<span>You do need the slope. It's not obvious in "Standard Form".
Ax + By = C ==> y = -(A/B)x + (C/B)
There's your slope to compare. Find -A/B for each.
3x + 2y = 4 ==> Slope = -3/2
6x + 4y = 5 ==> Slope = -6/4 = -3/2
3x + y = 4 ==> Slope = -3
The top two examples COULD be parallel. If the constant is the same, that's a bit sneaky because they are really the SAME line. That's not really parallel.</span>
Multiply the number of choices for each position together. Three of the numbers can be repeated with the one (5) only being used once.
(4 possible choices) × (3 possible choices) × (3 possible choices) × (3 possible choices) = 4 × 3 × 3 × 3 = 108
Split up the interval [0, 2] into 4 subintervals, so that
![[0,2]=\left[0,\dfrac12\right]\cup\left[\dfrac12,1\right]\cup\left[1,\dfrac32\right]\cup\left[\dfrac32,2\right]](https://tex.z-dn.net/?f=%5B0%2C2%5D%3D%5Cleft%5B0%2C%5Cdfrac12%5Cright%5D%5Ccup%5Cleft%5B%5Cdfrac12%2C1%5Cright%5D%5Ccup%5Cleft%5B1%2C%5Cdfrac32%5Cright%5D%5Ccup%5Cleft%5B%5Cdfrac32%2C2%5Cright%5D)
Each subinterval has width
. The area of the trapezoid constructed on each subinterval is
, i.e. the average of the values of
at both endpoints of the subinterval times 1/2 over each subinterval
.
So,


Answer:
p = 1.5 and q = 9
Step-by-step explanation:
Expand the right side then compare the coefficients of like terms on both sides, that is
4(x + p)² - q ← expand (x + p)² using FOIL
= 4(x² + 2px + p²) - q ← distribute parenthesis
= 4x² + 8px + 4p² - q
Comparing coefficients of like terms on both sides
8p = 12 ( coefficients of x- terms ) ← divide both sides by 8
p = 1.5
4p² - q = 0 ( constant terms ), that is
4(1.5)² - q = 0
9 - q = 0 ( subtract 9 from both sides )
- q = - 9 ( multiply both sides by - 1 )
q = 9