A quadratic in vertex form reads as
(<em>x</em> - <em>a</em>)² + <em>b</em>
where (<em>a</em>, <em>b</em>) is the vertex.
To get the given quadratic in this form, complete the square:
<em>x</em>² - 6<em>x</em> - 40 = <em>x</em>² - 6<em>x</em> + 9 - 49 = (<em>x</em> - 3)² - 49
Or, work backwards by expanding the vertex form and solving for <em>a</em> and <em>b</em> :
(<em>x</em> - <em>a</em>)² + <em>b</em> = <em>x</em>² - 2<em>ax</em> + <em>a</em>² + <em>b</em>
So if
<em>x</em>² - 6<em>x</em> - 40 = <em>x</em>² - 2<em>ax</em> + <em>a</em>² + <em>b</em>,
then
-2<em>a</em> = -6 → <em>a</em> = 3
<em>a</em>² + <em>b</em> = -40 → <em>b</em> = -49
Answer:
The area is given by:
And replacing we got:
So then we can conclude that the area of the coin is 
mm^2
Step-by-step explanation:
For this case we know that we have a coin with a diamter of 
, and by definition the radius is given by:
The area is given by:
And replacing we got:
So then we can conclude that the area of the coin is mm^2
Answer:
x=50
Step-by-step explanation:
This is a vertical angle, so the angle on top and the bottom are equal
[2(x+10)]=3x-30
2(x+10)=3x-30
2x+20=3x-30
50=x
Answer:
Answer- 0
Step-by-step explanation:
2+2+2-2+4-8= 4-2+4-8=0
hope this helps :)
Answer:
Step-by-step explanation:
the graph shifts 2 units right and 7 units down
