The vase of the triangle would be x because it is unknown and the height would be x+2 because it is 2 more units than the base the formula for the area of a triangle is (base)(height)% 2 =area so (x)(x+2)%2=12 so then you have 1/2x^2+x=12 at this point I would move the 12 to the other side by subtracting to get 1/2x^2+x-12=0 then I would multiply it all by 2 to get x^2 + 2x-24 from there I would factor to get (x+6)(x-4) and your answers would be x= -6 and 4 and because 6 is negative it would not work because distances are always positive so the base would equal 4
Answer:
option B. ![x=38^o](https://tex.z-dn.net/?f=x%3D38%5Eo)
Step-by-step explanation:
we know that
1) The two diagonals of a rhombus are perpendicular
2) The sum of the interior angles in any triangle must be equal to 180 degrees
Let
O ----> the intersection point of the diagonals of the rhombus
In the right triangle OAD
![x^o+(x+14)^o+90^o=180^o](https://tex.z-dn.net/?f=x%5Eo%2B%28x%2B14%29%5Eo%2B90%5Eo%3D180%5Eo)
solve for x
![x^o+(x+14)^o=90^o](https://tex.z-dn.net/?f=x%5Eo%2B%28x%2B14%29%5Eo%3D90%5Eo)
![2x=90^o-14^o](https://tex.z-dn.net/?f=2x%3D90%5Eo-14%5Eo)
![2x=76^o](https://tex.z-dn.net/?f=2x%3D76%5Eo)
![x=38^o](https://tex.z-dn.net/?f=x%3D38%5Eo)
Answer:
answer for the question is 87
Each large box weighs 15 kilograms and each small box weighs 13.5 kilograms.
Step-by-step explanation:
Let,
Weight of large box = x
Weight of small box = y
According to given statement;
5x+2y=102 Eqn 1
3x+8y=153 Eqn 2
Multiyplying Eqn 1 by 4
![4(5x+2y=102)\\20x+8y=408\ \ \ Eqn\ 3](https://tex.z-dn.net/?f=4%285x%2B2y%3D102%29%5C%5C20x%2B8y%3D408%5C%20%5C%20%5C%20Eqn%5C%203)
Subtracting Eqn 2 from Eqn 3
![(20x+8y)-(3x+8y)=408-153\\20x+8y-3x-8y=255\\17x=255](https://tex.z-dn.net/?f=%2820x%2B8y%29-%283x%2B8y%29%3D408-153%5C%5C20x%2B8y-3x-8y%3D255%5C%5C17x%3D255)
Dividing both sides by 17
![\frac{17x}{17}=\frac{255}{17}\\x=15](https://tex.z-dn.net/?f=%5Cfrac%7B17x%7D%7B17%7D%3D%5Cfrac%7B255%7D%7B17%7D%5C%5Cx%3D15)
Putting x=15 in Eqn 2
![15(3)+8y=153\\45+8y=153\\8y=153-45\\8y=108](https://tex.z-dn.net/?f=15%283%29%2B8y%3D153%5C%5C45%2B8y%3D153%5C%5C8y%3D153-45%5C%5C8y%3D108)
Dividing both sides by 8
![\frac{8y}{8}=\frac{108}{8}\\y=13.5](https://tex.z-dn.net/?f=%5Cfrac%7B8y%7D%7B8%7D%3D%5Cfrac%7B108%7D%7B8%7D%5C%5Cy%3D13.5)
Each large box weighs 15 kilograms and each small box weighs 13.5 kilograms.
Keywords: linear equation, elimination method
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