Answer:
Consider points (-1, 0) and (0, 1) :
![{ \tt{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ { \tt{slope = \frac{1 - 0}{0 - ( - 1)} }} \\ { \boxed{ \bf{slope = 1}}}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7Bslope%20%3D%20%20%5Cfrac%7By%20_%7B2%7D%20%20-%20y%20_%7B1%7D%20%7D%7Bx%20_%7B2%7D%20-%20x%20_%7B1%7D%20%7D%20%7D%7D%20%5C%5C%20%7B%20%5Ctt%7Bslope%20%3D%20%20%5Cfrac%7B1%20-%200%7D%7B0%20-%20%28%20-%201%29%7D%20%7D%7D%20%5C%5C%20%7B%20%5Cboxed%7B%20%5Cbf%7Bslope%20%3D%201%7D%7D%7D)
Answer: y=-2
Step-by-step explanation: y=-2 is a horizontal line containing the points (2,-2) and (0,-2).
Answer:
2541 peanut cookies were sold
Step-by-step explanation:
A system of equations can be written to match the problem description. Let p and c represent the initial numbers of peanut and chocolate cookies, respectively. Then we have ...
p - c = 1820 . . . . Lyn had 1820 more peanut cookies
After selling 35% of her peanut cookies, Lyn had 1-0.35 = 0.65 of the original number left. Likewise, after selling 15% of her chocolate cookies, she had 1-0.15 = 0.85 of the original number left. Then after the sales, the difference in cookie count was 95:
0.65p -0.85c = 95
We only need to know the original number of peanut cookies (p), so we can use Cramer's rule to find the solution for p.
p = (-95 +0.85·1820)/(-0.65+0.85) = 1452/0.20 = 7260
The original number of peanut cookies Lyn had was 7260, so the number she sold is ...
0.35 · 7260 = 2541
_____
Cramer's rule says the solution to ...
ax +by =c
dx +ey =f
is given by ...
x = (ec-bf)/(ea-bd)
y = (fa-cd)/(ea-bd)
9514 1404 393
Answer:
{∛2e^(iπ), ∛2·e^(iπ/3), ∛2·e^(-iπ/3)}
Step-by-step explanation:
![\displaystyle \sqrt[3]{z}=(2e^{i\pi})^{\frac{1}{3}}=(2e^{i(2n+1)\pi})^{\frac{1}{3}}=\sqrt[3]{2}\cdot e^{i(2n+1)\pi/3}\quad\text{for $n=\{-1,0,1\}$}\\\\=\{\sqrt[3]{2}\cdot e^{-i\pi/3},\sqrt[3]{2}\cdot e^{i\pi/3},\sqrt[3]{2}\cdot e^{i\pi}\}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5B3%5D%7Bz%7D%3D%282e%5E%7Bi%5Cpi%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%282e%5E%7Bi%282n%2B1%29%5Cpi%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7B2%7D%5Ccdot%20e%5E%7Bi%282n%2B1%29%5Cpi%2F3%7D%5Cquad%5Ctext%7Bfor%20%24n%3D%5C%7B-1%2C0%2C1%5C%7D%24%7D%5C%5C%5C%5C%3D%5C%7B%5Csqrt%5B3%5D%7B2%7D%5Ccdot%20e%5E%7B-i%5Cpi%2F3%7D%2C%5Csqrt%5B3%5D%7B2%7D%5Ccdot%20e%5E%7Bi%5Cpi%2F3%7D%2C%5Csqrt%5B3%5D%7B2%7D%5Ccdot%20e%5E%7Bi%5Cpi%7D%5C%7D)
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<em>Additional comment</em>
z = -2. ∛z will be three points in the complex plane on a circle of radius ∛2 at angles ±π/3 and π radians (±60° and 180°). That is, the real cube root of -2 is -∛2.
Answer: B
Step-by-step explanation:
We can find the correct equation by finding the x-intercepts, or the zeroes.
To find the x-intercept, you have to make the y's value = 0. If y on the graph is zero, the x-intercept is (-1,0) and (3,0).
Then look at the equations and see which one has -1 and 3 as the values of x.
The answer is B.