Answer:
!!!
Step-by-step explanation:
The slope of a line perpendicular to another line has a
slope which is the negative reciprocal of that line or:
m1 = -1/m2
First, we convert the given equation into slope-intercept
form of a line: y = mx + b
8x + 15y = 12
15y = -8x + 12
y = (-8/15) x + 0.8
m1 = -8 / 15
Therefore the slope of the perpendicular line is:
m2 = 15 / 8
Since the perpendicular line crosses the point (11, 17), therefore
using the slope formula:
m = (y2 – y1) / (x2 – x1)
15 / 8 = (y2 – 17) / (x2 – 11)
1.875 (x2 – 11) = y2 – 17
1.875 x2 – 20.625 = y2 – 17
y2 = 1.875 x2 – 3.625
y = (15/8) x – 3.625
multiplying both sides by 8:
8y = 15x – 29
rewriting in standard form:
<span>15x – 8y = 29 (ANSWER)</span>
Answer:
Step-by-step explanation:
Part 1:
Given that a<span>
store had 235 MP3 players in the month of January and that every month, 30% of
the MP3 players were sold and 50 new MP3 players were stocked in the
store.
</span>The number of MP3 players in the store after the previous months sale is given by 0.7f(n - 1) and <span>the number of MP3 players in the store after new MP3 were added is 0.7f(n - 1) + 50.
Therefore, the </span><span>recursive function that best represents the number of MP3 players in the store f(n) after n months is given by </span><span>f(n) = 0.7 x f(n − 1) + 50, f(0) = 235, n > 0
Part 2:
The average rate of change of a function from a to b is given by
![average \ rate \ of \ change= \frac{f(b)-f(a)}{b-a}](https://tex.z-dn.net/?f=average%20%5C%20rate%20%5C%20of%20%5C%20change%3D%20%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%20)
Given that the </span><span>equation showing the value of her investment after x years is given by
![f(x)=500(1.05)^x](https://tex.z-dn.net/?f=f%28x%29%3D500%281.05%29%5Ex%20)
Thus, </span><span>the average rate of change of the value of Sophia's investment from the second year to the fourth year is given by
![Average \ rate \ of \ change= \frac{f(4)-f(2)}{4-2} \\ \\ = \frac{500(1.05)^4-500(1.05)^2}{2} = \frac{607.75-551.25}{2} \\ \\ = \frac{56.5}{2} =28.25](https://tex.z-dn.net/?f=Average%20%5C%20rate%20%5C%20of%20%5C%20change%3D%20%5Cfrac%7Bf%284%29-f%282%29%7D%7B4-2%7D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B500%281.05%29%5E4-500%281.05%29%5E2%7D%7B2%7D%20%3D%20%5Cfrac%7B607.75-551.25%7D%7B2%7D%20%20%5C%5C%20%20%5C%5C%20%3D%20%5Cfrac%7B56.5%7D%7B2%7D%20%3D28.25)
Therefore, the </span><span>average rate of change of the value of Sophia's investment from the second year to the fourth year is 28.25 dollars per year.</span>
Don’t trust my word I just need to answer questions i’m so sorry