Answer:
I have graphed them on desmos and given you three options to choose from:
Step-by-step explanation:
1. with lines (complete shape)
2. with lines (incomplete shape)
3. without lines
Hope this helps!
Answer:
![d < \frac{3}{2}x](https://tex.z-dn.net/?f=d%20%3C%20%5Cfrac%7B3%7D%7B2%7Dx)
Step-by-step explanation:
Represent a cup with x; the cat with c and the dog with d
From the first statement, we have:
![c < x](https://tex.z-dn.net/?f=c%20%3C%20x)
From the second, we have:
![c = \frac{1}{3}d + \frac{1}{2}x](https://tex.z-dn.net/?f=c%20%3D%20%20%5Cfrac%7B1%7D%7B3%7Dd%20%2B%20%5Cfrac%7B1%7D%7B2%7Dx)
Required
Express d in terms of x
We have:
and ![c < x](https://tex.z-dn.net/?f=c%20%3C%20x)
Merge both expressions to give:
![\frac{1}{3}d + \frac{1}{2}x < x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dd%20%2B%20%5Cfrac%7B1%7D%7B2%7Dx%20%3C%20x)
Collect Like Terms
![\frac{1}{3}d < x - \frac{1}{2}x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dd%20%3C%20x%20-%20%5Cfrac%7B1%7D%7B2%7Dx)
![\frac{1}{3}d < \frac{1}{2}x](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dd%20%3C%20%5Cfrac%7B1%7D%7B2%7Dx)
Multiply both sides by 3
![3 * \frac{1}{3}d < \frac{1}{2}x * 3](https://tex.z-dn.net/?f=3%20%2A%20%5Cfrac%7B1%7D%7B3%7Dd%20%3C%20%5Cfrac%7B1%7D%7B2%7Dx%20%2A%203)
![d < \frac{3}{2}x](https://tex.z-dn.net/?f=d%20%3C%20%5Cfrac%7B3%7D%7B2%7Dx)
Answer:
<u>Jamie's mistake</u>: The last term
and not
. Jamie multiply the signs incorrectly.
<u>Advice to avoid this mistake in the future</u>: Jamie should remember that when two negative numbers are multiplied, the result is a positive number.
Step-by-step explanation:
The correct procedure is the one shown below:
![=(3x-4)(2x-8)\\\\=(3x)(2x)+(3x)(-8)+(-4)(2x)+(-4)(-8)\\\\=6x^2-24x-8x+32\\\\=6x^2-32x+32](https://tex.z-dn.net/?f=%3D%283x-4%29%282x-8%29%5C%5C%5C%5C%3D%283x%29%282x%29%2B%283x%29%28-8%29%2B%28-4%29%282x%29%2B%28-4%29%28-8%29%5C%5C%5C%5C%3D6x%5E2-24x-8x%2B32%5C%5C%5C%5C%3D6x%5E2-32x%2B32)
You can identify that the last term is actually
and not
, so Jamie multiply the signs incorrectly.
To avoid that mistake in the future, Jamie must remember the mulitplication of signs:
![(+)(+)=+\\(-)(-)=+\\(-)(+)=-\\(+)(-)=-](https://tex.z-dn.net/?f=%28%2B%29%28%2B%29%3D%2B%5C%5C%28-%29%28-%29%3D%2B%5C%5C%28-%29%28%2B%29%3D-%5C%5C%28%2B%29%28-%29%3D-)
So when two negative numbers are multiplied, the result is a positive number.
equation of circle is given as
![{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} \\](https://tex.z-dn.net/?f=%20%7B%28x%20-%20h%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28y%20-%20k%29%7D%5E%7B2%7D%20%20%3D%20%20%7Br%7D%5E%7B2%7D%20%5C%5C%20)
where (h,k) is center of cirlce and r is radius.
so lets figure out it from graph.
as we can see in graph center is at ( -1, 1)
radius is 4 units as shown in graph but we can calculate it. take any point on circle and calculate its distance from center. lets take point (3, 1)
now distance = √((3+1)^2+(1-1)^2)
= √16 = 4
lets put it in equation
(x +1)^2 + (y-1)^2 = 4^2