We can start from the given line's coefficients and translate the line from the origin to the given point.
4(x -(-2)) -(y -3) = 0
4x +8 -y +3 = 0
The equation of the desired line is ...
4x -y = -11
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For standard form line ax+by=c, any parallel line will have only a different value of c. For c=0, the line goes through the origin (0, 0). To make it go through point (h, k) we can write it as
a(x-h) +b(y-k) = 0
which is completely equivalent to
ax +by = ah +bk
We can start to solve this problem by using what we know. The recipe calls for 2/3 cup of flour per 1/4 batch of cookies. Now, If we want to write the rate as a complex fraction, we can replace the per with a division sign. This makes it become (2/3)/(1/4) or
Answer:
(c) $3,93 more
(b) Mr. Sánchez's class earned more money.
(a) ![\displaystyle [42, 37] → [j, p]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5B42%2C%2037%5D%20%E2%86%92%20%5Bj%2C%20p%5D)
Step-by-step explanation:
{79 = p + j
{118,17 = 1,65p + 1,36j
−25⁄34[118,17 = 1,65p + 1,36j]
{79 = p + j
{−86 121⁄136 = −1 29⁄136p - j >> New Equation
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[Plug this back into both equations above to get the j-value of 42]; 
The next step is to plug the solution into the BOTTOM EQUATION to calculate the total money earned for each class:
<u>Sánchez's class</u>
![\displaystyle 61,05 = [37][1,65]](https://tex.z-dn.net/?f=%5Cdisplaystyle%2061%2C05%20%3D%20%5B37%5D%5B1%2C65%5D)
Altogether, <em>thirty-seven</em> fruit pies cost $61,05.
<u>Kelly's</u><u> </u><u>class</u>
![\displaystyle 57,12 = [42][1,36]](https://tex.z-dn.net/?f=%5Cdisplaystyle%2057%2C12%20%3D%20%5B42%5D%5B1%2C36%5D)
Altogether, <em>forty-two</em> bottles of fruit juice cost $57,12.
* Based on the calculation, it is perfectly clear that Mr. Sánchez's class earned more money by $3,93:
I am delighted to assist you anytime my friend!
This problem lends itself to the binomial probability approach.
Focus on students who are not secretly robots.
Then P(student is not a robot) = 2/6, or 1/3. Here n=6 and x=2.
Then the desired probability is binompdf(6,1/3, 2), which, by calculator, comes out to 0.329.
law's of exponents
e^(x-5)*e^(3x+8) = 19
e^(x-5+3x+8) = 19
e^(4x+3) = 19
take the natural log, which is base "e" of both sides.
ln[e^(4x+3)] = ln[19]
4x +3 = ln[19]
4x = ln[19] - 3
x = (ln[19] - 3) / 4
x = -0.0139
