Answer:
![x=\frac{132}{25}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B132%7D%7B25%7D)
Step-by-step explanation:
We have to solve for the value of "x". The equation is:
![\frac{1}{3}(12+x)=8(6-x)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%2812%2Bx%29%3D8%286-x%29)
We can use the distributive property shown below to simplify the expression and find the value of x.
<u>Distributive property:</u> ![a(b+c)=ab+ac](https://tex.z-dn.net/?f=a%28b%2Bc%29%3Dab%2Bac)
Now, we solve:
![\frac{1}{3}(12+x)=8(6-x)\\4+\frac{1}{3}x=48-8x\\\frac{1}{3}x+8x=48-4\\8\frac{1}{3}x=44\\\frac{25}{3}x=44\\x=\frac{44}{\frac{25}{3}}\\x=44*\frac{3}{25}\\x=\frac{132}{25}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%2812%2Bx%29%3D8%286-x%29%5C%5C4%2B%5Cfrac%7B1%7D%7B3%7Dx%3D48-8x%5C%5C%5Cfrac%7B1%7D%7B3%7Dx%2B8x%3D48-4%5C%5C8%5Cfrac%7B1%7D%7B3%7Dx%3D44%5C%5C%5Cfrac%7B25%7D%7B3%7Dx%3D44%5C%5Cx%3D%5Cfrac%7B44%7D%7B%5Cfrac%7B25%7D%7B3%7D%7D%5C%5Cx%3D44%2A%5Cfrac%7B3%7D%7B25%7D%5C%5Cx%3D%5Cfrac%7B132%7D%7B25%7D)
This is the improper fractional value of "x". So,
![x=\frac{132}{25}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B132%7D%7B25%7D)
Answer:
<em>A= 1256</em>
Step-by-step explanation:
<u>The formula for area of a circle is </u>![A=\pi r^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E%7B2%7D)
1. Diameter is DOUBLE of radius, so the diameter must be divided by 2. <em>40/2 = 20. </em>
<em>2. </em>Then, plug in the values into the area formula. <em>A= 3.14</em>![(20^{2})](https://tex.z-dn.net/?f=%2820%5E%7B2%7D%29)
3. Solve.<em> A= 1256</em>. (Remember that 20 squared is <em>20x20</em>)
Answer:
x = -5/2
Step-by-step explanation:
From the quadratic equation
the axis of symmetry for quadratics of the form
y = ax² + bx + c is
x = -b/2a
x² + 5x + 9
x = -5/2