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Delicious77 [7]
3 years ago
15

Solve: 2(x-2)=6 please! also calculate the area of a circle with a diametre of 6 if the pie= 3

Mathematics
1 answer:
Tamiku [17]3 years ago
5 0
Answer for x would be 4. the area of the circle would be approx. 28.3.
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2logx=3-2log(x+3) solve for x​
AVprozaik [17]

Answer:

\large\boxed{x=\dfrac{-3+\sqrt{40+10\sqrt{10}}}{2}}

Step-by-step explanation:

2\log x=3-2\log(x+3)\\\\Domain:\ x>0\ \wedge\ x+3>0\to x>-3\\\\D:x>0\\============================\\2\log x=3-2\log(x+3)\qquad\text{add}\ 2\log(x+3)\ \text{to both sides}\\\\2\log x+2\log(x+3)=3\qquad\text{divide both sides by 2}\\\\\log x+\log(x+3)=\dfrac{3}{2}\qquad\text{use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log\bigg(x(x+3)\bigg)=\dfrac{3}{2}\qquad\text{use the de}\text{finition of a logarithm}\\\\x(x+3)=10^\frac{3}{2}\qquad\text{use the distributive property}

x^2+3x=10^{1\frac{1}{2}}\\\\x^2+3x=10^{1+\frac{1}{2}}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\x^2+3x=10\cdot10^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\x^2+3x=10\sqrt{10}\qquad\text{subtract}\ 10\sqrt{10}\ \text{from both sides}\\\\x^2+3x-10\sqrt{10}=0\\\\\text{Use the quadratic formula}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=1,\ b=3,\ c=-10\sqrt{10}\\\\b^2-4ac=3^2-4(1)(-10\sqrt{10})=9+40\sqrt{10}\\\\x=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2(1)}=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2}\\\\x=\dfrac{-3-\sqrt{10+10\sqrt{10}}}{2}\notin D

6 0
3 years ago
A circle is centered at (5, 4) and has radius 6. Write its equation in standard form.
dimulka [17.4K]
A circle equation is (x – h)^2<span> + (y – k)^</span>2<span> = r^</span><span>2 where (h,k) is the center and r is the radius. Now all we have to do is plug in the variables. 

Since (h,k)=(5,4) and r= 6

The answer would be C. 

Your welcome ;)





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8 0
3 years ago
Calculate volume of a planet if radius is 6050 and answer in scientific notation
Gre4nikov [31]

Answer:

9.3*10^11

Step-by-step explanation:

4/3πr^3=9.3*10^11

6 0
2 years ago
Geometry help pretty please 15 points plus brainliest plus be my friend x3
SVEN [57.7K]
1. X(0,0) --> X'(3,-5).
    To go from (0,0) to (3,-5), you must go to the right 3 and down 5.

I cannot answer 2 or 3, as rotations are not my strong suit.
4 0
3 years ago
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How do the height and base length of the two triangles compare to the height and base length of the original piece of paper?
notka56 [123]

Answer : The two dimensions are the same in the triangles as they were in the rectangle.

4 0
3 years ago
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