The purpose of solving an algebraic expression in an equation is to find the unknown variable. When two expressions are equated, they form an equation and therefore, it becomes easier to solve for the unknown terms. To solve an equation, place the variables on one side and the constants on the other side.
Sure hope this helps
800,000,000.00
70,000,000.00
6,000,000.00
500,000.00
40,000.00
3,000.00
200.00
10.00
0.00
0.20
0.05
Answer:
x = -4
Step-by-step explanation:
2x+4(2x+7)=3(2x+4)
Distribute
2x+8x + 28 = 6x +12
Combine like terms
10x +28 = 6x +12
Subtract 6x from each side
10-6x+28 = 6x +12 -6x
4x +28 = 12
Subtract 28 from each side
4x+28-28 = 12-28
4x = -16
Divide each side by 4
4x/4 = -16/4
x = -4
Answer:
Step-by-step explanation:
To find the slope of the tangent at a point we will find the derivative of equation at that point.
a). y = x² - 10x
![\frac{dy}{dx}=\frac{d}{dx}(x^{2} -10x)](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7Bd%7D%7Bdx%7D%28x%5E%7B2%7D%20-10x%29)
y' = 2x - 10
At (x = 2),
y' = 2(2) - 10
y' = 4 - 10
y' = -6
From the given equation,
y = 2² - 10
y = -6
Therefore, y-coordinate of the point is y = -6
Equation of the tangent at (2, -6) having slope = -6
y - 2 = -6(x - 2)
y - 2 = -6x + 12
y = -6x + 14
b). y = ![x^{2}+\frac{2}{x}](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B%5Cfrac%7B2%7D%7Bx%7D)
At x = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
y = ![(\frac{1}{2})^2+\frac{2}{\frac{1}{2}}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%29%5E2%2B%5Cfrac%7B2%7D%7B%5Cfrac%7B1%7D%7B2%7D%7D)
y = ![\frac{1}{4}+4](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%2B4)
y = ![\frac{17}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B17%7D%7B4%7D)
Now we have to find the equation of a tangent at ![(\frac{1}{2},\frac{17}{4})](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B2%7D%2C%5Cfrac%7B17%7D%7B4%7D%29)
y' = 2x - ![\frac{2}{x^{2} }](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7Bx%5E%7B2%7D%20%7D)
At x = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
y' = ![2(\frac{1}{2})-\frac{2}{(\frac{1}{2})^2}](https://tex.z-dn.net/?f=2%28%5Cfrac%7B1%7D%7B2%7D%29-%5Cfrac%7B2%7D%7B%28%5Cfrac%7B1%7D%7B2%7D%29%5E2%7D)
y' = 1 - 8
y' = -7
Therefore, equation of the tangent at
will be,
![y-\frac{17}{4}=-7(x-\frac{1}{2})](https://tex.z-dn.net/?f=y-%5Cfrac%7B17%7D%7B4%7D%3D-7%28x-%5Cfrac%7B1%7D%7B2%7D%29)
y = -7x + ![\frac{7}{2}+\frac{17}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B2%7D%2B%5Cfrac%7B17%7D%7B4%7D)
y = -7x + ![\frac{31}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B31%7D%7B4%7D)
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