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.
When you plot the offered points on the graph, you find only one of them falls inside the shaded region:
... D. 43 pepperoni slices and 25 cheese slices
Answer:
A.200
Step-by-step explanation:
Answer:
New length is 3 3/20 ft.
Step-by-step explanation:
The total board is 2 5/8 feet long. And since 5/6 of a foot is trimmed off, that means each piece of wood is 5/6 feet.
We can now set up an equation like this ---> 5/6 ⋅ x = 2 5/8
Now we're going to simplify ---> 5/6 ⋅ x = 2 5/8
5/6 ⋅ x = 21/8
(multiply both sides by 6)
5x = 63/4
(divide both sides by 5)
x = 63/20
x= 3.15
So, the new length is 3.15 feet long, or 3 3/20 in mixed fraction.
The fraction 5/10 is the same as 50/100 because they are equivalent. It will take 10 group of 10 to get to the denominator 100, so it will take 10 groups of 5 in the numerator to make it equal.
The answer is 50/100.