Answer:
The equation in standard form is: 
Step-by-step explanation:
Since they give you the x-intercepts (the zeros of the quadratic expression) one knows that the binomials: (x-(-3)) and (x-4) must be factors of the quadratic expression.
We can therefore write the equation as:
using the binomial factors given above, and a numerical factor "k" that we can determine by using the information that the graph passes through the point (2,-20):
Then,the equation can be written as:
where we wrote the equation already in standard form
Two points determine a line. In slope intercept form we have:
y = -2x + b
So:
-12 = -2(3) + b and [first equation]
k = -2(6) + b [second equation]
We have a system of simultaneous equations with two unknowns. The first is trivially easy to solve:
-12 = -6 + b [Evaluate -2(3)]
-6 = b [Add +6 to each side]
So we substitute this into the second equation:
k = -2(6) + -6 = -18
We could double check our work knowing that m=Δy/Δx
We expect m to be -2. Does:
-2 = (-18 - -12)/(6 - 3) = -6/3 = -2?
;)
Answer:
She has 20 quarters.
Step-by-step explanation:
Alissa emptied her piggy bank for Disney world. She had $7.70.
If she had 10 pennies and twice as many times as quarters, then we can write the equation as
Q = 2P {Where, Q represents the number of quarters and P for pennies}
⇒ Q = 10 × 2
⇒ Q = 20
So, she has 20 quarters.
Therefore, she has 20 quarters. (Answer)
Answer:
Option A- 1.8x – 10 = –4; x = 1.8 x minus 10 equals negative 4; x equals StartFraction 10 Over 2 EndFraction.
The given function is
f(x) = 4x - 3/2
where
f(x) = number of assignments completed
x = number of weeks required to complete the assignments
We want to find f⁻¹ (30) as an estimate of the number of weeks required to complete 30 assignments.
The procedure is as follows:
1. Set y = f(x)
y = 4x - 3/2
2. Exchange x and y
x = 4y - 3/2
3. Solve for y
4y = x + 3/2
y = (x +3/2)/4
4. Set y equal to f⁻¹ (x)
f⁻¹ (x) = (x + 3/2)/4
5. Find f⁻¹ (30)
f⁻¹ (30) = (30 + 3/2)/4 = 63/8 = 8 (approxmately)
Answer:
Pedro needs about 8 weeks to complete 30 assignments.
