Answer:
V of the solid = 40 in³
Step-by-step explanation:
volume of the first rectangular (on left)
l*w*h = 2*4*2=16 in³
volume of the rectangular (on the right)
l*w*h = 2*2*6=24 in³
V1+V2 = 16 +24=40 in ³
Answers:
x intercept is (-7.5, 0)
y intercept is (0, 5.5)
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How to get these answers:
Simply look at where the graph crosses the x axis to determine the x intercept. This is directly halfway between the -8 and -7, so the line crosses through -7.5 on the x axis meaning that the x intercept is located at (-7.5, 0)
Similarly, the y intercept is (0, 5.5) as it crosses exactly halfway between the 5 and 6 on the y axis.
Any point is of the form (x,y)
The x intercept always has y = 0. The y intercept always has x = 0.
Answer:
C. 1 / (a(a - 1))
Step-by-step explanation:
View Image
Just know that:
n! = n(n-1)!
= n(n-1)(n-2)!
= n(n-1)(n-2)(n-3)!
= ...
![\bf \begin{array}{ccll} \stackrel{x}{hours}&\stackrel{y}{cost}\\ \cline{1-2} 2&70\\ 5&115 \end{array}~\hspace{10em}(\stackrel{x_1}{2}~,~\stackrel{y_1}{70})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{115}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{115-70}{5-2}\implies \cfrac{45}{3}\implies 15](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bccll%7D%20%5Cstackrel%7Bx%7D%7Bhours%7D%26%5Cstackrel%7By%7D%7Bcost%7D%5C%5C%20%5Ccline%7B1-2%7D%202%2670%5C%5C%205%26115%20%5Cend%7Barray%7D~%5Chspace%7B10em%7D%28%5Cstackrel%7Bx_1%7D%7B2%7D~%2C~%5Cstackrel%7By_1%7D%7B70%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B5%7D~%2C~%5Cstackrel%7By_2%7D%7B115%7D%29%20%5C%5C%5C%5C%5C%5C%20slope%20%3D%20m%5Cimplies%20%5Ccfrac%7B%5Cstackrel%7Brise%7D%7B%20y_2-%20y_1%7D%7D%7B%5Cstackrel%7Brun%7D%7B%20x_2-%20x_1%7D%7D%5Cimplies%20%5Ccfrac%7B115-70%7D%7B5-2%7D%5Cimplies%20%5Ccfrac%7B45%7D%7B3%7D%5Cimplies%2015)
![\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-70=15(x-2)\implies y-70=15x-30 \\\\\\ y=15x+40\impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20%5Ctextit%7Bpoint-slope%20form%7D%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y-y_1%3Dm%28x-x_1%29%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D%5Cimplies%20y-70%3D15%28x-2%29%5Cimplies%20y-70%3D15x-30%20%5C%5C%5C%5C%5C%5C%20y%3D15x%2B40%5Cimpliedby%20%5Cbegin%7Barray%7D%7B%7Cc%7Cll%7D%20%5Ccline%7B1-1%7D%20slope-intercept~form%5C%5C%20%5Ccline%7B1-1%7D%20%5C%5C%20y%3D%5Cunderset%7By-intercept%7D%7B%5Cstackrel%7Bslope%5Cqquad%20%7D%7B%5Cstackrel%7B%5Cdownarrow%20%7D%7Bm%7Dx%2B%5Cunderset%7B%5Cuparrow%20%7D%7Bb%7D%7D%7D%20%5C%5C%5C%5C%20%5Ccline%7B1-1%7D%20%5Cend%7Barray%7D)
as you already know, a direct proportional variation has a constant of variation "k", y = kx, which in this case that'd be the slope, namely 15.
I don't know if this is the answer that you are looking for, but would the answer be all solutions?