Let the two consecutive even integers be x and x+2.
Then x^2 = (x+2) + 10
Simplifying, x^2-x -2 - 10 = 0, or x^2 - x - 12 = 0. Factoring,
(x-4)(x+3) = 0. Solving for x: x=4 and x= -3.
If the first number is x = 4, then the second is x+2=4+2=6.
But wait! If the first number is -3, then the second is x+2 = -3+2 = -1.
Do NOT accept these answers until after you've checked them!
Answer: 22.94 cubic meters
I'm pretty sure it is this.
I think it's 25.23 cubic meters if not then I don't know
If the triangles are similar, the proportion of the legs on the left to the legs on the right will be equal. This proportion would look like:
![\frac{2x+1}{3x}=\frac{10}{14}](https://tex.z-dn.net/?f=%5Cfrac%7B2x%2B1%7D%7B3x%7D%3D%5Cfrac%7B10%7D%7B14%7D)
(You needed to combine the orange segment and the yellow segment to find the total length of the large triangle).
Now, cross multiply and solve for x:
28x+14=30x
<em>*Subtract 28x from both sides to isolate the variable*</em>
14=2x
<em>*Divide both sides by 2*</em>
7=x
Hope this helps!!
11.1803398875
Have a beautiful and joyful day ahead.
So we just need to plug in our values and solve
![v = 20 \sqrt{273 + t}](https://tex.z-dn.net/?f=v%20%3D%2020%20%5Csqrt%7B273%20%2B%20t%7D%20)
we are given v is 369 so we have
![369 = 20 \sqrt{273 + x}](https://tex.z-dn.net/?f=369%20%3D%2020%20%5Csqrt%7B273%20%2B%20x%7D%20)
now we solve for x.
divide both sides by 20
square both sides
subtract 273 from both sides
![369 = 20 \sqrt{273 + x} \\ 18.45 = \sqrt{273 + x} \\ 340.40 = 273 + x \\ x = 67.4](https://tex.z-dn.net/?f=369%20%3D%2020%20%5Csqrt%7B273%20%2B%20x%7D%20%20%5C%5C%2018.45%20%3D%20%20%5Csqrt%7B273%20%2B%20x%7D%20%20%5C%5C%20340.40%20%3D%20273%20%2B%20x%20%5C%5C%20x%20%3D%2067.4)
so a temp of about 67 degrees C