Answer:
p = ½ (x₁ + x₂)
q = a (x₁x₂ − ¼ (x₁ + x₂)²)
Step-by-step explanation:
y = a (x − x₁) (x − x₂)
Expand:
y = a (x² − x₁x − x₂x + x₁x₂)
y = a (x² − (x₁ + x₂)x + x₁x₂)
Distribute a to the first two terms:
y = a (x² − (x₁ + x₂)x) + ax₁x₂
Complete the square:
y = a (x² − (x₁ + x₂)x + ¼(x₁ + x₂)²) + ax₁x₂ − ¼ a(x₁ + x₂)²
y = a (x − ½ (x₁ + x₂))² + a (x₁x₂ − ¼ (x₁ + x₂)²)
Therefore:
p = ½ (x₁ + x₂)
q = a (x₁x₂ − ¼ (x₁ + x₂)²)
Answer:
is sometimes positive and sometimes negative.
Step-by-step explanation:
Take 
Take 
Hence 
for 
and 
for 
So is sometimes positive and sometimes negative in the interval.
Answer:
D
Step-by-step explanation:
The solution to a system of equations given graphically is at the points of intersection of the 2 graphs.
These occur at (4, 8 ) and (0, - 8 ) → D
Answer:
y=2x+3
Step-by-step explanation:
The coefficient has to be 2, since the graph has a slope of 2, and the constant has to be 3 because the y- intercept is 3.
y=2x+3
Hello there! Given there are 70 employees after downsizing by 30%, let x equal the number of employees prior to the layoffs:
70 would have to be 70% of x.
To find what 70 is 70% of, we can multiply by 100 because 100 is the base denominator:
70 • 100 = 7,000
Given this equation, we can now divide our result by 70 to get what the amount of employees before the layoffs is:
7,000 divided by 70 gives us 100.
x = 100
Now, we can plug our answer in to see if it makes sense.
Does 70/100 represent 70%?
Yes, it does. 70/100 reduces to 7/10, and by adding 3/10 to our 70%, we get the initial amount of employees.
Your final answer: There were 100 employees prior to the layoffs. If you have any extra questions, let me know and I will gladly assist you.
