Answer: h = 9
Step-by-step explanation: A system of linear equations is consistent when it has at least one solution.
The matrix given is:
![\left[\begin{array}{ccc}-15&21&h\\5&-7&-3\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C5%26-7%26-3%5Cend%7Barray%7D%5Cright%5D)
Transform this matrix in a row-echelon form:
![\left[\begin{array}{ccc}-15&21&h\\0&0&-9+h\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-15%2621%26h%5C%5C0%260%26-9%2Bh%5Cend%7Barray%7D%5Cright%5D)
For this row-echelon form to have solutions:
-9 + h = 0
h = 9
For this system to be consistent: h = 9.
Answer:
Exact Form:
73 over 2
Decimal Form:
36.5
Mixed Number Form:
36 1 over 2
Step-by-step explanation:
Substitute the value of the variable into the equation and simplify.
($3756/100)(100+12)/100
$37.56(1.12)
$42.0672
$42.07 (to nearest cent)
Answer:
radius=11.5
diameter=23
Step-by-step explanation:
The volume of a sphere is V=4/3 Pi r^3
We can use this to solve for the radius.
555.4= 4/3 (3.14)r^3
Solve for r how you would any other equation. Multiply 4/3 and 3.14.
555.4=4.187 r^3
Divide both sides by 4.187
132.65=r^3
To get rid of the ^3, find the cube root of both sides on a calcualtor.
r= 11.5
The diameter is the radius time two.
11.5 (2)=23.
Hope this helps!
Note: When I say both sides, I mean both sides of the = sign.
Answer:
d = 244
Step-by-step explanation:
