Answer:
The two linear equations are the same line
Step-by-step explanation:
two different linear equations can only possibly intersect at one point. once the two lines intersect, they cannot curve back to intersect once again.
The rule for this sequence is n + 3.
132 --> 135 is +3,
135 --> 138 is +3,
and 138 --> 141 is +3.
Let's use this rule until we find the 13th term.
132 (1)
135(2)
138(3)
141(4)
144(5)
147(6)
150(7)
153(8)
156(9)
159(10)
162(11)
165(12)
168(13)
168 is the 13th term in this sequence.
I hope this helps!
Answer:
s > 42
Step-by-step explanation: INCOMPLETE QUESTION, PROBLEM STATEMENT DOES NOT GIVE THE MODELING FUNCTION.
I´VE FOUND IN NTERNET PROFIT
p(s) = s² + 9*s - 142
Then we have
s² + 9*s - 142 > 2000
rearrange that inequation
s² + 9*s - 142 > 2000 ⇒ s² + 9*s - 2142 > 0
we complete the expression as a perfect quadratic, with the help of two number that add +9 and multiplying - 2142
Numbers are 51 and - 42
then
factoring that expression as a perfect quadratic
( s + 51 )* ( s - 42 ) > 0
For what have two solution, and we dismiss the negative value since the numbers of shirts could not be negative, we get
s - 42 > 0
s > 42 the solution
Y = 6 x² + 12 x - 10= 6 ( x² + 2 x ) - 10 = 6 ( ( x² + 2 x + 1 ) - 1 ) - 10=
6 ( x + 1 )² - 6 - 10 = 6 ( x + 1 )² - 16 ( vertex form)
recall your d = rt, distance = rate * time.
j = jet's rate
w = wind's rate
so with the wind the actual speed of the Jet is really j + w, because the wind is adding speed to it, and against it is j - w, since the wind is eroding speed from it.
![\bf \begin{array}{lcccl} &\stackrel{miles}{distance}&\stackrel{mph}{rate}&\stackrel{hours}{time}\\ \cline{2-4}&\\ \textit{against the wind}&8730&j-w&9\\ \textit{with the wind}&7260&j+w&6 \end{array}~\hfill \begin{cases} 8730=(j-w)(9)\\ 7260=(j+w)(6) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{using the 1st equation}}{\cfrac{8730}{9}=j-w\implies }970=j-w\implies 970+w=j \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blcccl%7D%20%26%5Cstackrel%7Bmiles%7D%7Bdistance%7D%26%5Cstackrel%7Bmph%7D%7Brate%7D%26%5Cstackrel%7Bhours%7D%7Btime%7D%5C%5C%20%5Ccline%7B2-4%7D%26%5C%5C%20%5Ctextit%7Bagainst%20the%20wind%7D%268730%26j-w%269%5C%5C%20%5Ctextit%7Bwith%20the%20wind%7D%267260%26j%2Bw%266%20%5Cend%7Barray%7D~%5Chfill%20%5Cbegin%7Bcases%7D%208730%3D%28j-w%29%289%29%5C%5C%207260%3D%28j%2Bw%29%286%29%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Busing%20the%201st%20equation%7D%7D%7B%5Ccfrac%7B8730%7D%7B9%7D%3Dj-w%5Cimplies%20%7D970%3Dj-w%5Cimplies%20970%2Bw%3Dj%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf \stackrel{\textit{using the 2nd equation}}{\cfrac{7260}{6}=j+w}\implies 1210=j+w\implies \stackrel{\textit{doing some substitution on \underline{j}}}{1210=(970+w)+w} \\\\\\ 1210=970+2w\implies 240=2w\implies \cfrac{240}{2}=w\implies \boxed{120=w} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know that}}{970+w=j}\implies 970+120=j\implies \boxed{1090=j}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Busing%20the%202nd%20equation%7D%7D%7B%5Ccfrac%7B7260%7D%7B6%7D%3Dj%2Bw%7D%5Cimplies%201210%3Dj%2Bw%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bdoing%20some%20substitution%20on%20%5Cunderline%7Bj%7D%7D%7D%7B1210%3D%28970%2Bw%29%2Bw%7D%20%5C%5C%5C%5C%5C%5C%201210%3D970%2B2w%5Cimplies%20240%3D2w%5Cimplies%20%5Ccfrac%7B240%7D%7B2%7D%3Dw%5Cimplies%20%5Cboxed%7B120%3Dw%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Bwe%20know%20that%7D%7D%7B970%2Bw%3Dj%7D%5Cimplies%20970%2B120%3Dj%5Cimplies%20%5Cboxed%7B1090%3Dj%7D)
