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!
The quadratic function given by:
is in vertex form. The graph of 
is a parabola whose axis is the vertical line 
and whose vertex is the point 
. So:
To translate the graph of a function to the right, left, upward or downward we have:
By knowing this things, we can solve our problem as follows:
FIRST.
- Translating <em>11 units to the left:</em>
- Then translating<em> 5 units down:</em>
Since the new function is fatter, the factor we need to multiply the term 
<em>must be</em> less than 1, to make the graph fatter. So, according to our options, there are two factors 1/2 and 2.
<em>Therefore, the right answer is </em><em>b. f(x) = 1/2(x + 11)^2 - 5</em>
SECOND.
- Translating <em>8 units to the right:</em>
- Then translating<em> 1 unit down:</em>
As explained in the previous case, there are two factors 1/3 and 3, so we choose the first one.
<em>Therefore, the right answer is </em><em>a. g(x) = 1/3(x - 8)^2 - 1</em>
Since you have to distribute both numbers, you'll end up with x^2-3x+4x-12 then simplify and it is x^2+x-12
Answer:9a^2+18a-72
Step-by-step explanation:
9(a+1)^2-81
9(a+1)(a+1)-81
Open brackets
9(a^2+a+a+1)-81
9(a^2+2a+1)-81
9a^2+18a+9-81
9a^2+18a-72
Two thirds of the one cup that he added is 80g, so he went over by 48g
