An x-intercept is namely a "solution" or "zero" or "root" often called, and when that happens, y = 0, just like with any other x-intercept.
![\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \boxed{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\ -------------------------------\\\\ \begin{cases} h=3\\ k=-2 \end{cases}\implies y=a(x-3)^2-2 \\\\\\ \textit{we also know that } \begin{cases} x=0\\ y=7 \end{cases}\implies 7=a(0-3)^2-2 \\\\\\ 9=9a\implies \cfrac{9}{9}=a\implies 1=a\qquad therefore\qquad \boxed{y=(x-3)^2-2}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~%5Ctextit%7Bparabola%20vertex%20form%7D%0A%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Cboxed%7By%3Da%28x-%20h%29%5E2%2B%20k%7D%5C%5C%5C%5C%0Ax%3Da%28y-%20k%29%5E2%2B%20h%0A%5Cend%7Barray%7D%0A%5Cqquad%5Cqquad%0Avertex~~%28%5Cstackrel%7B%7D%7B%20h%7D%2C%5Cstackrel%7B%7D%7B%20k%7D%29%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0Ah%3D3%5C%5C%0Ak%3D-2%0A%5Cend%7Bcases%7D%5Cimplies%20y%3Da%28x-3%29%5E2-2%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Bwe%20also%20know%20that%20%7D%0A%5Cbegin%7Bcases%7D%0Ax%3D0%5C%5C%0Ay%3D7%0A%5Cend%7Bcases%7D%5Cimplies%207%3Da%280-3%29%5E2-2%0A%5C%5C%5C%5C%5C%5C%0A9%3D9a%5Cimplies%20%5Ccfrac%7B9%7D%7B9%7D%3Da%5Cimplies%201%3Da%5Cqquad%20therefore%5Cqquad%20%5Cboxed%7By%3D%28x-3%29%5E2-2%7D)
so what is its x-intercept anyway?
Answer:
There are 48 children.
Step-by-step explanation:
Given :There are 3 times as many boys as girls.
There are 24 more boys than girls,
To Find : how many children are there?
Solution:
Let the number of girls be x
Now we are given that there are 3 times as many boys as girls.
So, no. of boys = 3x
Now we are given that there are 24 more boys than girls.
So, ![3x-x=24](https://tex.z-dn.net/?f=3x-x%3D24)
![2x=24](https://tex.z-dn.net/?f=2x%3D24)
![x=12](https://tex.z-dn.net/?f=x%3D12)
So, no. of girls = 12
No. of boys = 3x = 3(12) = 36
Now the total no. of children = 12+36 = 48
Hence there are 48 children.
Answer:
-89 +4i sqrt (3)
Step-by-step explanation:
sqrt(-48) - 89
sqrt(-1) sqrt(48) - 89
We know that sqrt(-1) = ±i
±i sqrt(48) - 89
±i sqrt(16)sqrt(3) - 89
±4i sqrt(3) - 89
Taking the principal square root
-89 +4i sqrt (3)
Distance formula
D = √((x1 - x2)2 + (y1 - y2)2) We have three distances that we are dealing with. Between the Theater and the Park, between the Theater and the Pier, and between the Park and the pier. In both routes we have to go between the Theater and the Park. The distance between those is the same regardless of which way we go, so we can ignore doing the math for that. That leaves us two distances. Let's plug them in. Theater to PierD = √((0 - 10)2 + (3 - 9)2) = √(100 + 36) ≈ 11.6619 Park to PierD = √((2 - 10)2 + (1 - 9)2) = √(64 + 64) ≈ 11.3137 11.3 < 11.7