Answer:
3 over 2
Step-by-step explanation:
Consider ΔAQD. This triangle has the area
![A_{AQD}=\dfrac{1}{2}\cdot AD\cdot H,](https://tex.z-dn.net/?f=A_%7BAQD%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20AD%5Ccdot%20H%2C)
where H is the heigh drawn from the point Q to the side AD.
Note that the height H is also the height of the parallelogram. So the area of the parallelogram ABCD is
![A_{ABCD}=AD\cdot H.](https://tex.z-dn.net/?f=A_%7BABCD%7D%3DAD%5Ccdot%20H.)
From these two statements you can conclude that
![A_{ABCD}=2A_{AQD}.](https://tex.z-dn.net/?f=A_%7BABCD%7D%3D2A_%7BAQD%7D.)
Now consider ΔDMQ. The ratio between the area of triangles DMQ and AQD is
![\dfrac{A_{\triangle DMQ}}{A_{\triangle AQD}}=\dfrac{\frac{1}{2}\cdot MQ\cdot h}{\frac{1}{2}\cdot AQ\cdot h}=\dfrac{MQ}{AQ}.](https://tex.z-dn.net/?f=%5Cdfrac%7BA_%7B%5Ctriangle%20DMQ%7D%7D%7BA_%7B%5Ctriangle%20AQD%7D%7D%3D%5Cdfrac%7B%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20MQ%5Ccdot%20h%7D%7B%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20AQ%5Ccdot%20h%7D%3D%5Cdfrac%7BMQ%7D%7BAQ%7D.)
Since
you have that
and
![\dfrac{A_{\triangle DMQ}}{A_{\triangle AQD}}=\dfrac{2}{5}.](https://tex.z-dn.net/?f=%5Cdfrac%7BA_%7B%5Ctriangle%20DMQ%7D%7D%7BA_%7B%5Ctriangle%20AQD%7D%7D%3D%5Cdfrac%7B2%7D%7B5%7D.)
Thus,
![\dfrac{A_{\triangle DMQ}}{A_{ABCD}}=\dfrac{A_{\triangle DMQ}}{2A_{\triangle AQD}}=\dfrac{1}{2}\cdot \dfrac{2}{5}=\dfrac{1}{5}.](https://tex.z-dn.net/?f=%5Cdfrac%7BA_%7B%5Ctriangle%20DMQ%7D%7D%7BA_%7BABCD%7D%7D%3D%5Cdfrac%7BA_%7B%5Ctriangle%20DMQ%7D%7D%7B2A_%7B%5Ctriangle%20AQD%7D%7D%3D%5Cdfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cdfrac%7B2%7D%7B5%7D%3D%5Cdfrac%7B1%7D%7B5%7D.)
Answer: correct choice is B
Answer:
v = -15
Step-by-step explanation:
-25 = v - 10 (add 25 to both sides)
0 = v - 10 + 25
0 = v + 15 (subtract 15 from both sides)
0 - 15 = v + 15 - 15
-15 = v
v = -15
Hope this helps.
Answer:
Erie to Rochester is 145 miles
Step-by-step explanation:
If we designate the points of interest as C, E, and R, we are told that ...
CE + ER = CR . . . . . the various distances are segments of a straight line
For CE = 94 and CR = 239, we can fill in the given information and solve for ER.
94 + ER = 239
ER = 239 -94 . . . . . . subtract 94 from both sides of the equation
ER = 145
The distance from Erie to Rochester is 145 miles.