Recall that A = 1/2bh.
We are given that h = 4+2b
So, putting it all together:
168 = 1/2 b(4+2b)
168 = 1/2(4b + 2b^2)
168 = 2b + b^2
b^2 + 2b - 168 = 0.
Something that multiplies to -168 and adds to 2? There's a trick to this.
Notice 13^2 = 169. So, it's more than likely in the middle of the two numbers we're trying to find. So let's try 12 and 14. Yep. 12 x 14 = 168. So this factors into (b+14)(b-12) So b = -14 or b =12. Is it possible to have a negative length on a base? No. So 12 must be our answer.
Let's check this. If 12 is our base, then according to our problem, 2*12 + 4 would be our height... or 28. so what is 12 * 28 /2?
196. Check.
Hope this helped!
The answer on APEX would be $2430
Answer: x=-2 and y=-2
Step-by-step-explaination:
To solve the system of equations you have to cancel out a variable. I chose to cancel out Y. First, the coefficients of y need to be the same in both equations. To do this multiply to the top equation by 2 so you get
2(2x) +2(y) = 2(-6)
4x + 2y = -12
Next, subtract the second equation from the first to cancel out the y’s
4x + 2y =-12
-(-8x + 2y = -12)
————————
12x = -24
Solve
X = -24/12
X=-2
Plug x into the original equation to find y
2(-2) + y = -6
-4 + y = -6
Y = -6 +4
Y=-2
You can substitute x and y into the original equations to double check
Rolling an even number would be 1/2 possibility while flipping tails would be 1/2 possibility hence the answer is 1/4
