Answer:
They both represent the same equation
Step-by-step explanation:
Given
![Point\ (x,y) = (4,2)](https://tex.z-dn.net/?f=Point%5C%20%28x%2Cy%29%20%3D%20%284%2C2%29)
![Slope,\ m = -5](https://tex.z-dn.net/?f=Slope%2C%5C%20m%20%3D%20-5)
The question is not properly presented.
However, I can pick the following from the question.
Paul's workings:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
Where
and ![m = -5](https://tex.z-dn.net/?f=m%20%3D%20-5)
So:
![2 = -5*4 + b](https://tex.z-dn.net/?f=2%20%3D%20-5%2A4%20%2B%20b)
![2 = -20 + b](https://tex.z-dn.net/?f=2%20%3D%20-20%20%2B%20b)
![b = 2+20](https://tex.z-dn.net/?f=b%20%3D%202%2B20)
![b = 22](https://tex.z-dn.net/?f=b%20%3D%2022)
Seth's workings:
![m = \frac{y - y_1}{x - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By%20-%20y_1%7D%7Bx%20-%20x_1%7D)
![m(x - x_1) = y - y_1](https://tex.z-dn.net/?f=m%28x%20-%20x_1%29%20%3D%20y%20-%20y_1)
![-5(x - 4) = y - 2](https://tex.z-dn.net/?f=-5%28x%20-%204%29%20%3D%20y%20-%202)
Required
Determine if both workings represent the same equation
Step 1: Analyze Paul's workings
Paul applied slope intercept to determine the equation of the line and his workings is correct.
Step 2: Analyze Seth's workings
Seth applied slope formula in determining the equation of the line and up till where Seth's stopped, Seth was correct.
The next step is to complete Seth's workings as follows:
Seth's workings:
![m = \frac{y - y_1}{x - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By%20-%20y_1%7D%7Bx%20-%20x_1%7D)
![m(x - x_1) = y - y_1](https://tex.z-dn.net/?f=m%28x%20-%20x_1%29%20%3D%20y%20-%20y_1)
![-5(x - 4) = y - 2](https://tex.z-dn.net/?f=-5%28x%20-%204%29%20%3D%20y%20-%202)
Open bracket
![-5x + 20 = y - 2](https://tex.z-dn.net/?f=-5x%20%2B%2020%20%3D%20y%20-%202)
Collect Like Terms
![-5x + 20 + 2 = y](https://tex.z-dn.net/?f=-5x%20%2B%2020%20%2B%202%20%3D%20y)
![-5x + 22 = y](https://tex.z-dn.net/?f=-5x%20%2B%2022%20%3D%20y)
Reorder
![y = -5x + 22](https://tex.z-dn.net/?f=y%20%3D%20-5x%20%2B%2022)
Comparing the end results of Seth and Paul's workings.
We have that both results are the same.
i.e.
![y = -5x + 22](https://tex.z-dn.net/?f=y%20%3D%20-5x%20%2B%2022)
<em>Hence, they both represent the same equation</em>
Answer:
3 1/20
Step-by-step explanation:
First, we will convert the mixed numbers into improper fractions...
9 3/10 (9*10=90+3=93) so the improper fraction is 93/10
5 3/4 (5*4=20+3=23) therefore the improper fraction is 23/4
We then want to make the denominator the same...
93/10 (*4) = 372/40
23/4 (*10) = 230/40
We then put it into the question...
372/40 - 230/40 = 142/40
Lastly, we now need to turn this into a mixed number...
142/40=3.55 so the answer is 3 2/40
3 2/40 in it's simplest form is 3 1/20
Hope this helps!
<u>L</u><u>a</u><u>w</u><u> </u><u>o</u><u>f</u><u> </u><u>E</u><u>x</u><u>p</u><u>o</u><u>n</u><u>e</u><u>n</u><u>t</u>
![\displaystyle \large{ {a}^{ - n} = \frac{1}{ {a}^{n} } }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7B%20%7Ba%7D%5E%7B%20-%20n%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B%20%7Ba%7D%5E%7Bn%7D%20%7D%20%7D)
Compare the terms.
![\displaystyle \large{ {a}^{ - n} = {( - 2)}^{ - 3} }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7B%20%7Ba%7D%5E%7B%20-%20n%7D%20%20%3D%20%20%20%7B%28%20-%202%29%7D%5E%7B%20-%203%7D%20%7D)
Therefore, a = -2 and n = 3. From the law of exponent above, we receive:
![\displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{ {( - 2)}^{ 3} } }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7B%20%7B%28%20-%202%29%7D%5E%7B%20-%203%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B%20%7B%28%20-%202%29%7D%5E%7B%203%7D%20%7D%20%7D)
<u>E</u><u>x</u><u>p</u><u>o</u><u>n</u><u>e</u><u>n</u><u>t</u><u> </u><u>D</u><u>e</u><u>f</u><u>.</u> (For cubic)
![\displaystyle \large{ {a}^{3} = a \times a \times a }](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7B%20%7Ba%7D%5E%7B3%7D%20%20%3D%20a%20%5Ctimes%20a%20%5Ctimes%20a%20%7D)
Factor (-2)^3 out.
![\displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{( - 2) \times ( - 2) \times ( - 2)}}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7B%20%7B%28%20-%202%29%7D%5E%7B%20-%203%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B%28%20-%202%29%20%5Ctimes%20%28%20-%202%29%20%5Ctimes%20%28%20-%202%29%7D%7D)
(-2) • (-2) = 4 | Negative × Negative = Positive.
![\displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{4 \times ( - 2)}}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7B%20%7B%28%20-%202%29%7D%5E%7B%20-%203%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B4%20%5Ctimes%20%28%20-%202%29%7D%7D)
4 • (-2) = -8 | Negative Multiply Positive = Negative.
![\displaystyle \large{ {( - 2)}^{ - 3} = \frac{1}{ - 8}}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%7B%20%7B%28%20-%202%29%7D%5E%7B%20-%203%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B%20%20-%208%7D%7D)
If either denominator or numerator is in negative, it is the best to write in the middle or between numerator and denominators.
Hence,
![\displaystyle \large \boxed{ {( - 2)}^{ - 3} = - \frac{1}{ 8}}](https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Clarge%20%5Cboxed%7B%20%7B%28%20-%202%29%7D%5E%7B%20-%203%7D%20%20%3D%20%20-%20%20%5Cfrac%7B1%7D%7B%20%208%7D%7D)
The answer is - 1 / 8
It is actualy A = w * l
so
A = 264
then we minus 30 which equals both areas of the triangles combined, so the final answer is...... 234
I think the turkey plus tax will equal 19.50