Answer:
![\bold{n =2t-1}](https://tex.z-dn.net/?f=%5Cbold%7Bn%20%3D2t-1%7D)
Step-by-step explanation:
Given table is:
![\begin{center}\begin{tabular}{ c c}Term Number (t) & Number of triangles (n) \\ 1 & 1 \\ 2 & 3 \\ 3 & 5 \\ 4 & 7 \\\end{tabular}\end{center}](https://tex.z-dn.net/?f=%5Cbegin%7Bcenter%7D%5Cbegin%7Btabular%7D%7B%20c%20c%7DTerm%20Number%20%28t%29%20%26%20Number%20of%20triangles%20%28n%29%20%5C%5C%201%20%26%201%20%20%5C%5C%20%202%20%26%203%20%20%5C%5C%20%20%203%20%26%205%20%20%20%5C%5C%204%20%26%207%20%20%5C%5C%5Cend%7Btabular%7D%5Cend%7Bcenter%7D)
i.e. when term number, t = 1, number of triangles (n) = 1
when term number, t = 2, number of triangles (n) = 3
when term number, t = 3, number of triangles (n) = 5
when term number, t = 4, number of triangles (n) = 7
If we closely look at the pattern, number of triangles (n) in each row are 1 lesser than twice of term number (t).
i.e. for ![t=1, n = 2\times 1 -1=1](https://tex.z-dn.net/?f=t%3D1%2C%20n%20%3D%202%5Ctimes%201%20-1%3D1)
![t=2, n = 2\times 2 -1=3](https://tex.z-dn.net/?f=t%3D2%2C%20n%20%3D%202%5Ctimes%202%20-1%3D3)
![t=3, n = 2\times 3 -1=5](https://tex.z-dn.net/?f=t%3D3%2C%20n%20%3D%202%5Ctimes%203%20-1%3D5)
![t=4, n = 2\times 4 -1=7](https://tex.z-dn.net/?f=t%3D4%2C%20n%20%3D%202%5Ctimes%204%20-1%3D7)
Therefore, the number of triangles in the nth term will be given as:
![\bold{n =2t-1}](https://tex.z-dn.net/?f=%5Cbold%7Bn%20%3D2t-1%7D)
Fist find the slope. The equation is m=y2-y1/x2-x1. Then use slope point form and select a point. Then use the equation y-y1=m(x-x1). Simplify and isolate y.
Answer:
![\%Absent = 80.20\%](https://tex.z-dn.net/?f=%5C%25Absent%20%3D%2080.20%5C%25)
Step-by-step explanation:
Given
The attached data
Required
%Absentee on Friday
First, calculate the total present
![Present = 42 + 36 + 40 + 36 + 38](https://tex.z-dn.net/?f=Present%20%3D%2042%20%2B%2036%20%2B%2040%20%2B%2036%20%2B%2038)
![Present = 192](https://tex.z-dn.net/?f=Present%20%3D%20192)
Calculate the %Present on Friday
![\%Present = \frac{Friday}{Present} * 100\%](https://tex.z-dn.net/?f=%5C%25Present%20%3D%20%5Cfrac%7BFriday%7D%7BPresent%7D%20%2A%20100%5C%25)
![\%Present = \frac{38}{192} * 100\%](https://tex.z-dn.net/?f=%5C%25Present%20%3D%20%5Cfrac%7B38%7D%7B192%7D%20%2A%20100%5C%25)
![\%Present = \frac{3800}{192}\%](https://tex.z-dn.net/?f=%5C%25Present%20%3D%20%5Cfrac%7B3800%7D%7B192%7D%5C%25)
![\%Present = 19.80\%](https://tex.z-dn.net/?f=%5C%25Present%20%3D%2019.80%5C%25)
Using complement rule:
![\%Absent = 100\% - \%Present](https://tex.z-dn.net/?f=%5C%25Absent%20%3D%20100%5C%25%20-%20%5C%25Present)
![\%Absent = 100\% - 19.80\%](https://tex.z-dn.net/?f=%5C%25Absent%20%3D%20100%5C%25%20-%2019.80%5C%25)
![\%Absent = 80.20\%](https://tex.z-dn.net/?f=%5C%25Absent%20%3D%2080.20%5C%25)
A
Slope intercept form is y=mx+b. Plug in the m to make the equation y=6x+b. Then plug in the b to make the equation y=6x+4.2.
Answer:
y= 6x-9
Step-by-step explanation:
1. First find the gradient between the two points. Gradient =6
2. Using the formula y= mx+c substitute the gradient into the equation. You'll get something like this: y= 6x+c
3. Substitute the point (4,15) into the equation. You'll get something like this: 15= 6(4) +c.
4. Calculate the value of c. You'll get - 9 as an answer to that.
5. Substitute the value of c into the original equation. Your final answer will be y= 6x-9