Answer:
y = -2
Step-by-step explanation:
To find the equation of the tangent we apply implicit differentiation, and then we take apart dy/dx
The equation is

implicit differentiation give us
![\frac{d}{dx}[y^2(y^2-4)=x^2(x^2-5)]\\\\2y\frac{dy}{dx}(y^2-4)+y^2(2y\frac{dy}{dx})=2x(x^2-5)+x^2(2x)\\\\4y^3\frac{dy}{dx}-8y\frac{dy}{dx}=2x^3-10x+2x^3\\\\\frac{dy}{dx}=\frac{4x^3-10x}{4y^3-8y}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5By%5E2%28y%5E2-4%29%3Dx%5E2%28x%5E2-5%29%5D%5C%5C%5C%5C2y%5Cfrac%7Bdy%7D%7Bdx%7D%28y%5E2-4%29%2By%5E2%282y%5Cfrac%7Bdy%7D%7Bdx%7D%29%3D2x%28x%5E2-5%29%2Bx%5E2%282x%29%5C%5C%5C%5C4y%5E3%5Cfrac%7Bdy%7D%7Bdx%7D-8y%5Cfrac%7Bdy%7D%7Bdx%7D%3D2x%5E3-10x%2B2x%5E3%5C%5C%5C%5C%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B4x%5E3-10x%7D%7B4y%5E3-8y%7D)
But we know that

Hence, for the point (0,-2) and by replacing for dy/dx

Hence m=0, that is, the tangent line to the point is a horizontal line that cross the y axis for y=-2. The equation is:
y=(0)x+b = -2
HOPE THIS HELPS!!
Danica has -$23, but deposits $40
Add the two numbers
40 + (-23) = 40 - 23 = 17
Danica has $17 in her bank.
hope this helps
Answer:
3. ![\displaystyle x-intercept: [-4\frac{1}{2}, 0] \\ y-intercept: [0, -9] \\ Slope-Intercept\:Form: y = -2x - 9](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x-intercept%3A%20%5B-4%5Cfrac%7B1%7D%7B2%7D%2C%200%5D%20%5C%5C%20y-intercept%3A%20%5B0%2C%20-9%5D%20%5C%5C%20Slope-Intercept%5C%3AForm%3A%20y%20%3D%20-2x%20-%209)
2. ![\displaystyle x-intercept: [5, 0] \\ y-intercept: [0, 1] \\ Slope-Intercept\:Form: y = -\frac{1}{5}x + 1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x-intercept%3A%20%5B5%2C%200%5D%20%5C%5C%20y-intercept%3A%20%5B0%2C%201%5D%20%5C%5C%20Slope-Intercept%5C%3AForm%3A%20y%20%3D%20-%5Cfrac%7B1%7D%7B5%7Dx%20%2B%201)
1. ![\displaystyle x-intercept: [4, 0] \\ y-intercept: [0, -3] \\ Slope-Intercept\:Form: y = \frac{3}{4}x - 3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x-intercept%3A%20%5B4%2C%200%5D%20%5C%5C%20y-intercept%3A%20%5B0%2C%20-3%5D%20%5C%5C%20Slope-Intercept%5C%3AForm%3A%20y%20%3D%20%5Cfrac%7B3%7D%7B4%7Dx%20-%203)
Step-by-step explanation:
−2x - y = 9
x-intercept → Plug in 0 for <em>y</em><em> </em>to get −4½ for <em>x</em>
y-intercept → Plug in 0 for <em>x</em><em> </em>to get −9 for <em>y</em>
−2x - y = 9
+ 2x + 2x
_________

<em>Slope-Intercept</em><em> </em><em>Form</em>
_______________________________________________
x + 5y = 5
x-intercept → Plug in 0 for y to get 5 for x
y-intercept → Plug in 0 for x to get 1 for y
x + 5y = 5
- x - x
_________

<em>Slope-Intercept Form</em>
_______________________________________________
3x - 4y = 12
x-intercept → Plug in 0 for y to get 4 for x
y-intercept → Plug in 0 for x to get −3 for y
3x - 4y = 12
- 3x - 3x
_________

<em>Slope-Intercept Form</em>
I am joyous to assist you anytime.
Answer:
125 degree
Step-by-step explanation:
As m // n, so angle 2 and angle 6 is the same so angle 2 = 55 degree, then angle 1 + angle 2 = 180 degree, so angle 1 = 180 - 55 = 125 degree.
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