Answer:
10 or -10,
Read the explanation
Step-by-step explanation:
Rewrite this problem as a numerical expression. As per the wording of this problem, there can be two expressions derived.
1. ![((\frac{1}{6}(10*3)*4)-30](https://tex.z-dn.net/?f=%28%28%5Cfrac%7B1%7D%7B6%7D%2810%2A3%29%2A4%29-30)
2. ![30-((\frac{1}{6}(10*3)*4)](https://tex.z-dn.net/?f=30-%28%28%5Cfrac%7B1%7D%7B6%7D%2810%2A3%29%2A4%29)
Simplify, remember the order of operations. The order of operations is the sequence by which one is supposed to perform operations in a numerical expression. This order is the following:
1. Parenthesis
2. Exponents
3. Multiplication or division
4. Addition or Subtraction
Use this sequence when simplifying and solving the expression:
Expression 1
![((\frac{1}{6}(10*3)*4)-30\\\\=((\frac{1}{6}(30)*4)-30\\\\=(5*4)-30\\\\=20 - 30\\\\= -10](https://tex.z-dn.net/?f=%28%28%5Cfrac%7B1%7D%7B6%7D%2810%2A3%29%2A4%29-30%5C%5C%5C%5C%3D%28%28%5Cfrac%7B1%7D%7B6%7D%2830%29%2A4%29-30%5C%5C%5C%5C%3D%285%2A4%29-30%5C%5C%5C%5C%3D20%20-%2030%5C%5C%5C%5C%3D%20-10)
Expression 2
![30-((\frac{1}{6}(10*3)*4)\\\\=30-((\frac{1}{6}(30)*4)\\\\=30-(5*4)\\\\= 30-20\\\\= 10](https://tex.z-dn.net/?f=30-%28%28%5Cfrac%7B1%7D%7B6%7D%2810%2A3%29%2A4%29%5C%5C%5C%5C%3D30-%28%28%5Cfrac%7B1%7D%7B6%7D%2830%29%2A4%29%5C%5C%5C%5C%3D30-%285%2A4%29%5C%5C%5C%5C%3D%2030-20%5C%5C%5C%5C%3D%2010)
Multilpy -2 on both sides of the < sign this will get u 1x < 24 in other words x < 24
Answer:
x=18
QR=29
RS=29
QS=29
Step-by-step explanation: 2X-7=5x-61=x+11 solve for x since all sides are equal
Answer:
![\frac{(x--3)^2}{49} -\frac{(y-6)^2}{32}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x--3%29%5E2%7D%7B49%7D%20-%5Cfrac%7B%28y-6%29%5E2%7D%7B32%7D%3D1)
Step-by-step explanation:
The standard equation of a horizontal hyperbola with center (h,k) is
![\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-h%29%5E2%7D%7Ba%5E2%7D-%5Cfrac%7B%28y-k%29%5E2%7D%7Bb%5E2%7D%3D1)
The given hyperbola has vertices at (–10, 6) and (4, 6).
The length of its major axis is
.
![\implies 2a=|14|](https://tex.z-dn.net/?f=%5Cimplies%202a%3D%7C14%7C)
![\implies 2a=14](https://tex.z-dn.net/?f=%5Cimplies%202a%3D14)
![\implies a=7](https://tex.z-dn.net/?f=%5Cimplies%20a%3D7)
The center is the midpoint of the vertices (–10, 6) and (4, 6).
The center is ![(\frac{-10+4}{2},\frac{6+6}{2}=(-3,6)](https://tex.z-dn.net/?f=%28%5Cfrac%7B-10%2B4%7D%7B2%7D%2C%5Cfrac%7B6%2B6%7D%7B2%7D%3D%28-3%2C6%29)
We need to use the relation
to find
.
The c-value is the distance from the center (-3,6) to one of the foci (6,6)
![c=|6--3|=9](https://tex.z-dn.net/?f=c%3D%7C6--3%7C%3D9)
![\implies 7^2+b^2=9^2](https://tex.z-dn.net/?f=%5Cimplies%207%5E2%2Bb%5E2%3D9%5E2)
![\implies b^2=9^2-7^2](https://tex.z-dn.net/?f=%5Cimplies%20b%5E2%3D9%5E2-7%5E2)
![\implies b^2=81-49](https://tex.z-dn.net/?f=%5Cimplies%20b%5E2%3D81-49)
![\implies b^2=32](https://tex.z-dn.net/?f=%5Cimplies%20b%5E2%3D32)
We substitute these values into the standard equation of the hyperbola to obtain:
![\frac{(x--3)^2}{7^2} - \frac{(y-6)^2}{32}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x--3%29%5E2%7D%7B7%5E2%7D%20-%20%5Cfrac%7B%28y-6%29%5E2%7D%7B32%7D%3D1)
![\frac{(x+3)^2}{49} -\frac{(y-6)^2}{32}=1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x%2B3%29%5E2%7D%7B49%7D%20-%5Cfrac%7B%28y-6%29%5E2%7D%7B32%7D%3D1)