Mathematics, 04.03.2021 21:50 tiffanibell71

You purchase a new car for $12,000 in 2013. After one year (in 2014), the dealership you purchased the car from says it is valued at $10,112.
a. Is this situation growth or decay?
b. What is the growth factor or decay factor? Round to three decimal places.
c. What is the percent change? Round to the nearest tenth of a percent.
%
d. Write a function to determine the value of the car V given the number of years t after
its purchase. V =
(
Dt
e. In what year will the car be worth about $3,500?
It

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Answer from: Quest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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step-by-step explanation:

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

Answer from: Quest

$r(x)=-\frac{1}{50}x^2+14x$

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

$x=200,p=10$

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

$m=-\frac{1}{50}$

now, we can use point slope form of line

$p(x)=mx+b$

now, we can plug values

$p(x)=-\frac{1}{50}x+b$

we can use point

$x=200,p=10$

and find b

$10=-\frac{1}{50}\times 200+b$

$10=-4+b$

$b=14$

now, we can plug it back

and we get

$p(x)=-\frac{1}{50}x+14$

now, we can find revenue

we know that

revenue = price*quantity

so, we get

$r(x)=x\times p(x)$

$r(x)=x\times (-\frac{1}{50}x+14)$

$r(x)=-\frac{1}{50}x^2+14x$

Answer from: Quest

answer: - (a) $a_n=16+6n$

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term= $a_1 =22$

second term= $a_2 =28$

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula : $a_n=a_1+(n-1)(d)$

$a_n=22+(n-1)6\\\rightarrow\ a_n=22+6n-6\\\rightarrow\ a_n=16+6n$

b) let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

$a_{12} = 16+6\times12\\\rightarrow\ a_{12}=16+72\\\rightarrow\ a_{12}=88\ seats$

∴there are 88 seats in 12 rows.

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You purchase a new car for $12,000 in 2013. After one year (in 2014), the dealership you purchased...

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