the sign - indicates displacement to the right and the value 4 indicates the amount that the graph shifted
.
The answer is, 
I'm about to basically type up a report on explaining this answer so bear with me :P
<em>Step 1.)</em> Factor
using Polynomial Division.
Just a basic rundown of what polynomial division is. When using polynomial division for this problem we find all the factors of our constant, 84, and then see which one, when substituted for x, makes the expression equal zero. After we find our variable that makes the problem equal zero, we divide it into our original expression. Here's how it's done:
These are our factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
strating from one and plugging in these numbers, the first one we come upon that works is 4. So, now we will divide. below is a picture of what it should look like.
After we divide, we get an answer of
<em>Step 2.)</em> split into two terms
To do that we multiply the coefficient of the first term (2) by the constant (-21)
So:
Now we ask "which two numbers add up to equal 11, but multiply to equal -42". Those two numbers are 14 and -3.
Now we basically split 11x as the sum of 14 and -3. So now our problem should look like this:
<span><span>
</span></span><em>Step 3.)</em> Factor out the common terms in the first two terms, then the last two like this:
From this:
To this:
<em>Step 4.)</em> Factor the term (x + 7) out of the parenthesis
After we do that, we are left with our problem looking like this:
The last thing we do is set each parenthesis equal to zero and work it out to find our zeros.
That gives us our answer of our zeros being
Thank you for our question! I hope this helped! Have an amazing day! :D
I'm about to basically type up a report on explaining this answer so bear with me :P
<em>Step 1.)</em> Factor
Just a basic rundown of what polynomial division is. When using polynomial division for this problem we find all the factors of our constant, 84, and then see which one, when substituted for x, makes the expression equal zero. After we find our variable that makes the problem equal zero, we divide it into our original expression. Here's how it's done:
These are our factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
strating from one and plugging in these numbers, the first one we come upon that works is 4. So, now we will divide. below is a picture of what it should look like.
After we divide, we get an answer of
<em>Step 2.)</em> split
To do that we multiply the coefficient of the first term (2) by the constant (-21)
So:
Now we ask "which two numbers add up to equal 11, but multiply to equal -42". Those two numbers are 14 and -3.
Now we basically split 11x as the sum of 14 and -3. So now our problem should look like this:
<span><span>
</span></span><em>Step 3.)</em> Factor out the common terms in the first two terms, then the last two like this:
From this:
To this:
<em>Step 4.)</em> Factor the term (x + 7) out of the parenthesis
After we do that, we are left with our problem looking like this:
The last thing we do is set each parenthesis equal to zero and work it out to find our zeros.
That gives us our answer of our zeros being
Thank you for our question! I hope this helped! Have an amazing day! :D