Answer: there are 200 girls in the school.
Step-by-step explanation:
In a school, there is a ratio of 4 boys to 5 girls. The total ratio would be the sum of the proportion of boys and the proportion of girls. Therefore,
Total ratio = 4 + 5 = 9
If there are a total of 450 students, it means that the number of girls in the school would be
Proportion of girls/ total ratio × total number of students. Therefore,
The number of girls is
5/9 × 450 = 200
![\bf \textit{perimeter of a rectangle}=p=side+side+side+side \\\\ or\implies p=w+w+l+l\implies p=2w+2l \\\\ p=2(w+l)\qquad \begin{cases} w=width\\ l=length\\ ------\\ p=48 \end{cases}\implies 40=2(w+l)\\\\ -----------------------------\\\\ \textit{area of it}=A=w\cdot l\qquad \begin{cases} w=width\\ l=length\\ ------\\ A=40 \end{cases}\implies 40=wl\\\\ -----------------------------\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bperimeter%20of%20a%20rectangle%7D%3Dp%3Dside%2Bside%2Bside%2Bside%0A%5C%5C%5C%5C%0Aor%5Cimplies%20p%3Dw%2Bw%2Bl%2Bl%5Cimplies%20p%3D2w%2B2l%0A%5C%5C%5C%5C%0Ap%3D2%28w%2Bl%29%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0Aw%3Dwidth%5C%5C%0Al%3Dlength%5C%5C%0A------%5C%5C%0Ap%3D48%0A%5Cend%7Bcases%7D%5Cimplies%2040%3D2%28w%2Bl%29%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ctextit%7Barea%20of%20it%7D%3DA%3Dw%5Ccdot%20l%5Cqquad%20%5Cbegin%7Bcases%7D%0Aw%3Dwidth%5C%5C%0Al%3Dlength%5C%5C%0A------%5C%5C%0AA%3D40%0A%5Cend%7Bcases%7D%5Cimplies%2040%3Dwl%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%20)
![\bf thus\qquad \begin{cases} 40=2(w+l)\to \frac{40}{2}=w+l\to\frac{40}{2}-l=\boxed{w} \\\\ 40=wl\\ --------------\\ 40=\left( \boxed{\frac{40}{2}-l} \right)\cdot l \end{cases}](https://tex.z-dn.net/?f=%5Cbf%20thus%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0A40%3D2%28w%2Bl%29%5Cto%20%5Cfrac%7B40%7D%7B2%7D%3Dw%2Bl%5Cto%5Cfrac%7B40%7D%7B2%7D-l%3D%5Cboxed%7Bw%7D%0A%5C%5C%5C%5C%0A40%3Dwl%5C%5C%0A--------------%5C%5C%0A40%3D%5Cleft%28%20%5Cboxed%7B%5Cfrac%7B40%7D%7B2%7D-l%7D%20%5Cright%29%5Ccdot%20l%0A%5Cend%7Bcases%7D)
solve for "l" to find its length
The equation for slope is:
(y2 - y1) / (x2 - x1)
-2 -(-7) = 5
-9 -(-1) = -8
Slope of the line:
5/-8 or -5/8
Answer:
-2(x^2+15)
Step-by-step explanation:
f(x) = −2(x − 4)^2 + 2.
Expanding (x-4)^2
(x-4)(x+4)
x(x+4)-4(x+4)
x^2+4x-4x-16
x^2-16
F(x) = -2(x^2-16)+2
-2x^2-32+2
-2x^2-30
-2(x^2+15)