The first equation
6x^2 -18x-24=0
-the graph opens up
6(x^2 -3x -4)=0
6(x^2 -3x +9/4-4-9/4)=0
6(x-3/2)-25x6/4=
6(x-3/2)-75/2
-Vertex is at (3/2, -75/2)
-Axis of symmetry is x=3/2
Second equation
3r^2 -16r -12=0
-the graph opens up
...
To create a perfect square trinomial, halve the x coefficient, square it, and then add that value.
In the case of x² + 6x, we would have 6 to get 3, then square 3 to get 9.
We would add 9 to make a perfect square trinomial.
<u>
</u><u>Why this works</u>
A perfect square trinomial is designed to factor to some value (x+n)².
When you FOIL this you get x² + 2nx + n².
As you can see, if you wanted to find the value of that n², you could take that x coefficient 2n, halve it to get n, and then square it to get n²!
Answer: ↓↓↓
Step-by-step explanation:
1. EF || HG, HE || FG
2. Reflexive Property
3. Alternate Interior Angles
4. SAS
Answer:
$12.31
Step-by-step explanation:
Think of the original rate of pay as being 100%.
If your rate is increasing by 7%, it will now be 107% of the original rate (since 100% + 7% = 107%)
To find 107% of $11.50, convert 107% into a decimal
⇒ 107% = 107/100 = 1.07
then multiply this by the original rate to get the new increased rate:
⇒ $11.50 × 1.07 = $12.305
Rounding this to the nearest hundred = $12.31
Alternatively, you can find 7% of $11.50 and then add this to $11.50.
⇒ 7% = 7/100 = 0.07
Therefore, 7% of $11.50 = 0.07 × $11.50 = $0.805
Add this to the original rate:
$11.50 + $0.805 = $12.305
Rounding this to the nearest hundred = $12.31
