Answer:
The perimeter of rectangle is ![18\ cm](https://tex.z-dn.net/?f=18%5C%20cm)
Step-by-step explanation:
Let
x------> the length of rectangle
y----> the width of rectangle
we know that
The area of the constructed figure is equal to
![A=xy+2x^{2} +2y^{2}\\A=120\ cm^{2}](https://tex.z-dn.net/?f=A%3Dxy%2B2x%5E%7B2%7D%20%2B2y%5E%7B2%7D%5C%5CA%3D120%5C%20cm%5E%7B2%7D)
so
-----> equation A
-----> equation B
substitute equation B in equation A
![120=y(y+5)+2(y+5)^{2} +2y^{2}\\120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\5y^{2}+25y+50-120=0\\5y^{2}+25y-70=0](https://tex.z-dn.net/?f=120%3Dy%28y%2B5%29%2B2%28y%2B5%29%5E%7B2%7D%20%2B2y%5E%7B2%7D%5C%5C120%3Dy%5E%7B2%7D%2B5y%2B2%28y%5E%7B2%7D%2B10y%2B25%29%2B2y%5E%7B2%7D%5C%5C120%3Dy%5E%7B2%7D%2B5y%2B2y%5E%7B2%7D%2B20y%2B50%2B2y%5E%7B2%7D%5C%5C5y%5E%7B2%7D%2B25y%2B50-120%3D0%5C%5C5y%5E%7B2%7D%2B25y-70%3D0)
using a graphing calculator to resolve the quadratic equation
the solution is
![y=2\ cm](https://tex.z-dn.net/?f=y%3D2%5C%20cm)
Find the value of x
![x=2+5=7\ cm](https://tex.z-dn.net/?f=x%3D2%2B5%3D7%5C%20cm)
Find the perimeter of rectangle
The perimeter of rectangle is equal to
![P=2(x+y)\\P=2(7+2)=18\ cm](https://tex.z-dn.net/?f=P%3D2%28x%2By%29%5C%5CP%3D2%287%2B2%29%3D18%5C%20cm)
Answer:
You must look for 2 integer number taht added give you 3, and multiplied, give you - 18.
Step-by-step explanation:
The inverse of a function produced the reverse coordinates of the parent function. For every (x,y) of the parent function, the inverse will produce points (y,x). This has the effect of rotating the parent function about the line:
y=x
Answer:
Answer:
a).
The amount spent on school materials for each term of all ST201students
b).
a).
It is not a random sample. This looks like a convenience sampling and there is sampling bias. This sample is not representative of the entire population. Since it is not a random sample it is not appropriate to generalize the results to all students.
b).
The sample size is 80 which is greater than 30. It is large enough to assume normal distribution according to central limit theorem.
c).
mean: $617
z critical value at 95%: 1.96
standard error = σ/sqrt(n) =500/sqrt(80) = 55.9017
lower limit= mean-1.96*se = 617-1.96*55.9017=507.43
upper limit= mean+1.96*se = 617+1.96*55.9017=726.57
d).
The amount spent on school materials for each term for the 80 ST201students is $617. We are 95% confident that amount spent on school materials for each term of all ST201students falls in the interval ($507.43, $726.57).
Step-by-step explanation:
Answer:
England, Scotland and Northern Ireland
Step-by-step explanation: