2x-3>11-5x
Simplify both sides of the equation
2x-3>-5x+11
Add 5x to both sides
2x-3+5x>-5x+11+5x
7x-3>11
Add 3 to both sides
7x-3+3>11+3
7x>14
Divide both sides by 7
7x/7>14/7
x>2
I hope that's help !
Answer:
![2 \sqrt{2} + i \sqrt{2}](https://tex.z-dn.net/?f=2%20%5Csqrt%7B2%7D%20%20%2B%20i%20%5Csqrt%7B2%7D%20)
Step-by-step explanation:
The square of a complex number is a complex number. Here, we have:
![{(a + bi)}^{2} = 6 + 8i](https://tex.z-dn.net/?f=%20%7B%28a%20%2B%20bi%29%7D%5E%7B2%7D%20%20%3D%206%20%2B%208i)
![{a}^{2} + 2abi - {b}^{2} = 6 + 8i](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%2B%202abi%20-%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%206%20%20%2B%208i)
We then have this system of equations:
![{a}^{2} - {b}^{2} = 6](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%7Bb%7D%5E%7B2%7D%20%20%3D%206)
![2ab = 8](https://tex.z-dn.net/?f=2ab%20%3D%208)
Solving this system:
![ab = 4](https://tex.z-dn.net/?f=ab%20%3D%204)
![b = \frac{4}{a}](https://tex.z-dn.net/?f=b%20%3D%20%20%5Cfrac%7B4%7D%7Ba%7D%20)
![{a}^{2} - {( \frac{4}{a}) }^{2} = 6](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%7B%28%20%5Cfrac%7B4%7D%7Ba%7D%29%20%7D%5E%7B2%7D%20%3D%206%20)
![{a}^{2} - \frac{16}{ {a}^{2} } = 6](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20-%20%20%5Cfrac%7B16%7D%7B%20%7Ba%7D%5E%7B2%7D%20%7D%20%3D%206%20)
![{a}^{4} - 16 = 6{a}^{2}](https://tex.z-dn.net/?f=%20%20%7Ba%7D%5E%7B4%7D%20%20-%2016%20%3D%20%206%7Ba%7D%5E%7B2%7D%20)
![{a}^{4} - 6 {a}^{2} - 16 = 0](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B4%7D%20%20-%206%20%7Ba%7D%5E%7B2%7D%20%20-%2016%20%3D%200)
![( {a}^{2} - 8)( {a}^{2} + 2) = 0](https://tex.z-dn.net/?f=%28%20%7Ba%7D%5E%7B2%7D%20%20-%208%29%28%20%7Ba%7D%5E%7B2%7D%20%20%2B%202%29%20%3D%200)
![{a}^{2} = 8](https://tex.z-dn.net/?f=%20%7Ba%7D%5E%7B2%7D%20%20%20%3D%208)
![a = 2 \sqrt{2}](https://tex.z-dn.net/?f=%20a%20%3D%202%20%5Csqrt%7B2%7D%20)
![b = \frac{4}{2 \sqrt{2} } = \sqrt{2}](https://tex.z-dn.net/?f=b%20%3D%20%20%5Cfrac%7B4%7D%7B2%20%5Csqrt%7B2%7D%20%7D%20%3D%20%20%5Csqrt%7B2%7D%20%20)
Te x intercepts are where the graph crosses the x axis or wher y=0
the y intercept is where the graph crosses the y axis or where x=0
to find vertex, here is a hack
the x coordinate of the vertex for an equation in form ax^b+bx+c=y is -b/2a
so
y=3x^2+12x+7
-b/2a=-12/2(3)=-12/6=-2
sub that back
y=3(-2)^2+12(-2)+7
y=3(3)-24+7
y=9-17
y=-8
vertex is (-2,-8)
intercepts
x intercept is where y=0
0=3x^2+12x+7
using quadratic formula
x=(-6-√15)/3 and (-6+√15)/3
xints at ((-6-√15)/3,0) and ((-6+√15)/3,0)
yint is where x=0
set x=0
y=7
yint is at y=7 or (0,7)
vertex at (-2,-8)
xints at x=
![\frac{-6+ \sqrt{15} }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-6%2B%20%5Csqrt%7B15%7D%20%7D%7B3%7D%20)
and
![\frac{-6- \sqrt{15} }{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B-6-%20%5Csqrt%7B15%7D%20%7D%7B3%7D%20)
or at the points
![( \frac{-6+ \sqrt{15} }{3} , 0)](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B-6%2B%20%5Csqrt%7B15%7D%20%7D%7B3%7D%20%2C%200%29%20)
and
![(\frac{-6- \sqrt{15} }{3},0)](https://tex.z-dn.net/?f=%20%28%5Cfrac%7B-6-%20%5Csqrt%7B15%7D%20%7D%7B3%7D%2C0%29%20)
yint at y=7 or at (7,0)
Answer:
The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.
Step-by-step explanation:
Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.
hope this helps a little
Answer:
hello world
Step-by-step explanation: