No. this is because a triangle’s short sides added together must be equal to or dreamer than the length of the longest side. for example a triangle with the side lengths 2,5,7 could be a triangle because 2+5 is equal to 7. even if the longest side was 6 units long it would still be a triangle. in this situation though the side lengths are 3,4,9. 3+4=7 and 7<9. this is not a triangle.
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Answer:
165
Step-by-step explanation:
![5c^{2} -3d+15](https://tex.z-dn.net/?f=5c%5E%7B2%7D%20-3d%2B15)
c = 6 and d = 10
= 5 × 6² = 5 × 36 = 180
- ( 3 d ) = 180 - ( 3 × 10 ) = 180 - 30 = 150
- 3 d ( + 15 ) = 150 + 15 = 165
Answer:
Speed of boat is still water: 16 miles per hour.
Speed of current: 8 miles per hour.
Step-by-step explanation:
Let x represent speed of boat in still water and y represent speed of current.
Downstream speed would be
.
Upstream speed would be
.
We have been given that a boat traveled 96 miles downstream and back. The trip downstream took 4 hours.
![\text{Rate}=\frac{\text{Distance}}{\text{Time}}](https://tex.z-dn.net/?f=%5Ctext%7BRate%7D%3D%5Cfrac%7B%5Ctext%7BDistance%7D%7D%7B%5Ctext%7BTime%7D%7D)
![x+y=\frac{96}{4}...(1)](https://tex.z-dn.net/?f=x%2By%3D%5Cfrac%7B96%7D%7B4%7D...%281%29)
![x+y=24...(1)](https://tex.z-dn.net/?f=x%2By%3D24...%281%29)
We are also told that the trip back took 12 hours. We can represent this information in an equation as:
![x-y=\frac{96}{12}...(2)](https://tex.z-dn.net/?f=x-y%3D%5Cfrac%7B96%7D%7B12%7D...%282%29)
![x-y=8...(2)](https://tex.z-dn.net/?f=x-y%3D8...%282%29)
Upon adding equation (1) and equation (2), we will get:
![x+x+y-y=24+8](https://tex.z-dn.net/?f=x%2Bx%2By-y%3D24%2B8)
![2x=32](https://tex.z-dn.net/?f=2x%3D32)
![\frac{2x}{2}=\frac{32}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%7D%7B2%7D%3D%5Cfrac%7B32%7D%7B2%7D)
![x=16](https://tex.z-dn.net/?f=x%3D16)
Therefore, the speed of boat in the still water is 16 miles per hour.
Upon substituting
in equation (1), we will get:
![16+y=24](https://tex.z-dn.net/?f=16%2By%3D24)
![16-16+y=24-16](https://tex.z-dn.net/?f=16-16%2By%3D24-16)
![y=8](https://tex.z-dn.net/?f=y%3D8)
Therefore, the speed of the current is 8 miles per hour.
Question 1:To change the new image back into the original image, just do the opposite.
To change the original image to the new image, we added x by 3 and subtracted 7 from y.
To change the new image back to the original image, subtract x by 3 and add 7 to y.
Writing this into an equation gives us the following:
Question 2:An isometry is a transformation of an image where the new image is congruent to the preimage.
The second and third choices are incorrect because the preimage is not congruent to the new image in these two choices.
The fourth choice is incorrect because having the same position is not an isometric transformation.
Thus, the answer is the first choice.
Answer:
C
Step-by-step explanation:
(2x+3)(x+4) = 2x² + 8x + 3x + 12
= 2x² + 11x + 12 ≠ 2x² + 10x + 12