![\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ y = 4\frac{2}{3}x\qquad \qquad yes\qquad \checkmark\qquad \qquad k = 4\frac{2}{3} \\\\[-0.35em] ~\dotfill\\\\ y=3(x-1)\implies \stackrel{\textit{distributing}}{y=3x-3}\qquad \qquad yes\qquad \checkmark \qquad \qquad k=3](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bdirect%20proportional%20variation%7D%20%5C%5C%5C%5C%20%5Ctextit%7B%5Cunderline%7By%7D%20varies%20directly%20with%20%5Cunderline%7Bx%7D%7D%5Cqquad%20%5Cqquad%20y%3Dkx%5Cimpliedby%20%5Cbegin%7Barray%7D%7Bllll%7D%20k%3Dconstant%5C%20of%5C%5C%20%5Cqquad%20variation%20%5Cend%7Barray%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20y%20%3D%204%5Cfrac%7B2%7D%7B3%7Dx%5Cqquad%20%5Cqquad%20yes%5Cqquad%20%5Ccheckmark%5Cqquad%20%5Cqquad%20k%20%3D%204%5Cfrac%7B2%7D%7B3%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20y%3D3%28x-1%29%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bdistributing%7D%7D%7By%3D3x-3%7D%5Cqquad%20%5Cqquad%20yes%5Cqquad%20%5Ccheckmark%20%5Cqquad%20%5Cqquad%20k%3D3)
bear in mind that, direct proportional equations have a y-intercept.
for y = kx, is pretty much y = kx + 0, where 0 = y-intercept.
and the "k" constant of proportionality, is pretty much just its slope.
<span>9a + -3(2a + -4) = 15
Reorder the terms:
9a + -3(-4 + 2a) = 15
9a + (-4 * -3 + 2a * -3) = 15
9a + (12 + -6a) = 15
Reorder the terms:
12 + 9a + -6a = 15
Combine like terms: 9a + -6a = 3a
12 + 3a = 15
Solving
12 + 3a = 15
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 3a = 15 + -12
Combine like terms: 12 + -12 = 0
0 + 3a = 15 + -12
3a = 15 + -12
Combine like terms: 15 + -12 = 3
3a = 3
Divide each side by '3'.
a = 1
Simplifying
a = 1</span>
It will take the roller coaster 171.652 seconds to pass over the hill and reach ground level
<h3>How to determine the time to hit the ground?</h3>
The function is given as:
h = –.025t^2 + 4t + 50
Set h = 0.
So, we have:
–.025t^2 + 4t + 50 = 0
Using a graphing calculator, we have:
t = -11.652 and t = 171.652
Time cannot be negative.
So, we have:
t = 171.652
Hence, it will take the roller coaster 171.652 seconds to pass over the hill and reach ground level
Read more about quadratic functions at:
brainly.com/question/27958964
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Answer:
37
Step-by-step explanation:
Right Scalene Triangle
Side a = 37
Side b = 12
Side c = 35
Angle ∠A = 90° = 1.5708 rad = π/2
Angle ∠B = 18.925° = 18°55'29" = 0.3303 rad
Angle ∠C = 71.075° = 71°4'31" = 1.2405 rad
C=71.075°B=18.925°A=90°b=12a=37c=35
Area = 210
Perimeter p = 84
Semiperimeter s = 42
Height ha = 11.35135
Height hb = 35
Height hc = 12
Median ma = 18.5
Median mb = 35.51056
Median mc = 21.2191
Inradius r = 5
Circumradius R = 18.5
Vertex coordinates: A[0, 0] B[35, 0] C[0, 12]
Centroid: [11.66667, 4]
Inscribed Circle Center: [5, 5]
Circumscribed Circle Center: [17.5, 6]
