Each time x goes up by 1, y also goes up by 1 as well.
slope = rise/run = 1/1 = 1
Or we can use the slope formula to get
m = (y2-y1)/(x2-x1) = (3-2)/(2-1) = 1/1 = 1
I used the first two rows as the points to plug into the slope formula.
You can pick any two rows you want and you'll get the same slope value.
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Because we get the same result of 1 each time, this means the rate of change is <u>constant</u> and this function is <u>linear</u>. Plotting all four points will show a single straight line goes through all of them. See diagram below.
Answer:
it's one
Step-by-step explanation:
.
Answer:
Look below
Step-by-step explanation:
(a) The area of a triangle is:
![A=\frac{1}{2}bh](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7Dbh)
The height of this triangle is h and it's base is 4+h so...
![A=\frac{1}{2}*[h*(h+4)]](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%2A%5Bh%2A%28h%2B4%29%5D)
![A=\frac{1}{2}*(h^2+4h)\\A=\frac{h^2}{2}+2h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%2A%28h%5E2%2B4h%29%5C%5CA%3D%5Cfrac%7Bh%5E2%7D%7B2%7D%2B2h)
(b) If the height is 8 cm, then the base is 4+8 which is 12 cm so...
![A=\frac{1}{2}*8*12=4*12=48 \ cm^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%2A8%2A12%3D4%2A12%3D48%20%5C%20cm%5E2)
Answer:
See below.
Step-by-step explanation:
![\frac{6z^2-12z}{4z^2-16z+16} +\frac{3z}{z^2-z-2} \\\\](https://tex.z-dn.net/?f=%5Cfrac%7B6z%5E2-12z%7D%7B4z%5E2-16z%2B16%7D%20%2B%5Cfrac%7B3z%7D%7Bz%5E2-z-2%7D%20%5C%5C%5C%5C)
First, factor the numerators and the denominators:
![=\frac{6z(z-2)}{4(z^2-4x+4)}+\frac{3z}{z^2-z-2}\\=\frac{6z(z-2)}{4(z-2)^2}+\frac{3z}{(z-2)(z+1)}\\=\frac{3z}{2(z-2)}+\frac{3z}{(z-2)(z+1)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B6z%28z-2%29%7D%7B4%28z%5E2-4x%2B4%29%7D%2B%5Cfrac%7B3z%7D%7Bz%5E2-z-2%7D%5C%5C%3D%5Cfrac%7B6z%28z-2%29%7D%7B4%28z-2%29%5E2%7D%2B%5Cfrac%7B3z%7D%7B%28z-2%29%28z%2B1%29%7D%5C%5C%3D%5Cfrac%7B3z%7D%7B2%28z-2%29%7D%2B%5Cfrac%7B3z%7D%7B%28z-2%29%28z%2B1%29%7D)
Now, make the two denominators equivalent. To do this, we can multiply the first term by (z+1) and multiply the second term by 2. This will give us:
![(\frac{z+1}{z+1} )(\frac{3z}{2(z-2)})+(\frac{2}{2})(\frac{3z}{(z-2)(z+1)})\\=\frac{3z(z+1)}{2(z-2)(z+1)}+\frac{6z}{2(z-2)(z+1)} \\](https://tex.z-dn.net/?f=%28%5Cfrac%7Bz%2B1%7D%7Bz%2B1%7D%20%29%28%5Cfrac%7B3z%7D%7B2%28z-2%29%7D%29%2B%28%5Cfrac%7B2%7D%7B2%7D%29%28%5Cfrac%7B3z%7D%7B%28z-2%29%28z%2B1%29%7D%29%5C%5C%3D%5Cfrac%7B3z%28z%2B1%29%7D%7B2%28z-2%29%28z%2B1%29%7D%2B%5Cfrac%7B6z%7D%7B2%28z-2%29%28z%2B1%29%7D%20%20%5C%5C)
Now, combine them since they have a common denominator:
![=\frac{3z^2+3z+6z}{2(z-2)(z+1)}\\ =\frac{3z^2+9z}{2(z-2)(z+1)} \\=\frac{3z(z+3)}{2(z-2)(z+1)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B3z%5E2%2B3z%2B6z%7D%7B2%28z-2%29%28z%2B1%29%7D%5C%5C%20%3D%5Cfrac%7B3z%5E2%2B9z%7D%7B2%28z-2%29%28z%2B1%29%7D%20%5C%5C%3D%5Cfrac%7B3z%28z%2B3%29%7D%7B2%28z-2%29%28z%2B1%29%7D)
This cannot be simplified further.