Answer:
- π = S/2πrh
- v = √2E/m
- b = (-7a+c)/2
- x =3y-1
Step-by-step explanation:
1.
![S = 2\pi rh\\Divide\:both\sides\:of\:the\:equation\:by\:2rh\\\\\frac{S}{2rh} = \frac{2 \pi rh}{2 rh} \\\\\pi = \frac{S}{2rh}](https://tex.z-dn.net/?f=S%20%3D%202%5Cpi%20rh%5C%5CDivide%5C%3Aboth%5Csides%5C%3Aof%5C%3Athe%5C%3Aequation%5C%3Aby%5C%3A2rh%5C%5C%5C%5C%5Cfrac%7BS%7D%7B2rh%7D%20%3D%20%5Cfrac%7B2%20%5Cpi%20rh%7D%7B2%20rh%7D%20%5C%5C%5C%5C%5Cpi%20%3D%20%5Cfrac%7BS%7D%7B2rh%7D)
2.
![E = \frac{1}{2} mv^2\\\\E = \frac{mv^2}{2} \\\\Cross\:multiply\\\\2E =mv^2\\Divide\:both\:sides\:of\:the\:equation\:by\:m\\\frac{2E}{m} = \frac{mv^2}{m} \\\\\frac{2E}{m} =v^2\\Square\:root\:both\:sides\:of\:the\:equation\\\sqrt{\frac{2E}{m} } = \sqrt{v^2} \\\\\sqrt{\frac{2E}{m} } =v\\\\v =\sqrt{\frac{2E}{m} }](https://tex.z-dn.net/?f=E%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20mv%5E2%5C%5C%5C%5CE%20%3D%20%5Cfrac%7Bmv%5E2%7D%7B2%7D%20%5C%5C%5C%5CCross%5C%3Amultiply%5C%5C%5C%5C2E%20%3Dmv%5E2%5C%5CDivide%5C%3Aboth%5C%3Asides%5C%3Aof%5C%3Athe%5C%3Aequation%5C%3Aby%5C%3Am%5C%5C%5Cfrac%7B2E%7D%7Bm%7D%20%3D%20%5Cfrac%7Bmv%5E2%7D%7Bm%7D%20%5C%5C%5C%5C%5Cfrac%7B2E%7D%7Bm%7D%20%3Dv%5E2%5C%5CSquare%5C%3Aroot%5C%3Aboth%5C%3Asides%5C%3Aof%5C%3Athe%5C%3Aequation%5C%5C%5Csqrt%7B%5Cfrac%7B2E%7D%7Bm%7D%20%7D%20%3D%20%5Csqrt%7Bv%5E2%7D%20%5C%5C%5C%5C%5Csqrt%7B%5Cfrac%7B2E%7D%7Bm%7D%20%7D%20%3Dv%5C%5C%5C%5Cv%20%3D%5Csqrt%7B%5Cfrac%7B2E%7D%7Bm%7D%20%7D)
3.
![7a+2b =c\\Isolate\:b\\\\2b =c-7a\\2b= -7a+c\\Divide\:both\:sides\:of\:the\:equation\:by \:2\\\frac{2b}{2} =\frac{-7a+c}{2} \\\\b = \frac{-7a+c}{2}](https://tex.z-dn.net/?f=7a%2B2b%20%3Dc%5C%5CIsolate%5C%3Ab%5C%5C%5C%5C2b%20%3Dc-7a%5C%5C2b%3D%20-7a%2Bc%5C%5CDivide%5C%3Aboth%5C%3Asides%5C%3Aof%5C%3Athe%5C%3Aequation%5C%3Aby%20%5C%3A2%5C%5C%5Cfrac%7B2b%7D%7B2%7D%20%3D%5Cfrac%7B-7a%2Bc%7D%7B2%7D%20%5C%5C%5C%5Cb%20%3D%20%5Cfrac%7B-7a%2Bc%7D%7B2%7D)
4.
![y = \frac{1}{3} (x+1)\\\\y = \frac{x+1}{3}\\\\Cross\:multiply \\3y =x+1\\Isolate \:x\\3y -1=x\\\\x =3y-1](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%28x%2B1%29%5C%5C%5C%5Cy%20%3D%20%5Cfrac%7Bx%2B1%7D%7B3%7D%5C%5C%5C%5CCross%5C%3Amultiply%20%5C%5C3y%20%3Dx%2B1%5C%5CIsolate%20%5C%3Ax%5C%5C3y%20-1%3Dx%5C%5C%5C%5Cx%20%3D3y-1)
What is the binomial raised to? you can’t do this problem without it
Answer: $25 spent
Step-by-step explanation: the boy spent $15/total.
15/total=3/8
Divide by common factor: $15/3=$5 (1/8 total money
$5x8=$40
$40-$15=$25 spent
Answer:
68 aliens
Step-by-step explanation:
Take the fraction of aliens that had 3 eyes and multiply by the number of aliens
17 / 40 * 160 =
17 * 160/40
17 *4
68