Answer:
3
Step-by-step explanation:
Given the 2 equations
2x + 3y = 9 → (1)
- 2x + 2y = 6 → (2)
Adding the 2 equations term by term will eliminate x
(2x - 2x) + (3y + 2y) = (9 + 6), that is
5y = 15 ( divide both sides by 5 )
y = 3
Answer:
30/35=85.71%
Step-by-step explanation:
Observations with A,B,C: 30
Total Observations: 35
![\bf ~~~~~~~~~~~~\textit{angle between two vectors } \\\\ cos(\theta)=\cfrac{\stackrel{\textit{dot product}}{u \cdot v}}{\stackrel{\textit{magnitude product}}{||u||~||v||}} \implies \measuredangle \theta = cos^{-1}\left(\cfrac{u \cdot v}{||u||~||v||}\right) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} u=i+\sqrt{7}j\implies &\\\\ v=-i+9j\implies & \end{cases} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bangle%20between%20two%20vectors%20%7D%20%5C%5C%5C%5C%20cos%28%5Ctheta%29%3D%5Ccfrac%7B%5Cstackrel%7B%5Ctextit%7Bdot%20product%7D%7D%7Bu%20%5Ccdot%20v%7D%7D%7B%5Cstackrel%7B%5Ctextit%7Bmagnitude%20product%7D%7D%7B%7C%7Cu%7C%7C~%7C%7Cv%7C%7C%7D%7D%20%5Cimplies%20%5Cmeasuredangle%20%5Ctheta%20%3D%20cos%5E%7B-1%7D%5Cleft%28%5Ccfrac%7Bu%20%5Ccdot%20v%7D%7B%7C%7Cu%7C%7C~%7C%7Cv%7C%7C%7D%5Cright%29%20%5C%5C%5C%5C%5B-0.35em%5D%20%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%20%5Cbegin%7Bcases%7D%20u%3Di%2B%5Csqrt%7B7%7Dj%5Cimplies%20%26%3C1%2C%5Csqrt%7B7%7D%3E%5C%5C%5C%5C%20v%3D-i%2B9j%5Cimplies%20%26%3C-1%2C9%3E%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf u\cdot v\implies (1)(-1)~+~(\sqrt{7})(9)\implies -1+9\sqrt{7}\implies 9\sqrt{7}-1~\hfill dot~product \\\\[-0.35em] ~\dotfill\\\\ ||u||\implies \sqrt{1^2+(\sqrt{7})^2}\implies \sqrt{1+7}\implies \sqrt{8}~\hfill magnitudes \\\\\\ ||v||\implies \sqrt{(-1)^2+9^2}\implies \sqrt{1+81}\implies \sqrt{82} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20u%5Ccdot%20v%5Cimplies%20%281%29%28-1%29~%2B~%28%5Csqrt%7B7%7D%29%289%29%5Cimplies%20-1%2B9%5Csqrt%7B7%7D%5Cimplies%209%5Csqrt%7B7%7D-1~%5Chfill%20dot~product%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%7C%7Cu%7C%7C%5Cimplies%20%5Csqrt%7B1%5E2%2B%28%5Csqrt%7B7%7D%29%5E2%7D%5Cimplies%20%5Csqrt%7B1%2B7%7D%5Cimplies%20%5Csqrt%7B8%7D~%5Chfill%20magnitudes%20%5C%5C%5C%5C%5C%5C%20%7C%7Cv%7C%7C%5Cimplies%20%5Csqrt%7B%28-1%29%5E2%2B9%5E2%7D%5Cimplies%20%5Csqrt%7B1%2B81%7D%5Cimplies%20%5Csqrt%7B82%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
make sure your calculator is in Degree mode.
Answer:
The midpoint of the x-intercepts of the function is (0, 0)
Step-by-step explanation:
Notice that since the function comes in factor form, we know that its roots (which are actually the intercepts the function has with the x-axis) are: x = 4 and x = -4 (the x-values for which the function renders zero).
These two points are equidistant from the origin of coordinates (0, 0), and therefore the midpoint of these x-intercepts is (0, 0).
Answer = $160
Using the formula 100+4n, we need to substitute 15 with n. Therefore making the formula, 100 + 4×15. 4×15 = 60. 60+100= $160.
-Hope it helps!
