1.You have two ways for solving this.
First, you could use a graphing utility or calculator to graph both functions on the same plane, and given that the functions do not have a
![y](https://tex.z-dn.net/?f=y)
coordinate, the solution of
![f(x)=g(x)](https://tex.z-dn.net/?f=f%28x%29%3Dg%28x%29)
will be the
![x](https://tex.z-dn.net/?f=x)
coordinate in which the tow graphs intercept (cross each other) as you can see in the picture (1).
The other way is equating the two equations and solve for x:
We know that
![f(x)=2x+1](https://tex.z-dn.net/?f=f%28x%29%3D2x%2B1)
and
![g(x)=-x+7](https://tex.z-dn.net/?f=g%28x%29%3D-x%2B7)
, so
![f(x)=g(x)](https://tex.z-dn.net/?f=f%28x%29%3Dg%28x%29)
is equivalent to
![2x+1=-x+7](https://tex.z-dn.net/?f=2x%2B1%3D-x%2B7)
. The only thing left is solving the equation for x:
![2x+1=-x+7](https://tex.z-dn.net/?f=2x%2B1%3D-x%2B7)
![3x=6](https://tex.z-dn.net/?f=3x%3D6)
![x=2](https://tex.z-dn.net/?f=x%3D2)
As you can see, both ways gives us the same answer: the solution to the equation
![f(x)=g(x)](https://tex.z-dn.net/?f=f%28x%29%3Dg%28x%29)
is
![x=2](https://tex.z-dn.net/?f=x%3D2)
.
2. For this one we can repeat the exact same procedures as before:
Graph the functions on the same plane using a graph calculator or graphing utility, and identify the
![x](https://tex.z-dn.net/?f=x)
coordinate in which the two graphs intercept as you can see in the picture (2), or you we can also equate both equations, and solve for
![x](https://tex.z-dn.net/?f=x)
:
![x+2=2x+1](https://tex.z-dn.net/?f=x%2B2%3D2x%2B1)
![x=1](https://tex.z-dn.net/?f=x%3D1)
And just like before, both ways gives us the same answer: the solution to the equation
![f(x)=g(x)](https://tex.z-dn.net/?f=f%28x%29%3Dg%28x%29)
is
![x=1](https://tex.z-dn.net/?f=x%3D1)
So, the answer that you should enter in your boxes are:
2 in the first, and
1 in the second one.
The amount of variance for y that is predicted by its relationship with x is 64%.
<h3>
How much variance is predicted?</h3>
Variance measures the rate of dispersion of a data point around the dataset. It can be calculated by finding the square of the standard deviation of a dataset. Variance measures the variation of a data set.
Correlation is a statistical measure used to measure the linear relationship that exists between two variables. The greater the correlation coefficient is closer to one, the greater the linear relationship that exists between the two variables. A positive correlation occurs when the two variables move in the same direction.
Variance = (correlation coefficient²) x 100
(0.80²) x 100
0.64 x 100 = 64%
To learn more about correlation, please check: brainly.com/question/27246345
#SPJ1
The Neptune's time period of orbit is 164.3 earth years.
We have given that the mass of the sun is 2 × 1030 kg.
The distance between neptune and the sun is 30 au
<h3>What is the mathematical expression of Kepler's law ?</h3>
![T^2 = 4\pi ^2a^3/GM](https://tex.z-dn.net/?f=T%5E2%20%3D%204%5Cpi%20%5E2a%5E3%2FGM)
Where T is in earth years, a is astronomical units and
M = solar masses.
4π²/GM = 1,
Therefore we get
![T^2 = a^3](https://tex.z-dn.net/?f=T%5E2%20%3D%20a%5E3)
![T = \sqrt(a^3)](https://tex.z-dn.net/?f=T%20%3D%20%5Csqrt%28a%5E3%29)
![T = \sqrt(30^3)](https://tex.z-dn.net/?f=T%20%20%3D%20%5Csqrt%2830%5E3%29)
![T = 164.3](https://tex.z-dn.net/?f=T%20%3D%20164.3)
Therefore, the Neptune's time period of orbit is 164.3 earth years.
To learn more about the time period visit:
brainly.com/question/329317
I recommend using the Rational root theorem and finding the zeros through synthetic division. The first zero is x = 1, so the first factorization is (x-1). That leaves a remainder of x^2 -3x-10. Now try to factor that. That factors out to (x-5)(x+2) so the factors of that cubic are (x-1)(x-5)(x+2)