12 is 20% of 60 because 12/60 = 0.2.
(X+3)^2+(X-2)^2=9................
Let <em>a</em> and <em>b</em> be the zeroes of <em>x</em>² + <em>kx</em> + 12 such that |<em>a</em> - <em>b</em>| = 1.
By the factor theorem, we can write the quadratic in terms of its zeroes as
<em>x</em>² + <em>kx</em> + 12 = (<em>x</em> - <em>a</em>) (<em>x</em> - <em>b</em>)
Expand the right side and equate the coefficients:
<em>x</em>² + <em>kx</em> + 12 = <em>x</em>² - (<em>a</em> + <em>b</em>) <em>x</em> + <em>ab</em>
Then
<em>a</em> + <em>b</em> = -<em>k</em>
<em>ab</em> = 12
The condition that |<em>a</em> - <em>b</em>| = 1 has two cases, so without loss of generality assume <em>a</em> > <em>b</em>, so that |<em>a</em> - <em>b</em>| = <em>a</em> - <em>b</em>.
Then if <em>a</em> - <em>b</em> = 1, we get <em>b</em> = <em>a</em> - 1. Substitute this into the equations above and solve for <em>k</em> :
<em>a</em> + (<em>a</em> - 1) = -<em>k</em> → 2<em>a</em> = 1 - <em>k</em> → <em>a</em> = (1 - <em>k</em>)/2
<em>a</em> (<em>a</em> - 1) = 12 → (1 - <em>k</em>)/2 • ((1 - <em>k</em>)/2 - 1) = 12
→ (1 - <em>k</em>)²/4 - (1 - <em>k</em>)/2 = 12
→ (1 - <em>k</em>)² - 2 (1 - <em>k</em>) = 48
→ (1 - 2<em>k</em> + <em>k</em>²) - 2 (1 - <em>k</em>) = 48
→ <em>k</em>² - 1 = 48
→ <em>k</em>² = 49
→ <em>k</em> = ± √(49) = ±7
I am going to do this problem with more of an algebraic approach weather or not its the way your teacher wants you to do it like this.
The way to do things algebraically is to just set variables for what you want to find and set up equations to represent each sentence.
As seen there are hamburgers and chickens in this problem. So let's set the numbers of hamburgers to x, and the numbers of chickens to y.
Now write out each sentence using variables.
1.) Tia sold 78 hamburgers and chicken tenders.
x+y=78
2.) If she sold 24 more hamburgers than chicken tenders.
x=y+24
Now that we have the 2 equations, its time to solve.
Since we have x=y+24, we can replace the x in the first equation with the second equation
y+24+y=78
2y+24=78
Now we can subtract 24 from both sides.
2y=54
Simplify
y=27
Solve for x
x=27+24=51
Done!
This is true, it's A!
Students grades are most likely coorelated with some event that influenced them directly, or that is influenced by the same factor. Here having completed the exam revieq packet means that the students have studied, so they will likely get good grades.
