Answer:
The radius of the circle is:
units
Step-by-step explanation:
Given the equation
![\left(x\:+\:5\right)^2\:+\:\left(y\:-\:3\right)^2=\:42](https://tex.z-dn.net/?f=%5Cleft%28x%5C%3A%2B%5C%3A5%5Cright%29%5E2%5C%3A%2B%5C%3A%5Cleft%28y%5C%3A-%5C%3A3%5Cright%29%5E2%3D%5C%3A42)
As we know that
![\left(x\:-\:a\right)^2\:+\:\left(y\:-\:b\right)^2=\:r^2\:](https://tex.z-dn.net/?f=%5Cleft%28x%5C%3A-%5C%3Aa%5Cright%29%5E2%5C%3A%2B%5C%3A%5Cleft%28y%5C%3A-%5C%3Ab%5Cright%29%5E2%3D%5C%3Ar%5E2%5C%3A)
is the equation of the circle with a radius 'r', centered at (a, b)
![\mathrm{Rewrite}\:\left(x+5\right)^2+\left(y-3\right)^2=4^2\:\mathrm{in\:the\:form\:of\:the\:standard\:circle\:equation}](https://tex.z-dn.net/?f=%5Cmathrm%7BRewrite%7D%5C%3A%5Cleft%28x%2B5%5Cright%29%5E2%2B%5Cleft%28y-3%5Cright%29%5E2%3D4%5E2%5C%3A%5Cmathrm%7Bin%5C%3Athe%5C%3Aform%5C%3Aof%5C%3Athe%5C%3Astandard%5C%3Acircle%5C%3Aequation%7D)
so, the circle properties are:
![\left(x-\left(-5\right)\right)^2+\left(y-3\right)^2=4^2](https://tex.z-dn.net/?f=%5Cleft%28x-%5Cleft%28-5%5Cright%29%5Cright%29%5E2%2B%5Cleft%28y-3%5Cright%29%5E2%3D4%5E2)
Therefore, the radius of the circle is:
units
We know that the slope is -5, so:
y = -5x + b
Input (1, 2)
2 = -5 + b
b = 7
So:
y = -5x + 7
For the 1st one RSV = TSU (Vertical angles are congruent)
9x - 28 = 6x + 2
3x = 30
x = 10
RSV = 62
The 2nd one
Alternate exterior angles are congruent
Thus
10x + 5 = 125
10x = 120
x = 12
The 3rd one
When triangles are similar their sides are promotional and their angles are congruent
thus
A and D
The 4th one
Find Angle A
Angle A + 3Angle A + 76 = 180
4 Angle A = 104
Angle A = 26
Answer:
7.5 cups
Step-by-step explanation:
120/4= 30. 30x1/4= 7.5 cups
Answer:
![x=\frac{3}{4}+i\frac{\sqrt{7}}{4},\:x=\frac{3}{4}-i\frac{\sqrt{7}}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B4%7D%2Bi%5Cfrac%7B%5Csqrt%7B7%7D%7D%7B4%7D%2C%5C%3Ax%3D%5Cfrac%7B3%7D%7B4%7D-i%5Cfrac%7B%5Csqrt%7B7%7D%7D%7B4%7D)
Step-by-step explanation:
simplify
by putting the negative sign on the outside. ![\frac{2x}{x-1}-\frac{2x-5}{x^2-3x+2}=-\frac{3}{x-2}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7Bx-1%7D-%5Cfrac%7B2x-5%7D%7Bx%5E2-3x%2B2%7D%3D-%5Cfrac%7B3%7D%7Bx-2%7D)
find the LCM of the denominators. It is (x-1)(x-2). Multiply by the LCM:
![\frac{2x}{x-1}\left(x-1\right)\left(x-2\right)-\frac{2x-5}{x^2-3x+2}\left(x-1\right)\left(x-2\right)=-\frac{3}{x-2}\left(x-1\right)\left(x-2\right)](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7Bx-1%7D%5Cleft%28x-1%5Cright%29%5Cleft%28x-2%5Cright%29-%5Cfrac%7B2x-5%7D%7Bx%5E2-3x%2B2%7D%5Cleft%28x-1%5Cright%29%5Cleft%28x-2%5Cright%29%3D-%5Cfrac%7B3%7D%7Bx-2%7D%5Cleft%28x-1%5Cright%29%5Cleft%28x-2%5Cright%29)
Simplify:
![2x\left(x-2\right)-\left(2x-5\right)=-3\left(x-1\right)](https://tex.z-dn.net/?f=2x%5Cleft%28x-2%5Cright%29-%5Cleft%282x-5%5Cright%29%3D-3%5Cleft%28x-1%5Cright%29)
solve: ![x=\frac{3}{4}+i\frac{\sqrt{7}}{4},\:x=\frac{3}{4}-i\frac{\sqrt{7}}{4}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B4%7D%2Bi%5Cfrac%7B%5Csqrt%7B7%7D%7D%7B4%7D%2C%5C%3Ax%3D%5Cfrac%7B3%7D%7B4%7D-i%5Cfrac%7B%5Csqrt%7B7%7D%7D%7B4%7D)