Answer:
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
2(3x−6)−2x+1=25
(2)(3x)+(2)(−6)+−2x+1=25(Distribute)
6x+−12+−2x+1=25
(6x+−2x)+(−12+1)=25(Combine Like Terms)
4x+−11=25
4x−11=25
Step 2: Add 11 to both sides.
4x−11+11=25+11
4x=36
Step 3: Divide both sides by 4.
4x
4
=
36
4
x=9
Look at the picture.
![\csc\theta=\dfrac{1}{\sin\theta}=\dfrac{1}{\frac{y}{r}}=\dfrac{r}{y}](https://tex.z-dn.net/?f=%5Ccsc%5Ctheta%3D%5Cdfrac%7B1%7D%7B%5Csin%5Ctheta%7D%3D%5Cdfrac%7B1%7D%7B%5Cfrac%7By%7D%7Br%7D%7D%3D%5Cdfrac%7Br%7D%7By%7D)
We have the right triangle x, y and r. From the Pythagorean theorem we have:
![r^2=x^2+y^2\to r=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=r%5E2%3Dx%5E2%2By%5E2%5Cto%20r%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
We have the point
![\left(-\dfrac{2}{3};\ \dfrac{\sqrt5}{3}\right)](https://tex.z-dn.net/?f=%5Cleft%28-%5Cdfrac%7B2%7D%7B3%7D%3B%5C%20%5Cdfrac%7B%5Csqrt5%7D%7B3%7D%5Cright%29)
Substitute:
![r=\sqrt{\left(-\dfrac{2}{3}\right)^2+\left(\dfrac{\sqrt5}{3}\right)^2}\\\\r=\sqrt{\dfrac{4}{9}+\dfrac{5}{9}}\\\\r=\sqrt{\dfrac{9}{9}}\\\\r=1](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B%5Cleft%28-%5Cdfrac%7B2%7D%7B3%7D%5Cright%29%5E2%2B%5Cleft%28%5Cdfrac%7B%5Csqrt5%7D%7B3%7D%5Cright%29%5E2%7D%5C%5C%5C%5Cr%3D%5Csqrt%7B%5Cdfrac%7B4%7D%7B9%7D%2B%5Cdfrac%7B5%7D%7B9%7D%7D%5C%5C%5C%5Cr%3D%5Csqrt%7B%5Cdfrac%7B9%7D%7B9%7D%7D%5C%5C%5C%5Cr%3D1)
![\csc\theta=\dfrac{1}{\frac{\sqrt5}{3}}=\dfrac{3}{\sqrt5}=\dfrac{3\cdot\sqrt5}{\sqrt5\cdot\sqrt5}=\boxed{\dfrac{3\sqrt5}{5}}](https://tex.z-dn.net/?f=%5Ccsc%5Ctheta%3D%5Cdfrac%7B1%7D%7B%5Cfrac%7B%5Csqrt5%7D%7B3%7D%7D%3D%5Cdfrac%7B3%7D%7B%5Csqrt5%7D%3D%5Cdfrac%7B3%5Ccdot%5Csqrt5%7D%7B%5Csqrt5%5Ccdot%5Csqrt5%7D%3D%5Cboxed%7B%5Cdfrac%7B3%5Csqrt5%7D%7B5%7D%7D)
I personally think Natalie's bill is the greatest because $24.25 × 10 =x
Answer:
44x +56y = 95
Step-by-step explanation:
To write the equation of the perpendicular bisector, we need to know the midpoint and we need to know the differences of the coordinates.
The midpoint is the average of the coordinate values:
((-2.5, -2) +(3, 5))/2 = (0.5, 3)/2 = (0.25, 1.5) = (h, k)
The differences of the coordinates are ...
(3, 5) -(-2.5, -2) = (3 -(-2.5), 5 -(-2)) = (5.5, 7) = (Δx, Δy)
Then the perpendicular bisector equation can be written ...
Δx(x -h) +Δy(y -k) = 0
5.5(x -0.25) +7(y -1.5) = 0
5.5x -1.375 +7y -10.5 = 0
Multiplying by 8 and subtracting the constant, we get ...
44x +56y = 95 . . . . equation of the perpendicular bisector