If G is the midpoint of FH find FG
fg=11x-7 gh= 3x+9
Answer:
-23, -24
Step-by-step explanation:
Adding negative numbers gets you another negative number. Therefore the numbers must be -23 and -24.
- Quadratic Formula:
, with a = x^2 coefficient, b = x coefficient, and c = constant.
Firstly, starting with the y-intercept. To find the y-intercept, set the x variable to zero and solve as such:
![y=3*0^2+24*0-51\\y=0+0-51\\y=-51](https://tex.z-dn.net/?f=y%3D3%2A0%5E2%2B24%2A0-51%5C%5Cy%3D0%2B0-51%5C%5Cy%3D-51)
<u>Your y-intercept is (0,-51).</u>
Next, using our equation plug the appropriate values into the quadratic formula:
![x=\frac{-24\pm \sqrt{24^2-4*3*(-54)}}{2*3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-24%5Cpm%20%5Csqrt%7B24%5E2-4%2A3%2A%28-54%29%7D%7D%7B2%2A3%7D)
Next, solve the multiplications and exponent:
![x=\frac{-24\pm \sqrt{576-(-648)}}{6}\\\\x=\frac{-24\pm \sqrt{576+648}}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-24%5Cpm%20%5Csqrt%7B576-%28-648%29%7D%7D%7B6%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B-24%5Cpm%20%5Csqrt%7B576%2B648%7D%7D%7B6%7D)
Next, solve the addition:
![x=\frac{-24\pm \sqrt{1224}}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-24%5Cpm%20%5Csqrt%7B1224%7D%7D%7B6%7D)
Now, simplify the radical using the product rule of radicals as such:
- Product Rule of Radicals: √ab = √a × √b
√1224 = √12 × √102 = √2 × √6 × √6 × √17 = 6 × √2 × √17 = 6√34
![x=\frac{-24\pm 6\sqrt{34}}{6}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-24%5Cpm%206%5Csqrt%7B34%7D%7D%7B6%7D)
Next, divide:
![x=-4\pm \sqrt{34}](https://tex.z-dn.net/?f=x%3D-4%5Cpm%20%5Csqrt%7B34%7D)
<u>The exact values of your x-intercepts are (-4 + √34, 0) and (-4 - √34, 0).</u>
Now to find the approximate values, solve this twice: once with the + symbol and once with the - symbol:
![x=-4+ \sqrt{34},-4- \sqrt{34}\\x\approx 1.83, -9.83](https://tex.z-dn.net/?f=x%3D-4%2B%20%5Csqrt%7B34%7D%2C-4-%20%5Csqrt%7B34%7D%5C%5Cx%5Capprox%201.83%2C%20-9.83)
<u>The approximate values of your x-intercepts (rounded to the hundredths) are (1.83,0) and (-9.83,0).</u>
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