Answer:
(P•q)(-3)=-32
(q•P)(-3)=-32
Step-by-step explanation:
The functions are :
![p(x) = 3x + 5](https://tex.z-dn.net/?f=p%28x%29%20%3D%203x%20%2B%205)
![q(x) = - 2x + 2](https://tex.z-dn.net/?f=q%28x%29%20%3D%20%20-%202x%20%2B%202)
We want to evaluate (p*g)(x) at x=-3.
![(p \cdot \: q)(x) = (3x + 5)( - 2x + 2)](https://tex.z-dn.net/?f=%28p%20%5Ccdot%20%5C%3A%20q%29%28x%29%20%3D%20%283x%20%2B%205%29%28%20-%202x%20%2B%202%29)
When we put x=-3, we get:
![(p \cdot \: q)( - 3) = (3 \times - 3 + 5)( - 2 \times - 3 + 2)](https://tex.z-dn.net/?f=%28p%20%5Ccdot%20%5C%3A%20q%29%28%20-%203%29%20%3D%20%283%20%5Ctimes%20%20-%203%20%2B%205%29%28%20-%202%20%5Ctimes%20%20-%203%20%2B%202%29)
![(p \cdot \: q)( - 3) = ( - 9 + 5)( 6 + 2)](https://tex.z-dn.net/?f=%28p%20%5Ccdot%20%5C%3A%20q%29%28%20-%203%29%20%3D%20%28%20-%209%20%2B%205%29%28%206%20%2B%202%29)
![(p \cdot \: q)( - 3) = ( - 4)( 8) = - 32](https://tex.z-dn.net/?f=%28p%20%5Ccdot%20%5C%3A%20q%29%28%20-%203%29%20%3D%20%28%20-%204%29%28%208%29%20%3D%20%20-%2032)
Also,
![(q \cdot p)( x) = ( - 2x + 2)(3x + 5)](https://tex.z-dn.net/?f=%28q%20%20%5Ccdot%20p%29%28%20x%29%20%3D%20%28%20-%202x%20%2B%202%29%283x%20%2B%205%29)
![(q \cdot p)( - 3) = ( - 2 \times - 3+ 2)(3 \times - 3+ 5)](https://tex.z-dn.net/?f=%28q%20%20%5Ccdot%20p%29%28%20%20-%203%29%20%3D%20%28%20-%202%20%5Ctimes%20%20-%203%2B%202%29%283%20%20%5Ctimes%20-%203%2B%205%29)
![(q \cdot p)( - 3) = ( 6+ 2)( - 9+ 5)](https://tex.z-dn.net/?f=%28q%20%20%5Ccdot%20p%29%28%20%20-%203%29%20%3D%20%28%206%2B%202%29%28%20-%209%2B%205%29)
![(q \cdot p)( - 3) = ( 8)( - 4) = - 32](https://tex.z-dn.net/?f=%28q%20%20%5Ccdot%20p%29%28%20%20-%203%29%20%3D%20%28%208%29%28%20-%204%29%20%3D%20%20-%2032)
Answer:
96
Step-by-step explanation:
The maximum height reached by the pebble modeled by the quadratic function,
, can be found by finding the vertex.
Let's first find the t-coordinate of the vertex . The max height will correspond to this value of t which means we have to find the h(t)-coordinate.
When comparing
to
, we see that:
![a=-16](https://tex.z-dn.net/?f=a%3D-16)
![b=32](https://tex.z-dn.net/?f=b%3D32)
![c=80](https://tex.z-dn.net/?f=c%3D80)
We need to evaluate the following to find the t-coordinate of the vertex:
![t=\frac{-b}{2a}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-b%7D%7B2a%7D)
![t=\frac{-32}{2(-16)}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-32%7D%7B2%28-16%29%7D)
![t=\frac{-32}{-32}](https://tex.z-dn.net/?f=t%3D%5Cfrac%7B-32%7D%7B-32%7D)
![t=1](https://tex.z-dn.net/?f=t%3D1)
So now to find the correspond h(t)-coordinate, we will need to replace t in
with 1:
![-16(1)^2+32(1)+80](https://tex.z-dn.net/?f=-16%281%29%5E2%2B32%281%29%2B80)
![-16(1)+32+80](https://tex.z-dn.net/?f=-16%281%29%2B32%2B80)
![-16+32+80](https://tex.z-dn.net/?f=-16%2B32%2B80)
![16+80](https://tex.z-dn.net/?f=16%2B80)
![96](https://tex.z-dn.net/?f=96)
Answer:
25,400
Step-by-step explanation:
round the three in the hundreds place up since to the right there is a 9
Answer:
no solution
Step-by-step explanation:
L1 = 3y=3/2x+6
L2 = 1/2y-1/4x=3
Divide L1 by 3: y = 0.5x + 2
Multiply L2 by 2: y - 0.5x = 6, now isolate y: y = 0.5x + 6
we can see that both lines have the same gradient but different y-intercepts, therefore they never cross
Answer:
D
Step-by-step explanation:
(2x+3)(3x-5)
6x^2 -10x +9x -15
6x^2 - x -15