From information given, we know
208 miles was at rate of 65 mph. so divide total mileage by speed to get time spent.
208 ÷ 65 = 3.2 hours
So the rest of the trip took 6 - 3.2 = 2.8hours to travel another 348 total miles minus the 208 miles driven at 65mph is 140 miles.
140 miles divided by 2.8 hours gives speed
140 ÷ 2.8 = 50 miles per hour
In the problem, the first equation should be represented like this base on the variable given in the problem:
20p + 9t = 44.4
with that equation, the second equation would is given by this formula, in response with the additional number of paperback and textbook
21p + 14t = 51
to get the system equation in getting the mass of each variable, you should subtract the two equation to simplified the formula.
20p + 9t = 44.4
- 21p + 14t = 51
-------------------------
p + 5t = 6.6 // this is the system equation that could be use in getting the mass of each object
Answer:
Step-by-step explanation:
20 gallons of water for 5 days...
20/5 = 4 gallons per day
1 gallon = 3.8 liters.....so 4 gallons = (3.8 * 4) = 15.2 liters per day <==
There is a formula which employs the use of determinants and which helps us calculate the area of a triangle if the vertices are given as
. The formula is as shown below:
Area=![\frac{1}{2}\begin{vmatrix}x_1&y_1&1 \\ x_2&y_2&1\\ x_3&y_3&1\end{vmatrix}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Cbegin%7Bvmatrix%7Dx_1%26y_1%261%20%5C%5C%20x_2%26y_2%261%5C%5C%20x_3%26y_3%261%5Cend%7Bvmatrix%7D)
Now, in our case, we have: ![(x_1,y_1)=(3,3)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%3D%283%2C3%29)
, and
![(x_3,y_3)=(-2,-5)](https://tex.z-dn.net/?f=%28x_3%2Cy_3%29%3D%28-2%2C-5%29)
Thus, the area in this case will become:
Area=![\frac{1}{2}\begin{vmatrix}3&3&1 \\ 3&-1&1\\ -2&-5&1\end{vmatrix}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Cbegin%7Bvmatrix%7D3%263%261%20%5C%5C%203%26-1%261%5C%5C%20-2%26-5%261%5Cend%7Bvmatrix%7D)
Therefore, Area=![\frac{1}{2}\times [[3(-1\times 1-(-5)\times 1]-3[3\times 1-(-2)\times 1]+1[3\times -5-2]]= \frac{1}{2}\times -20=-10](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20%5B%5B3%28-1%5Ctimes%201-%28-5%29%5Ctimes%201%5D-3%5B3%5Ctimes%201-%28-2%29%5Ctimes%201%5D%2B1%5B3%5Ctimes%20-5-2%5D%5D%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20-20%3D-10)
We know that area cannot be negative, so the area of the given triangle is <u>10 squared units</u>.