Answer:
35
Step-by-step explanation:
7 orchids can be lined as 7!. This means that for the first orchid of the line, you can select 7 options. When you place the first orchid, for the second option you can select among 6 since 1 orchid has already been placed. Similarly, for the 3rd orchid of the line, you have left 5 options. The sequence goes in this fashion and for 7 orchids, you have 7*6*5*4*3*2*1 possibilities. However, there is a restriction here. 3 of the orchids are white and 4 are levender. This means that it does not make a difference if we line 3 white orchids in an arbitrary order since it will seem the same from the outside. As a result, the options for lining the 7 orchids diminish. The reduction should eliminate the number of different lining within the same colors. Similar to 7! explanation above, 3 white orchids can be lined as 3! and 4 levender orchids can be lined as 4!. To eliminate these options, we divide all options by the restrictions. The result is:
= 35. [(7*6*5*4*3*2*1/(4*3*2*1*3*2*1)]
3x + 4y = 16 Write original equation
3x + 4y - 4y = -4y + 16 Subtract 4y from each side
3x = -4y +16 Simplify
3x/3 = -4y/3 + 16/3 Divide each side by three
x = -4y/3 +16/3 Simplify
I hope this helps!
Answer:
The average rate of change from x=0 to x=1 for f(x) is 0.
Step-by-step explanation:
We are given the function
.
Now, the rate average rate of change of a function from
to
is given by
.
As, we need the rate of change from x = 0 to x = 1.
So, we will find the values of f(0) and f(1).
i.e.
i.e. f(0) = 3
and
i.e.
i.e. f(1) = 3
Thus, the rate of change from x=0 to x=1 is
i.e.
i.e. 0
Hence, the average rate of change from x=0 to x=1 for f(x) is 0.
A quadratic equation has the general form
of: <span>
y=ax² + bx + c
It can be converted to the vertex form in order
to determine the vertex of the parabola. It has the standard form of:
y = a(x+h)² - k
This can be done by completing a square. The steps are as follows:
</span><span>y = 3x2 + 9x – 18
</span>y = 3(x2 <span>+ 3x) – 18
</span>y + 27/4= 3(x2 <span>+ 3x+ 9/4) – 18
</span>y = 3(x2 + 3/2)^2 – 99<span>/4
</span>
Therefore, the first step is to group terms with the variable x and factoring out the coefficient of x^2.