The standard form of a quadratic equation is
,
where
,
, and
are coefficients. You want to get the given equation into this form. You can accomplish this by putting all the non-zero values on the left side on the equation.
In this case, the given equation is

Since
is on the right side of the equation, we subtract that from both sides. The resulting equation is

Looking at the standard form equation
, we can see that

Answer:
absolute vlaue inequality: |x-3| > 9; solved: x<-6 and x>12
Step-by-step explanation:
I’m going to start this off by saying I learned all this right now by just searching up how to solve an absolute inequality equation and watching one video, so this might not be an accurate explanation. (I’m pretty sure the answer’s right though)
So an absolute value inequality must be written like this:
| x - a | *inequality* b
a is going to be the number that the inequality is centered around, in this case, 3. b will be how far you can deviate from that number, which in this case is 9.
Now, you will have this:
|x - 3| *inequality* 9
Now, to find the inequality, you need to understand the wording. If it says “more than” as it does here, then you would have the greater-than symbol (>). If you have “less than” then you’d have the less-than symbol (<). If the problem says “at least b away” then it would be greater-than-or-equal to (≥), and likewise, if it says “at most b away” then it would be less-than-or-equal-to (≤).
So now we're at:
|x - 3| > 9
To solve the equation, you just need to subtract 9(b) from 3(a) and add 9(a) to 3(b) to get -6 and 12. Since x must be more than 9 units away, you would get:
x<-6 and x>12
Hope this is helpful!
Answer:
It helps because it gets you thinking. Personally, it would motivate me because that process itself is very helpful. Brainstorm will get you your idea, you can decide if you want to do it or not, then you work on it, and because you have the right attitude towards whatever you are working on, you'll enjoy it!
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Answer:
(c) BK = 65
Step-by-step explanation:
Corresponding sides are proportional in similar triangles, so ...
ZT/ZQ = KF/KB
27/(2x +7) = 45/(4x+1)
27(4x+1) = 45(2x +7) . . . cross-multiply
3(4x +1) = 5(2x +7) . . . . divide by 9
12x +3 = 10x +35 . . . . . eliminate parentheses
2x = 32 . . . . . . . . . . . . . subtract 10x+3
x = 16 . . . . . divide by 2
Then the length of BK is ...
BK = 4x+1 = 4·16 +1
BK = 65