Say you're making a recipe that needs 2 1/2 cups of water. But you want to make two servings, so you need to know what 2 1/2 + 2 1/2 equals. Or maybe you need a half cup of milk but you don't have enough. You need to know how much left you need so you can buy or borrow the right amount.
Answer:
5 bottle caps each second
Step-by-step explanation:
To find the unit rate, just divide the total number by the total time.
150/30
5
So 5 bottle caps per second
keeping in mind that perpendicular lines have <u>negative reciprocal</u> slopes, hmmm what's the slope of y=2/3x-1 anyway?
![\bf \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}~\hspace{7em}y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{2}{3}}x-1 \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%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~%5Chspace%7B7em%7Dy%3D%5Cstackrel%7B%5Cstackrel%7Bm%7D%7B%5Cdownarrow%20%7D%7D%7B%5Ccfrac%7B2%7D%7B3%7D%7Dx-1%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
so, notice, "one of his mistakes" is that he used 3/2 as the slope, not -3/2.
so, we're really looking for a line whose slope is -3/2 and runs through (-7, 1/2).
![\bf (\stackrel{x_1}{-7}~,~\stackrel{y_1}{\frac{1}{2}})~\hspace{10em} slope = m\implies -\cfrac{3}{2} \\\\\\ \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-\cfrac{1}{2}=-\cfrac{3}{2}[x-(-7)]\implies y-\cfrac{1}{2}=-\cfrac{3}{2}(x+7) \\\\\\ y-\cfrac{1}{2}=-\cfrac{3}{2}x-\cfrac{21}{2}\implies y=-\cfrac{3}{2}x-\cfrac{21}{2}+\cfrac{1}{2}\implies y=-\cfrac{3}{2}x-10](https://tex.z-dn.net/?f=%5Cbf%20%28%5Cstackrel%7Bx_1%7D%7B-7%7D~%2C~%5Cstackrel%7By_1%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D%29~%5Chspace%7B10em%7D%20slope%20%3D%20m%5Cimplies%20-%5Ccfrac%7B3%7D%7B2%7D%20%5C%5C%5C%5C%5C%5C%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-%5Ccfrac%7B1%7D%7B2%7D%3D-%5Ccfrac%7B3%7D%7B2%7D%5Bx-%28-7%29%5D%5Cimplies%20y-%5Ccfrac%7B1%7D%7B2%7D%3D-%5Ccfrac%7B3%7D%7B2%7D%28x%2B7%29%20%5C%5C%5C%5C%5C%5C%20y-%5Ccfrac%7B1%7D%7B2%7D%3D-%5Ccfrac%7B3%7D%7B2%7Dx-%5Ccfrac%7B21%7D%7B2%7D%5Cimplies%20y%3D-%5Ccfrac%7B3%7D%7B2%7Dx-%5Ccfrac%7B21%7D%7B2%7D%2B%5Ccfrac%7B1%7D%7B2%7D%5Cimplies%20y%3D-%5Ccfrac%7B3%7D%7B2%7Dx-10)
Answer:
UW = 36 units
Step-by-step explanation:
The question is incomplete. Here is the complete question
Point V lies between points U and W on Line segment U W. A line has points U, V, W. The length between U V is 2 x minus 4. The length between V W is 4 x + 10. If UW = 9x – 9, what is UW in units?
If a point V lies between points U and W on line segment UW, then based on vector notation, UV + VW = UW.
Given parameters
The length between U and V i.e UV = 2x-4
The length between V and W i.e VW= 4x + 10.
UW = 9x – 9
Required
The length between U and W in units
Since UW = UV+VW, we will substitute the given functions into the formula as shown;
9x-9 = 2x-4+4x + 10.
9x-9 = 2x+4x-4+10
9x-9 = 6x+6
collect like terms on both sides;
9x-6x = 6+9
3x = 15
x = 15/3
x = 5
Substitute x = 5 into the function UW = 9x-9 to ge the length of UW in units.
UW = 9(5)-9
UW = 45-9
UW = 36 units
<em>Hence the required length between line segment U and W in units is 36units.</em>
Answer:171 and 172
Step-by-step explanation;
171+172=343
