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mcalepcrager
22.07.2019 •
Mathematics
Maya's school held an aluminum collection program in which they collected aluminum and brought it to be recycled. in the first week, maya collected 4/20 lb of aluminum and her friend abigail collected 7/8 lb. a. which girl collected more aluminum? b. how much aluminum did the two girls collect?
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Ответ:
Ответ:
The y-intercept of AB is (4/3) and the equation of BC is y = (-1/6) x + (4/3)
If the y-coordinate of point C is 13, its x-coordinate is 4.
=====================================
Step-by-step explanation:
AB and BC form a right angle at their point of intersection, B.
So, AB ⊥ BC
A = (14 , -1) , B = (2,1)
Part A: Find the y-intercept of AB.
The general equation of the line y = mx + c
Where: m is the slope and c is constant represents y-intercept.
m = (y₂ - y₁)/(x₂ - x₁)
m =![\frac{1 - (-1)}{2-14} = \frac{2}{-12} = - \frac{1}{6}](/tpl/images/0460/3655/5c74e.png)
y = (-1/6) x + c
Substitute with the point (2,1) to find c
1 = (-1/6) * 2 + c
c = 1 + 2 *(1/6) = 4/3
y = (-1/6) x + 4/3
So, the y-intercept of AB is 4/3
=======================================
Part B: Find the equation of BC.
BC ⊥ AB at point B
if m is the slope of AB, the slope of BC = (-1/m)
m = (-1/6)
So, the slope of BC = (-1/m) = 6
The equation of the line BC ⇒ y = 6x + c
Substitute with the point (2,1) to find c
1 = 6 * 2 + c
c = 1 - 12 = -11
y = 6x - 11
=========================================
Part C: Find x-coordinate of C if y-coordinate of point C is 13.
The equation of the BC is y = 6x - 11
Substitute with the y-coordinate of point C = 13
13 = 6x - 11
6x = 13 + 11 = 24
x = 24/6 = 4