Answer:
y = -2x + 8
Step-by-step explanation:
The point slope form of an equation is written as
y = mx + c ...............(i)
Where m is the slope and c is the constant
Now we Know that the equation is
y + 2 = -2(x-5)
and the given points are
m= -2
x = 5
and y= -2
Putting these values in equation (i) to find the value of c
y = mx + c
it becomes
-2 = -2(5) + c
-2 = -10 + c
Adding 10 on both sides
-2 + 10 = -10 + 10 + c
8 = c
or c=8
Now we have the values of m and c
where m= -2 and c = 8
Point slope form of an equation is
y = mx + c
putting the values of m and c to get equation in slope intercept form is
y = (-2)x + 8
or
y = -2x + 8
Other method:
The given point slope form is
y + 2 = -2(x-5)
We have to change it in y= mx + c form
so solving it
y + 2 = -2x + 10
Subtracting 2 from both sides
y + 2 -2 = -2x + 10 -2
y = -2x + 8
which is same is
y=mx + c
so the required equation is
y = -2x + 8
a. The construct the expression for the area of the rectangle in terms of x is y=2.5x
b. The area should be 2,560.
Given that,
- the length of a rectangular house is two and a half times its width.
Based on the above information, the calculation is as follows:
a) The expression should be y = 2.5x
b) The area should be
= 2560
Learn more: brainly.com/question/1301963?referrer=searchResults
Suppose the length is 7x, the width is then 3x
7x*3x=525
21x²=525
x²=25
x=5
so the length is 7*5=35, and the width is 3*5=15
Answer:
can be written in power notation as ![a^{4}\times 13^{2}](https://tex.z-dn.net/?f=a%5E%7B4%7D%5Ctimes%2013%5E%7B2%7D)
Step-by-step explanation:
The given expression
![a\times (-a)\times 13\times a\times (-a)\times 13](https://tex.z-dn.net/?f=a%5Ctimes%20%28-a%29%5Ctimes%2013%5Ctimes%20a%5Ctimes%20%28-a%29%5Ctimes%2013)
Writing a\times (-a)\times 13\times a\times (-a)\times 13 in power notation:
Let
![a\times (-a)\times 13\times a\times (-a)\times 13](https://tex.z-dn.net/?f=a%5Ctimes%20%28-a%29%5Ctimes%2013%5Ctimes%20a%5Ctimes%20%28-a%29%5Ctimes%2013)
= ![[13\times13][(a\times (-a)\times a\times (-a)]](https://tex.z-dn.net/?f=%5B13%5Ctimes13%5D%5B%28a%5Ctimes%20%28-a%29%5Ctimes%20a%5Ctimes%20%28-a%29%5D)
As
,
,
So,
![=[13^{2}][a^2\times (-a)^2]](https://tex.z-dn.net/?f=%3D%5B13%5E%7B2%7D%5D%5Ba%5E2%5Ctimes%20%28-a%29%5E2%5D)
As
![(-a)^2 = a^{2}](https://tex.z-dn.net/?f=%28-a%29%5E2%20%3D%20a%5E%7B2%7D)
So,
![=[13^{2}][a^2\times a^2]](https://tex.z-dn.net/?f=%3D%5B13%5E%7B2%7D%5D%5Ba%5E2%5Ctimes%20a%5E2%5D)
As ∵![a^{m} \times a^{n}=a^{m+n}](https://tex.z-dn.net/?f=a%5E%7Bm%7D%20%5Ctimes%20a%5E%7Bn%7D%3Da%5E%7Bm%2Bn%7D)
![=[13^{2}][a^{2+2}]](https://tex.z-dn.net/?f=%3D%5B13%5E%7B2%7D%5D%5Ba%5E%7B2%2B2%7D%5D)
As ∵![a^{m} \times a^{n}=a^{m+n}](https://tex.z-dn.net/?f=a%5E%7Bm%7D%20%5Ctimes%20a%5E%7Bn%7D%3Da%5E%7Bm%2Bn%7D)
![=13^{2}\times a^{4}](https://tex.z-dn.net/?f=%3D13%5E%7B2%7D%5Ctimes%20a%5E%7B4%7D)
![=a^{4}\times 13^{2}](https://tex.z-dn.net/?f=%3Da%5E%7B4%7D%5Ctimes%2013%5E%7B2%7D)
Therefore,
can be written in power notation as ![a^{4}\times 13^{2}](https://tex.z-dn.net/?f=a%5E%7B4%7D%5Ctimes%2013%5E%7B2%7D)
<em>Keywords: power notation</em>
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