Hello!
Your answer is: 7
(X = "<em>A number</em>")
<em>"11 more than four times a number is 39"</em> in equation form is: 4X + 11 = 39
to solve, first subtract 11 from both sides:
4X = 28
then divide both sides by 4 to get:
X = 7
I hope this helps, and have a nice day!
Answer:
Diameter: Circumference
Step-by-step explanation:
Because this is Pi, which is the same for any circle.
Step-by-step explanation:
The discriminant of the quadratic equation
:
![\Delta=b^2-4ac](https://tex.z-dn.net/?f=%5CDelta%3Db%5E2-4ac)
If Δ < 0, then the equation has two complex roots ![x=\dfrac{-b\pm\sqrt\Delta}{2a}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%5CDelta%7D%7B2a%7D)
If Δ = 0, then the equation has one repeated root ![x=\dfrac{-b}{2a}[/tex If Δ > 0, then the equation has two discint roots [tex]x=\dfrac{-b\pm\sqrt\Delta}{2a}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-b%7D%7B2a%7D%5B%2Ftex%20%3C%2Fp%3E%3Cp%3EIf%20%CE%94%20%3E%200%2C%20then%20the%20equation%20has%20two%20discint%20roots%20%5Btex%5Dx%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%5CDelta%7D%7B2a%7D)
![1.\ x^2-4x+2=0\\\\a=1,\ b=-4,\ c=2\\\\\Delta=(-4)^2-4(1)(2)=16-8=8>0,\ \bold{two\ distinct\ roots}\\\sqrt\Delta=\sqrt8=\sqrt{4\cdot2}=2\sqrt2\\\\x=\dfrac{-(-4)\pm2\sqrt2}{2(1)}=\dfrac{4\pm2\sqrt2}{2}=2\pm\sqrt2\\\\==============================\\\\2.\ 5x^2-2x+3=0\\\\a=5,\ b=-2,\ c=3\\\\\Delta=(-2)^2-4(5)(3)=4-60=-56](https://tex.z-dn.net/?f=1.%5C%20x%5E2-4x%2B2%3D0%5C%5C%5C%5Ca%3D1%2C%5C%20b%3D-4%2C%5C%20c%3D2%5C%5C%5C%5C%5CDelta%3D%28-4%29%5E2-4%281%29%282%29%3D16-8%3D8%3E0%2C%5C%20%5Cbold%7Btwo%5C%20distinct%5C%20roots%7D%5C%5C%5Csqrt%5CDelta%3D%5Csqrt8%3D%5Csqrt%7B4%5Ccdot2%7D%3D2%5Csqrt2%5C%5C%5C%5Cx%3D%5Cdfrac%7B-%28-4%29%5Cpm2%5Csqrt2%7D%7B2%281%29%7D%3D%5Cdfrac%7B4%5Cpm2%5Csqrt2%7D%7B2%7D%3D2%5Cpm%5Csqrt2%5C%5C%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%5C%5C2.%5C%205x%5E2-2x%2B3%3D0%5C%5C%5C%5Ca%3D5%2C%5C%20b%3D-2%2C%5C%20c%3D3%5C%5C%5C%5C%5CDelta%3D%28-2%29%5E2-4%285%29%283%29%3D4-60%3D-56%3C0%2C%5C%20%5Cbold%7Btwo%5C%20complex%5C%20roots%7D%5C%5C%5Csqrt%5CDelta%3D%5Csqrt%7B-56%7D%3D%5Csqrt%7B%28-4%29%2814%29%7D%3D2%5Csqrt%7B14%7D%5C%20i%5C%5C%5C%5Cx%3D%5Cdfrac%7B-%28-2%29%5Cpm2%5Csqrt%7B14%7D%5C%20i%7D%7B%282%29%285%29%7D%3D%5Cdfrac%7B1%5Cpm%5Csqrt%7B14%7D%5C%20i%7D%7B5%7D%5C%5C%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D)
![3.\ 2x^2+x-6=0\\\\a=2,\ b=1,\ c=-6\\\\\Delta=1^2-4(2)(-6)=1+48=49>0,\ \bold{two\ distinct\ roots}\\\sqrt\Delta=\sqrt{49}=7\\\\x=\dfrac{-1\pm7}{(2)(2)}\\\\x_1=\dfrac{-8}{4}=-2,\ x_2=\dfrac{6}{4}=\dfrac{3}{2}\\\\==============================\\\\4.\ 13x^2-4=0\qquad\text{add 4 to both sides}\\\\13x^2=4\qquad\text{divide both sides by 13}\\\\x^2=\dfrac{4}{13}\to x=\pm\sqrt{\dfrac{4}{13}},\ \bold{two\ distinct\ roots}\\\\==============================](https://tex.z-dn.net/?f=3.