Answer:
1st Circle
Radius = 9
Diameter = 18
Circumference = 2 ×
× r = 2 × 3.14 × 9 = 56.52
2nd Circle
Radius = 14
Diameter = 28
Circumference = 2 ×
× r = 2 × 3.14 × 14 = 87.92
:D
Answer:
![k=-5](https://tex.z-dn.net/?f=k%3D-5)
Step-by-step explanation:
we know that
The formula to solve a quadratic equation of the form
![ax^{2} +bx+c=0](https://tex.z-dn.net/?f=ax%5E%7B2%7D%20%2Bbx%2Bc%3D0)
is equal to
![x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E%7B2%7D-4ac%7D%7D%20%7B2a%7D)
in this problem we have
so
![a=6\\b=7\\c=k](https://tex.z-dn.net/?f=a%3D6%5C%5Cb%3D7%5C%5Cc%3Dk)
substitute in the formula
![x=\frac{-7\pm\sqrt{7^{2}-4(6)(k)}} {2(6)}\\\\x=\frac{-7\pm\sqrt{49-24k}} {12}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-7%5Cpm%5Csqrt%7B7%5E%7B2%7D-4%286%29%28k%29%7D%7D%20%7B2%286%29%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B-7%5Cpm%5Csqrt%7B49-24k%7D%7D%20%7B12%7D)
so
![x_1=\frac{-7+\sqrt{49-24k}} {12}\\\\x_2=\frac{-7-\sqrt{49-24k}} {12}](https://tex.z-dn.net/?f=x_1%3D%5Cfrac%7B-7%2B%5Csqrt%7B49-24k%7D%7D%20%7B12%7D%5C%5C%5C%5Cx_2%3D%5Cfrac%7B-7-%5Csqrt%7B49-24k%7D%7D%20%7B12%7D)
Remember that
![2x_1+3x_2=-4](https://tex.z-dn.net/?f=2x_1%2B3x_2%3D-4)
substitute
![2(\frac{-7+\sqrt{49-24k}} {12})+3(\frac{-7-\sqrt{49-24k}} {12})=-4\\\\(\frac{-14+2\sqrt{49-24k}} {12})+(\frac{-21-3\sqrt{49-24k}} {12})=-4](https://tex.z-dn.net/?f=2%28%5Cfrac%7B-7%2B%5Csqrt%7B49-24k%7D%7D%20%7B12%7D%29%2B3%28%5Cfrac%7B-7-%5Csqrt%7B49-24k%7D%7D%20%7B12%7D%29%3D-4%5C%5C%5C%5C%28%5Cfrac%7B-14%2B2%5Csqrt%7B49-24k%7D%7D%20%7B12%7D%29%2B%28%5Cfrac%7B-21-3%5Csqrt%7B49-24k%7D%7D%20%7B12%7D%29%3D-4)
Multiply by 12 both sides
![(-14+2\sqrt{49-24k})+(-21-3\sqrt{49-24k})=-48\\\\-35-\sqrt{49-24k}=-48\\\\\sqrt{49-24k}=48-35\\\\\sqrt{49-24k}=13](https://tex.z-dn.net/?f=%28-14%2B2%5Csqrt%7B49-24k%7D%29%2B%28-21-3%5Csqrt%7B49-24k%7D%29%3D-48%5C%5C%5C%5C-35-%5Csqrt%7B49-24k%7D%3D-48%5C%5C%5C%5C%5Csqrt%7B49-24k%7D%3D48-35%5C%5C%5C%5C%5Csqrt%7B49-24k%7D%3D13)
squared both sides
![49-24k=169\\24k=49-169\\24k=-120\\k=-5](https://tex.z-dn.net/?f=49-24k%3D169%5C%5C24k%3D49-169%5C%5C24k%3D-120%5C%5Ck%3D-5)
therefore
The equation is
![6x^{2} +7x-5=0](https://tex.z-dn.net/?f=6x%5E%7B2%7D%20%2B7x-5%3D0)
The roots are
![x=\frac{-7\pm\sqrt{49-24(-5)}} {12}\\\\x=\frac{-7\pm\sqrt{169}} {12}\\\\x=\frac{-7\pm13} {12}\\\\x_1=\frac{-7+13} {12}=\frac{1} {2}\\\\x_2=\frac{-7-13} {12}=-\frac{5} {3}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B-7%5Cpm%5Csqrt%7B49-24%28-5%29%7D%7D%20%7B12%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B-7%5Cpm%5Csqrt%7B169%7D%7D%20%7B12%7D%5C%5C%5C%5Cx%3D%5Cfrac%7B-7%5Cpm13%7D%20%7B12%7D%5C%5C%5C%5Cx_1%3D%5Cfrac%7B-7%2B13%7D%20%7B12%7D%3D%5Cfrac%7B1%7D%20%7B2%7D%5C%5C%5C%5Cx_2%3D%5Cfrac%7B-7-13%7D%20%7B12%7D%3D-%5Cfrac%7B5%7D%20%7B3%7D)
6x + 2 and 3x + 1 are both equal to y, so they are both equal to each other.
6x + 2 = 3x + 1
3x = -1
x = -1/3
And plugging -1/3 in for x yields y = 0.
Answer:
3/13
Step-by-step explanation:
three socks out of the 13 are black. therefore you have a 3/13 chance of picking black.