Answer:
One ml is equal to a cm3, then
m=2.67g/cm3*30.5cm3
m=81.435g
If we divide this quantity by 1000 to pass this to Kg we get:
m=81.435/1000=0.081435kg
Step-by-step explanation:
Remember the formula of density is density=mass/volume, if we solve for mass we get:
mass=density*volume
Step 1: Distributive Property
Step 2: Subtraction Property of Equality
Step 3: Addition Property of Equality
Step 4: Division Property of Equality
Answer:
Step-by-step explanation:
Answer:
Radius: 

Step-by-step explanation:
Given

Solving (a): The radius of the circle
First, we express the equation as:

Where


So, we have:

Divide through by 9

Rewrite as:

Group the expression into 2
![[x^2 + 3x] + [y^2+ \frac{12}{9}y] =- \frac{19}{9}](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B12%7D%7B9%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D)
![[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D)
Next, we complete the square on each group.
For ![[x^2 + 3x]](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D)
1: Divide the 
2: Take the 
3: Add this 
So, we have:
![[x^2 + 3x] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D)
![[x^2 + 3x + (\frac{3}{2})^2] + [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2](https://tex.z-dn.net/?f=%5Bx%5E2%20%20%2B%203x%20%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2%5D%20%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2)
Factorize
![[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y] =- \frac{19}{9}+ (\frac{3}{2})^2](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2)
Apply the same to y
![[x + \frac{3}{2}]^2+ [y^2+ \frac{4}{3}y +(\frac{4}{6})^2 ] =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%5E2%2B%20%5Cfrac%7B4%7D%7B3%7Dy%20%2B%28%5Cfrac%7B4%7D%7B6%7D%29%5E2%20%5D%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2%20%2B%28%5Cfrac%7B4%7D%7B6%7D%29%5E2)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ (\frac{3}{2})^2 +(\frac{4}{6})^2](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%28%5Cfrac%7B3%7D%7B2%7D%29%5E2%20%2B%28%5Cfrac%7B4%7D%7B6%7D%29%5E2)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =- \frac{19}{9}+ \frac{9}{4} +\frac{16}{36}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D-%20%5Cfrac%7B19%7D%7B9%7D%2B%20%5Cfrac%7B9%7D%7B4%7D%20%2B%5Cfrac%7B16%7D%7B36%7D)
Add the fractions
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{-19 * 4 + 9 * 9 + 16 * 1}{36}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D%5Cfrac%7B-19%20%2A%204%20%2B%209%20%2A%209%20%2B%2016%20%2A%201%7D%7B36%7D)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{21}{36}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D%5Cfrac%7B21%7D%7B36%7D)
![[x + \frac{3}{2}]^2+ [y +\frac{4}{6}]^2 =\frac{7}{12}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B4%7D%7B6%7D%5D%5E2%20%3D%5Cfrac%7B7%7D%7B12%7D)
![[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B2%7D%7B3%7D%5D%5E2%20%3D%5Cfrac%7B7%7D%7B12%7D)
Recall that:

By comparison:

Take square roots of both sides

Split

Rationalize





Solving (b): The center
Recall that:

Where


From:
![[x + \frac{3}{2}]^2+ [y +\frac{2}{3}]^2 =\frac{7}{12}](https://tex.z-dn.net/?f=%5Bx%20%2B%20%5Cfrac%7B3%7D%7B2%7D%5D%5E2%2B%20%5By%20%2B%5Cfrac%7B2%7D%7B3%7D%5D%5E2%20%3D%5Cfrac%7B7%7D%7B12%7D)
and 
Solve for h and k
and 
Hence, the center is:

Answer:
13 3/4
Step-by-step explanation:
2 3/4 is 11/4 when converted into an improper fraction.
5 is 5/1 when converted into a fraction.
11*5 is 55 (numerators)
4*1 is 4 (denominators)
55/4 is 13 with 3/4 remaining
13 3/4