![\bf 2=x^2+5x\implies 0=x^2+5x-2\\\\\\\qquad \qquad \qquad \textit{discriminant of a quadratic}\\\\\\0=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+5}x\stackrel{\stackrel{c}{\downarrow }}{-2}~~~~~~~~\stackrel{discriminant}{b^2-4ac}=\begin{cases}0&\textit{one solution}\\positive&\textit{two solutions}\\negative&\textit{no solution}\end{cases}\\\\\\(5)^2-4(1)(-2)\implies 25+8\implies 33](https://tex.z-dn.net/?f=%20%5Cbf%202%3Dx%5E2%2B5x%5Cimplies%200%3Dx%5E2%2B5x-2%5C%5C%5C%5C%5C%5C%5Cqquad%20%5Cqquad%20%5Cqquad%20%5Ctextit%7Bdiscriminant%20of%20a%20quadratic%7D%5C%5C%5C%5C%5C%5C0%3D%5Cstackrel%7B%5Cstackrel%7Ba%7D%7B%5Cdownarrow%20%7D%7D%7B1%7Dx%5E2%5Cstackrel%7B%5Cstackrel%7Bb%7D%7B%5Cdownarrow%20%7D%7D%7B%2B5%7Dx%5Cstackrel%7B%5Cstackrel%7Bc%7D%7B%5Cdownarrow%20%7D%7D%7B-2%7D~~~~~~~~%5Cstackrel%7Bdiscriminant%7D%7Bb%5E2-4ac%7D%3D%5Cbegin%7Bcases%7D0%26%5Ctextit%7Bone%20solution%7D%5C%5Cpositive%26%5Ctextit%7Btwo%20solutions%7D%5C%5Cnegative%26%5Ctextit%7Bno%20solution%7D%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%285%29%5E2-4%281%29%28-2%29%5Cimplies%2025%2B8%5Cimplies%2033%20)
so we have a 33, namely two real solutions for that quadratic.
usually that number goes into a √, if you have covered the quadratic formula, you'd see it there, namely that'd be equivalent to √(33), now 33 is a prime number, and √(33) is yields an irrational value, specifically because a prime number is indivisible other than by itself or 1.
so 33 can only afford us two real irrational roots.
Answer:
Independent variable- subway cost
dependent variable- nias money ($19.50)
Step-by-step explanation:
I believe the equation is 3x-50
hope this helps (:
Answer:
2 miles per hours
Step-by-step explanation:
You divide 1/3 mile by 1/6 hour
Use the reciprocal.
1/3 x 6/1 = 2/1
Simplify
2/1 = 2
You can also solve it this way:
If 1/6 hour is 10 minutes, and it takes 10 minutes to walk 1/3 a mile, then it would take 30 minutes to walk a mile.
30 x 2 = 60
Either way, Richard walks 2 miles per hour.
The slope of the first equation has a slope of one and a y intercept of -4. The second equation has a y intercept of -2.3333 as seen when plugging in 0 for x, so the same y-intercept and same line are out of the question. This means either they have the same slope and thus are parallel or intersect at some point. A simple way to find out? Plug in 1 for x on the second. If it isn't -1.33333, which is a slope of positive 1 such as in the first equation, they WILL INTERSECT somewhere. When plugging in 1, we get
3y - 1 = -7
3y = -6
y = -2
(1, -2) is the next point after (0, -2.3333)
That means it is most certainly not the same slope, and thus they will intersect at some point. The two slopes are 1/1 and 1/3 if you weren't aware.