The given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.
The given function is f(z)=3z-8.
We need to find the value of f(-4), f(2), f(z-7).
<h3>What is a function?</h3>
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Now to find f(-4), replace z from -4.
f(-4)=3(-4)-8=-12-8=-20
Now to find f(2), replace z from 2.
f(2)=3(2)-8=6-8=-2
Now to find f(z-7), replace z from z-7.
f(z-7)=3(z-7)-8=3z-21-8=3z-29.
Therefore, the given function is f(z)=3z-8 for the values f(-4), f(2) and f(z-7) respectively -20, -2 and 3z-29 respectively.
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Answer: 10
Step-by-step explanation:
10+10 = 20
10 x 10 = 100
mi would do another but i supposed to be in class :P
The explanation for this is one of my favorite pieces of mathematical reasoning. First, let's thing about distance; what's the shortest distance between two points? <em>A straight line</em>. If we just drew a straight line between A and B, though, we'd be missing a crucial element of the original problem: we also need to pass through a point on the line (the "river"). Here's where the mathemagic comes in.
If we take the point B and <em>reflect it over the line</em>, creating the point B' (see picture 1), we can draw a line straight from A to B' that passes through a point on the line. Notice the symmetry here; the distance from the intersection point to B' is<em> the same as its distance to B</em>. So, if we reflect that segment back up, we'll have a path to B, and because it came from of the line segment AB', we know that it's <em>the shortest possible distance that includes a point on the line</em>.
If we apply this same process to our picture, we see that the line segment AB' crosses the line
at the point (1, 1)
Ok so u have to multiply for this one
Work *Jake*:
So he spends 2 hours on each assignment. He has 3 assignments so u have to do :
2*3=6
He spend 6 hours a day doing home work so now u have to multiply that by 30:
6*30=180
Work *Orlando*:
So he spends 2 hours on each homework. He has 2 sheets each do so u have to multiply 2 and 2:
2*2=4
He spends 4 hours a day doing homwork so u have to multiply it by 30:
4*30=120
Answer:
So Jake spends 130 hours
Orlando spends 120 hours
Add both together:
120+130=250
They spend 250 hours together on work in 30 days/
A geometric sequence is defined by a starting point,
, and a common ratio 
The first term is
, and you get every next term by multiplying the previous one by r.
So, our terms are
![\left[\begin{array}{c|c}a_1&a\\a_2&ar\\a_3&ar^2\\a_4&ar^3=-12\\a_5&ar^4=-6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Cc%7Da_1%26a%5C%5Ca_2%26ar%5C%5Ca_3%26ar%5E2%5C%5Ca_4%26ar%5E3%3D-12%5C%5Ca_5%26ar%5E4%3D-6%5Cend%7Barray%7D%5Cright%5D)
We can see that when we pass from
to
the number gets halved (
)
This implies that the common ratio is 
So, the table becomes
![\left[\begin{array}{c|c}a_1&a\\a_2&\frac{1}{2}a\\a_3&\frac{1}{4}a\\a_4&\frac{1}{8}a=-12\\a_5&\frac{1}{16}a=-6\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Cc%7Da_1%26a%5C%5Ca_2%26%5Cfrac%7B1%7D%7B2%7Da%5C%5Ca_3%26%5Cfrac%7B1%7D%7B4%7Da%5C%5Ca_4%26%5Cfrac%7B1%7D%7B8%7Da%3D-12%5C%5Ca_5%26%5Cfrac%7B1%7D%7B16%7Da%3D-6%5Cend%7Barray%7D%5Cright%5D)
So, we can derive the starting point from either
or
:

The sequence is thus
![\left[\begin{array}{c|c}a_1&-96\\a_2&-48\\a_3&-24\\a_4&-12\\a_5&-6\\a_6&-3\\\vdots&\vdots\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Cc%7Da_1%26-96%5C%5Ca_2%26-48%5C%5Ca_3%26-24%5C%5Ca_4%26-12%5C%5Ca_5%26-6%5C%5Ca_6%26-3%5C%5C%5Cvdots%26%5Cvdots%5Cend%7Barray%7D%5Cright%5D)
And the recursive formula is
