Answer:
<h2>-9</h2>
Step-by-step explanation:
n - a number
five more: + 5
twice a number: 2 · n = 2n
five more than twice a number: 2n + 5
The equation:
2n + 5 = -13 <em>subtract 5 from both sides</em>
2n + 5 - 5 = -13 - 5
2n = -18 <em>divide both sides by 2</em>
2n/2 = -18/2
n = -9
Answer:
-8/5 = -1 and 3/5
Step-by-step explanation:
slope = change in y/change in x = (4-12)/(9-4) = -8/5 = -1 and 3/5
Answer:
Step-by-step explanation:
a1=2
r=4
n=8
![s_{8}=2\frac{4^8-1}{4-1} =\frac{2}{3} (4^8-1)=\frac{2}{3} (65536-1)=\frac{2}{3} (65535)=2 \times 21845=43690](https://tex.z-dn.net/?f=s_%7B8%7D%3D2%5Cfrac%7B4%5E8-1%7D%7B4-1%7D%20%3D%5Cfrac%7B2%7D%7B3%7D%20%284%5E8-1%29%3D%5Cfrac%7B2%7D%7B3%7D%20%2865536-1%29%3D%5Cfrac%7B2%7D%7B3%7D%20%2865535%29%3D2%20%5Ctimes%2021845%3D43690)
Answer:
The constant rate of change is <em>2 rectangles</em>
Step-by-step explanation:
Looking at this question, we can see that what we have is in the form of an arithmetic progression otherwise known as A.P
An arithmetic progression refers to a series of numbers that differ by a constant addition or subtraction of a certain constant number. What this means is that subsequent terms are formed by the addition of a certain constant number to preceding terms.
Now, let's look at the situation in the question;
1, 3 , 5, ?, ?
Looking at the first three terms, we can see that the difference between the first two terms is 2, the difference between the third term and the second term is 2 also. This gives us an ideas of an arithmetic progression, with the first term being 1 and the common difference being 2.
The common difference is what is referred to as the constant term in this questions which is equal to 2
Let
be the dimensions of the rectangle. We know the equations for both area and perimeter:
![A=xy=36](https://tex.z-dn.net/?f=A%3Dxy%3D36)
![P=2(x+y)=36 \iff x+y=18](https://tex.z-dn.net/?f=P%3D2%28x%2By%29%3D36%20%5Ciff%20x%2By%3D18)
So, we have the following system:
![\begin{cases}xy=36\\x+y=18\end{cases}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dxy%3D36%5C%5Cx%2By%3D18%5Cend%7Bcases%7D)
From the second equation, we can deduce
![y=18-x](https://tex.z-dn.net/?f=y%3D18-x)
Plug this in the first equation to get
![xy=x(18-x)=-x^2+18=36](https://tex.z-dn.net/?f=xy%3Dx%2818-x%29%3D-x%5E2%2B18%3D36)
Refactor as
![x^2-18x+36=0](https://tex.z-dn.net/?f=x%5E2-18x%2B36%3D0)
And solve with the usual quadratic formula to get
![x=9\pm3\sqrt{5}](https://tex.z-dn.net/?f=x%3D9%5Cpm3%5Csqrt%7B5%7D)
Both solutions are feasible, because they're both positive.
If we chose the positive solution, we have
![x=9+3\sqrt{5} \implies y=18-x=18-9-3\sqrt{5}=9-3\sqrt{5}](https://tex.z-dn.net/?f=x%3D9%2B3%5Csqrt%7B5%7D%20%5Cimplies%20y%3D18-x%3D18-9-3%5Csqrt%7B5%7D%3D9-3%5Csqrt%7B5%7D)
If we choose the negative solution, we have
![x=9-3\sqrt{5} \implies y=18-x=18-9+3\sqrt{5}=9+3\sqrt{5}](https://tex.z-dn.net/?f=x%3D9-3%5Csqrt%7B5%7D%20%5Cimplies%20y%3D18-x%3D18-9%2B3%5Csqrt%7B5%7D%3D9%2B3%5Csqrt%7B5%7D)
So, we're just swapping the role of
and
. The two dimensions of the rectangle are
and ![9-3\sqrt{5}](https://tex.z-dn.net/?f=9-3%5Csqrt%7B5%7D)