Answer:
Ima guess c
Step-by-step explanation:
dont choose mines I guessed
Check the picture below.
so the focus point is there, and the directrix is above it, meaning is a vertical parabola and is opening downwards, since the parabola opens up towards the focus.
now, the vertex is half-way between those two guys, at a "p" distance from either one, if we move over the y-axis from -5 to +2, we have 7 units, half-way is 3.5 units, and that puts us at -1.5 or -1½, as you see in the picture, so the vertex is then at (-3 , -1½).
so the distance from the vertex to the focus point is then 3½ units, however since the parabola is opening downwards, "p" is negative, thus "p = 3½".
![\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{using this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bparabola%20vertex%20form%20with%20focus%20point%20distance%7D%20%5C%5C%5C%5C%20%5Cbegin%7Barray%7D%7Bllll%7D%204p%28x-%20h%29%3D%28y-%20k%29%5E2%20%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Busing%20this%20one%7D%7D%7B4p%28y-%20k%29%3D%28x-%20h%29%5E2%7D%20%5Cend%7Barray%7D%20%5Cqquad%20%5Cbegin%7Barray%7D%7Bllll%7D%20vertex%5C%20%28%20h%2C%20k%29%5C%5C%5C%5C%20p%3D%5Ctextit%7Bdistance%20from%20vertex%20to%20%7D%5C%5C%20%5Cqquad%20%5Ctextit%7B%20focus%20or%20directrix%7D%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
![\bf \begin{cases} h=-3\\ k=-\frac{3}{2}\\[0.7em] p=-\frac{7}{2} \end{cases}\implies 4\left( -\cfrac{7}{2} \right)\left[ y-\left(-\cfrac{3}{2} \right) \right]=\left[ x-\left( -3 \right) \right]^2 \\\\\\ -14\left( y+\cfrac{3}{2} \right)=(x+3)^2\implies y+\cfrac{3}{2} =-\cfrac{(x+3)^2}{14} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{14}(x+3)^2-\cfrac{3}{2}~\hfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%20h%3D-3%5C%5C%20k%3D-%5Cfrac%7B3%7D%7B2%7D%5C%5C%5B0.7em%5D%20p%3D-%5Cfrac%7B7%7D%7B2%7D%20%5Cend%7Bcases%7D%5Cimplies%204%5Cleft%28%20-%5Ccfrac%7B7%7D%7B2%7D%20%5Cright%29%5Cleft%5B%20y-%5Cleft%28-%5Ccfrac%7B3%7D%7B2%7D%20%5Cright%29%20%5Cright%5D%3D%5Cleft%5B%20x-%5Cleft%28%20-3%20%5Cright%29%20%5Cright%5D%5E2%20%5C%5C%5C%5C%5C%5C%20-14%5Cleft%28%20y%2B%5Ccfrac%7B3%7D%7B2%7D%20%5Cright%29%3D%28x%2B3%29%5E2%5Cimplies%20y%2B%5Ccfrac%7B3%7D%7B2%7D%20%3D-%5Ccfrac%7B%28x%2B3%29%5E2%7D%7B14%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20~%5Chfill%20y%3D-%5Ccfrac%7B1%7D%7B14%7D%28x%2B3%29%5E2-%5Ccfrac%7B3%7D%7B2%7D~%5Chfill)
Answer:
T = - 3.2e + 80
Step-by-step explanation:
Given the following :
e = elevation in thousands of feets
T = temperature (°F)
e1 = 5 ; e2 = 10 (in thousands of feet)
T1 = 64° ; T2 = 48°
y = mx + c ; T = me + c
y = ; m = slope, c = intercept
64 = m5 + c - - - - (1)
48 = m10 + c - - - - (2)
From (1)
c = 64 - m5
Substitute c = 64 - m5 into (2)
48 = m10 + c - - - - (2)
48 = m10 + 64 - m5
48 - 64 = 10m - 5m
-16 = 5m
m = - 16 / 5
m = - 3.2
Substitute the value of m into c = 64 - m5
c = 64 - 5(-3.2)
c = 64 - (-16)
c = 64 + 16
c = 80
Inserting our c and m values into T = me + c
T = - 3.2e + 80
Where e is in thousands of feet
T is in °F
Your answer is C.The relation passed the vertical line test.
Answer:
Hey there!
The measure of angle ABD plus the measure of angle CBD equals 90 degrees or a right angle.
Thus, we can write the equation: ABD+51=90
Solving for ABD, we find that it is 39 degrees.
Let me know if this helps :)
