Answer:
$13,793
Step-by-step explanation:
Kate purchased a car for $23,000. It will depreciate by a rate of 12% a year. What is the value of the car in 4 years. *
The formula for Depreciation rate =
y = a(1 - r) ^t
Where
y = Value of the car after t years
a = Initial value of the car = $23,000
t= time in years = 4 years
r = Depreciation rate = 12% = 0.12)
y = $23000 (1 - 0.12)⁴
y = $13792.99328
Approximately = $13,793:
<span><span><span>1. An altitude of a triangle is a line segment from a vertex perpendicular to the opposite side. Find the equations of the altitudes of the triangle with vertices (4, 5),(-4, 1) and (2, -5). Do this by solving a system of two of two of the altitude equations and showing that the intersection point also belongs to the third line. </span>
(Scroll Down for Answer!)</span><span>Answer by </span>jim_thompson5910(34047) (Show Source):You can put this solution on YOUR website!
<span>If we plot the points and connect them, we get this triangle:
Let point
A=(xA,yA)
B=(xB,yB)
C=(xC,yC)
-------------------------------
Let's find the equation of the segment AB
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through AB is
-------------------------------
Let's find the equation of the segment BC
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through BC is
-------------------------------
Let's find the equation of the segment CA
Start with the general formula
Plug in the given points
Simplify and combine like terms
So the equation of the line through CA is
So we have these equations of the lines that make up the triangle
So to find the equation of the line that is perpendicular to that goes through the point C(2,-5), simply negate and invert the slope to get
Now plug the slope and the point (2,-5) into
Solve for y and simplify
So the altitude for vertex C is
Now to find the equation of the line that is perpendicular to that goes through the point A(4,5), simply negate and invert the slope to get
Now plug the slope and the point (2,-5) into
Solve for y and simplify
So the altitude for vertex A is
Now to find the equation of the line that is perpendicular to that goes through the point B(-4,1), simply negate and invert the slope to get
Now plug the slope and the point (-4,1) into
Solve for y and simplify
So the altitude for vertex B is
------------------------------------------------------------
Now let's solve the system
Plug in into the first equation
Add 2x to both sides and subtract 2 from both sides
Divide both sides by 3 to isolate x
Now plug this into
So the orthocenter is (-2/3,1/3)
So if we plug in into the third equation , we get
So the orthocenter lies on the third altitude
</span><span>
</span></span>
Answer:
$125
Step-by-step explanation:
if there was a discount of 20%, the sales price is 100 - 20 = 80% of the original price
let a = original price
this equation can be used to represent the question
a x 0.8 = 100 ]]divide both sides by 0.8
a = 100 / 0.8 = 125
Answer: is it supposed to be 2y+y=4?
Answer:
t(g)= -4g + 20
Step-by-step explanation:
James is playing his favorite game at the arcade. After playing the game 3 times, he has 8 tokens remaining. He initially had 20 tokens, and the game costs the same number of tokens each time. The number tt of tokens James has is a function of gg, the number of games he plays
Solution
Let
g=No. of games James plays
t= No. of tokens James has.
Find the slope using
y=mx + b
Where,
m = Slope of line,
b = y-intercept.
Before James started playing the games, he has a total of 20 tokens.
That is, when g=0, t=20
After James played the games 3 times, he has 8 tokens left
That is, when g=3, t=8
(x,y)
(0,20) (3,8)
m=y2-y1 / x2-x1
=(8-20) / (3-0)
= -12 / 3
m= -4
Slope of the line, m= -4
y=mx + b
No. of tokens left depend on No. of games James plays
t is a function of g.
t(g)
t(g)= -4g + 20
