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:
1.
40 students chose papa johns and 24 did not
2. 14 students chose dominos and 10 chose pizza hut
Step-by-step explanation:
1. set up a proportion like 5/8 x x/64 and cross mutliply like 8 times x and 5 times 64
Answer:
6
Step-by-step explanation:
The type of land form that Caleb most likely draws is a hill. The answer is option C- a hill.
Step-by-step explanation:
- Contour lines are <u>drawn to represent the changes in the elevation</u> which helps to know the slope of the figure drawn.
- If the contour lines are drawn close, then steeper the figure is. And more distant the lines are drawn, then less steep the figure is.
- Here, the lines seem to be likely circle in shape. The distance of the outermost contour line is 20 ft. The <u>next inner lines will have reduced values of 20 ft.</u>
- Therefore, <u>the elevation gets reduced from higher to lower points</u> which provides a diagram of a hill. Since there is no continuous high and low elevations, this cannot be a valley (a range of mountains).
- Furthermore, The contour diagram for option A and D such as creek(water stream) or shoreline will have different and mixed values of elevations that seems to be a messy structure of contour lines.
