Answer:
The constant between two consecutive terms is called the common difference. The common difference is the number added to any one term of an arithmetic sequence that generates the subsequent term.
Hey there!
When the value of something goes down over time- a house, a car, anything- it's called depreciation.
It would be expressed as exponential decay. This is because the value is going down exponentially as stated in the problem. Additionally, when it decays, the growth factor is less than one, so the value steadily decreases.
Let's rule out our other options:
B) Half-Life. This doesn't work because it's usually used for radioactive decay, which is usually a steady decrease of radioactivity and material that divides by two, hence the word half. For example:
Day 0) Started with 10 grams of plutonium
Day 1) 5 grams
Day 2) 2.5 grams
And so on.
C) Compound Interest. Like simple interest, but compunds usually at a certain point - yearly, monthly, every ten years, and so on. But, this is used for interest, mostly in a bank account or if you have a loan. It doesn't exhibit depreciation, and therefore it's not used to predict car value.
D) Exponential Growth- Exponential growth does not work for one main reason - it grows. That would mean that the value of the car goes up- and unless it's an old and very expensive car, that wouldn't be the case.
Hope this helps!
Original coordinates of the points:
A (8,15) ; B (12,13) ; C (8,10)
Dilated scale factor of 3.
A ⇒ 3x = 3(8) = 24 ; 3y = 3(15) = 45 ⇒ A' (24,45)
B ⇒ 3x = 3(12) = 36 ; 3y = 3(13) = 39 ⇒ B' (36, 39)
C ⇒ 3x = 3(8) = 24 ; 3y = 3(10) = 30 ⇒ C' (24, 30)
The given image forms a right triangle. So, I'll get the short leg and long leg of the right triangle to solve for the hypotenuse, length of CB.
Short leg: y value of B and C
39 - 30 = 9
Long leg: x value of B and C
36 - 24 = 12
a² + b² = c²
9² + 12² = c²
81 + 144 = c²
225 = c²
√225 = √c²
15 = c
The length of CB is 15 units.
