Answer:
7 times with 1 left over
Step-by-step explanation:
29/4=7
(28)
Remainder 1
3/12 divided by 1 gets you 1/4 because they are equivalent fractions
Answer:
![-\frac{1}{2}x^2-5x-8](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7Dx%5E2-5x-8)
Step-by-step explanation:
Since the graph passes through both (-8,0) and (-2,0), the vertex's x value must be the average of the two, or -5. To determine the y value, you need the third point, (-6,4). In a parabola without any dilation or stretching, the difference between the y value of the point 1 unit to the side of the vertex and the point 3 units away is 9-1=8. However, here it is 4, meaning that this graph has a dilation of 1/2. This means that the vertex has a y value of 9/2=4.5, and that the vertex is (-5,4.5). From here, you can simply plug in the known values to get the vertex form, and then convert to standard.
, which in standard form is
. Hope this helps!
ANSWER
The points (1,2) and (7,2) lie on the given curve.
EXPLANATION
The given parametric equations are:
![x = 3t + 4](https://tex.z-dn.net/?f=x%20%3D%203t%20%2B%204)
and
![y = 2 {t}^{2}](https://tex.z-dn.net/?f=y%20%3D%202%20%7Bt%7D%5E%7B2%7D%20)
We make t the subject in the first equation to obtain:
![t = \frac{x - 4}{3}](https://tex.z-dn.net/?f=t%20%3D%20%20%5Cfrac%7Bx%20-%204%7D%7B3%7D%20)
We substitute this into the second equation to get:
![y =2{(\frac{x - 4}{3} )}^{2}](https://tex.z-dn.net/?f=y%20%3D2%7B%28%5Cfrac%7Bx%20-%204%7D%7B3%7D%20%29%7D%5E%7B2%7D%20)
When x=1,
![y = 2 {(\frac{1 - 4}{3} )}^{2} = 2](https://tex.z-dn.net/?f=y%20%3D%202%20%7B%28%5Cfrac%7B1%20-%204%7D%7B3%7D%20%29%7D%5E%7B2%7D%20%20%3D%202)
When x=2
![y =2{(\frac{2- 4}{3} )}^{2} = \frac{8}{9}](https://tex.z-dn.net/?f=y%20%3D2%7B%28%5Cfrac%7B2-%204%7D%7B3%7D%20%29%7D%5E%7B2%7D%20%20%3D%20%20%5Cfrac%7B8%7D%7B9%7D%20)
When x=7,
![y =2{(\frac{7 - 4}{3} )}^{2} = 2](https://tex.z-dn.net/?f=y%20%3D2%7B%28%5Cfrac%7B7%20-%204%7D%7B3%7D%20%29%7D%5E%7B2%7D%20%20%3D%202)
Therefore the points (1,2) and (7,2) lie on the given curve.