i) The coefficients of the equation of the line are a = 20 / 3 and b = 160 / 21.
ii) The equation of the line in <em>standard</em> form is (20 / 3) · x + (160 / 21) · y = - 20.
iii) The x-intercept and y-intercept of the line are (- 3, 0) and (0, - 21 / 8).
iv) Two alternative solutions of the equation of the line are 20 · x + (160 / 7) · y = - 60 and 140 · x + 160 = 420.
<h3>How to derive the equation of a line?</h3>
In this problem we know that form of an equation of the line and two points, on which the line pass through. i) We determine the values of the coefficients a and b by solving the following system of <em>linear</em> equations:
5 · a - 7 · b = - 20
- 3 · a = - 20
Whose solution is a = 20 / 3 and b = 160 / 21.
ii) The equation of the line in <em>standard</em> form is (20 / 3) · x + (160 / 21) · y = - 20.
iii) Now we find the coordinates of the intercepts of the line:
x-Intercept
(20 / 3) · x = - 20
x = - 3
y-Intercept
(160 / 21) · y = - 20
y = - 21 / 8
iv) We can find two alternative solutions by using multiples:
20 · x + (160 / 7) · y = - 60
140 · x + 160 = 420
To learn more on equations of the line: brainly.com/question/21511618
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Answer:
n = (2 i π k)/log(3) - 2 for k element Z
Step-by-step explanation:
Solve for n:
3^n = 1/9
Take the logarithm base 3 of both sides:
Answer: n = (2 i π k)/log(3) - 2 for k element Z
2³-4²
= 8-16
=-8
Hopefully this helps! Good luck! :)
I hope this helps you
8.10+8.3+8.5v-2v
80+24+40v-2v
104+38v
Answer:
a. y = x + 3
Step-by-step explanation:
All three ordered pairs satisfy the first equation.
___
If you want to look into it a little further, you can notice that if you sort the ordered pairs by their x-values, you get ...
(-1, 2), (0, 3), (1, 4)
That is, the y-values increase (by 1) as the x-values increase (by 1).
All of the other answer choices have -1 as the coefficient for x, which means the y-values will decrease as x increases. None of these choices (b–d) is viable.