bearing in mind that "a" is the length of the traverse axis, and "c" is the distance from the center to either foci.
we know the center is at (0,0), we know there's a vertex at (-48,0), from the origin to -48, that's 48 units flat, meaning, the hyperbola is a horizontal one running over the x-axis whose a = 48.
we also know there's a focus point at (50,0), that's 50 units from the center, namely c = 50.
![\bf \textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ \textit{asymptotes}\quad y= k\pm \cfrac{b}{a}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bhyperbolas%2C%20horizontal%20traverse%20axis%20%7D%20%5C%5C%5C%5C%20%5Ccfrac%7B%28x-%20h%29%5E2%7D%7B%20a%5E2%7D-%5Ccfrac%7B%28y-%20k%29%5E2%7D%7B%20b%5E2%7D%3D1%20%5Cqquad%20%5Cbegin%7Bcases%7D%20center%5C%20%28%20h%2C%20k%29%5C%5C%20vertices%5C%20%28%20h%5Cpm%20a%2C%20k%29%5C%5C%20c%3D%5Ctextit%7Bdistance%20from%7D%5C%5C%20%5Cqquad%20%5Ctextit%7Bcenter%20to%20foci%7D%5C%5C%20%5Cqquad%20%5Csqrt%7B%20a%20%5E2%20%2B%20b%20%5E2%7D%5C%5C%20%5Ctextit%7Basymptotes%7D%5Cquad%20y%3D%20k%5Cpm%20%5Ccfrac%7Bb%7D%7Ba%7D%28x-%20h%29%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D)
Answer:
392
Step-by-step explanation:
2((7 - 10)^2 + 5)^2
2((-3)^2 + 5)^2
2(9 + 5)^2
2(14)^2
2(196)
392
We compute for the surface area of the triangular prism by the adding the areas of the bases and the sides. There are two triangles and the areas will be,
A = 2 (1/2)(9 cm)(12 cm) = 108 cm²
There are three sides which are in rectangular shape.
A1 = (10)(12) = 120 cm²
A2 = (10)(9) = 90 cm²
A3 = (10)(15) = 150 cm²
The sum of these areas is 468 cm².
Answer:
ordered pair(-2 , 3) is the solution
Step-by-step explanation:
y=x+5
y=-2x-1
x+5 = -2x-1 substitution
x+5+2x-5 = -2x-1+2x-5
3x = -6
x = -2
y = -2+5 = 3
ordered pair(-2 , 3) is the solution