%5C%202x%5E2%2Bx-6%3D0%5C%5C%5C%5Ca%3D2%2C%5C%20b%3D1%2C%5C%20c%3D-6%5C%5C%5C%5C%5CDelta%3D1%5E2-4%282%29%28-6%29%3D1%2B48%3D49%3E0%2C%5C%20%5Cbold%7Btwo%5C%20distinct%5C%20roots%7D%5C%5C%5Csqrt%5CDelta%3D%5Csqrt%7B49%7D%3D7%5C%5C%5C%5Cx%3D%5Cdfrac%7B-1%5Cpm7%7D%7B%282%29%282%29%7D%5C%5C%5C%5Cx_1%3D%5Cdfrac%7B-8%7D%7B4%7D%3D-2%2C%5C%20x_2%3D%5Cdfrac%7B6%7D%7B4%7D%3D%5Cdfrac%7B3%7D%7B2%7D%5C%5C%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%5C%5C4.%5C%2013x%5E2-4%3D0%5Cqquad%5Ctext%7Badd%204%20to%20both%20sides%7D%5C%5C%5C%5C13x%5E2%3D4%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%2013%7D%5C%5C%5C%5Cx%5E2%3D%5Cdfrac%7B4%7D%7B13%7D%5Cto%20x%3D%5Cpm%5Csqrt%7B%5Cdfrac%7B4%7D%7B13%7D%7D%2C%5C%20%5Cbold%7Btwo%5C%20distinct%5C%20roots%7D%5C%5C%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D)
![5.\ x^2-6x+16=0\\\\a=1,\ b=-6,\ c=16\\\\\Delta=(-6)^2-4(1)(16)=36-64=-28](https://tex.z-dn.net/?f=5.%5C%20x%5E2-6x%2B16%3D0%5C%5C%5C%5Ca%3D1%2C%5C%20b%3D-6%2C%5C%20c%3D16%5C%5C%5C%5C%5CDelta%3D%28-6%29%5E2-4%281%29%2816%29%3D36-64%3D-28%3C0%2C%5C%20%5Cbold%7Btwo%5C%20complex%5C%20roots%7D%5C%5C%5Csqrt%5CDelta%3D%5Csqrt%7B-28%7D%3D%5Csqrt%7B%28-4%29%287%29%7D%3D2%5Csqrt7%5C%20i%5C%5C%5C%5Cx%3D%5Cdfrac%7B-%28-6%29%5Cpm2%5Csqrt7%5C%20i%7D%7B%282%29%281%29%7D%3D3%5Cpm%5Csqrt7%5C%20i%5C%5C%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%5C%5C6.%5C%20x%5E2-8x%2B16%3D0%5C%5C%5C%5Ca%3D1%2C%5C%20b%3D-8%2C%5C%20c%3D16%5C%5C%5C%5C%5CDelta%3D%28-8%29%5E2-4%281%29%2816%29%3D64-64%3D0%2C%5C%20%5Cbold%7Bone%5C%20repea%7D%5Cbold%7Bted%5C%20root%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-%28-8%29%7D%7B%282%29%281%29%7D%3D%5Cdfrac%7B8%7D%7B2%7D%3D4%5C%5C%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%5C%5C)
![7.\ 4x^2+11=0\qquad\text{subtract 11 from both sides}\\\\4x^2=-11\qquad\text{divide both sides by 4}\\\\x^2=-\dfrac{11}{4}\to x=\pm\sqrt{-\dfrac{11}{4}}\\\\x=\pm\dfrac{\sqrt{11}}{2}\ i,\ \bold{two\ complex\ roots}](https://tex.z-dn.net/?f=7.%5C%204x%5E2%2B11%3D0%5Cqquad%5Ctext%7Bsubtract%2011%20from%20both%20sides%7D%5C%5C%5C%5C4x%5E2%3D-11%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%204%7D%5C%5C%5C%5Cx%5E2%3D-%5Cdfrac%7B11%7D%7B4%7D%5Cto%20x%3D%5Cpm%5Csqrt%7B-%5Cdfrac%7B11%7D%7B4%7D%7D%5C%5C%5C%5Cx%3D%5Cpm%5Cdfrac%7B%5Csqrt%7B11%7D%7D%7B2%7D%5C%20i%2C%5C%20%5Cbold%7Btwo%5C%20complex%5C%20roots%7D)
Answer:
Step-by-step explanation:
The answer is 0.000000014
Answer:
30 cubes
Step-by-step explanation:
To find the number of small cubes in the larger cuboid, you can multiply the number of cubes that make up the length, width and height together.
There are 5 cubes along the bottom, 2 along the side and 3 going up. The volume would be 5 × 2 × 3 which is 30 cubes.
Hope this helps!