Answer:
$0.80 per notebook
$0.40 per pencil
Step-by-step explanation:
To find the rate, we need to determine how much each item costs. That is, the cost per item.
Given that,
4 notebooks = $3.20
The cost of 1 notebook/rate = 
Rate = $0.80 per notebook
Given that,
12 pencils = $4.80
The cost of 1 notebook/rate = 
Rate = $0.40 per pencil.
Answer: the value of the car in 2019 is $5269
Step-by-step explanation:
It loses 12% of its value every year. This means that the value of the car is decaying exponentially. We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the value of the car after t years.
t represents the number of years.
P represents the initial value of the car.
r represents rate of decay.
From the information given,
P = $21500
r = 12% = 12/100 = 0.12
t = 2019 - 2008 = 11 years
Therefore
A = 21500(1 - 0.12)^11
A = 21500(0.88)^11
A = 5269
A typical exponential function is y=a

when x=3.5, y=16.2
when x=6, y=3936.6
plug these values into the exponential function:
16.2=a

3936.6=a

divide the second equation by the first to eliminate a:
243=

log both sides: log243=2.5logb
logb=log243/2.5
use your calculator to find b: b=3.6
plug b=3.6 in the first equation to find a:
16.2=a

a=0.183
please double check my calculation
Answer:
x=3,y=7
Step-by-step explanation:
8x+3y=45
2x+3y=27
8x-2x=6x
45-27=18
<u>6</u><u>x</u><u>=</u><u>1</u><u>8</u>
6. 6
x=3
2x+3y=27
2(3)+3y=27
6+3y=27
3y=27-6
<u>3</u><u>y</u> = <u>2</u><u>1</u>
3. 3
y=7
Answer:
-10
-5
5
Step-by-step explanation:
From the answers given, you probably mean f(x) = x^3 + 10x2 – 25x – 250
The Remainder Theorem is going to take a bit to solve.
You have to try the factors of 250. One way to make your life a lot easier is to graph the equation. That will give you the roots.
The graph appears below. Since the y intercept is -250 the graph goes down quite a bit and if you show the y intercept then it will not be easy to see the roots.
However just to get the roots, the graph shows that
x = -10
x = - 5
x = 5
The last answer is the right one. To use the remainder theorem, you could show none of the answers will give 0s except the last one. For example, the second one will give
f((10) = 10^3 + 10*10^2 - 25*10 - 250
f(10) = 1000 + 1000 - 250 - 250
f(10) = 2000 - 500
f(10) = 1500 which is not 0.
==================
f(1) = (1)^3 + 10*(1)^2 - 25(1) - 250
f(1) = 1 + 10 - 25 - 250
f(1) = -264 which again is not zero