Label the 3 distinct sides of the box. I arbitrarily chose the letters a, b and c.
Use the info about areas as follows:
ab=54 in^2
ac=90 in^2
bc=60 in^2
Here you have 3 equations in 3 unknowns (a, b and c), which is enough info to use to determine a, b and c. Then the volume of the box is a*b*c.
Example: bc = 90, but c = 60/b. You could subst. 60/b for c in the 2nd and 3rd equation, which will eliminate c completely and leave you with 2 equations in 2 unknowns.
Continuing this procedure, I determined that a=9, b=6 and c=10. Thus, the volume of the box is V = 9*6*10 = 540 cubic inches (answer)
First, set up the equation.
365x + 125 = 250x + 175
Second, combine like terms on the same side by subtracting 250x and 125 from both sides.
365x +125 = 250x + 175
-250x -125 -250x -125
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115x = 50
Third, divide both sides by 115 to solve for x.
115x = 50
---- ----
115 115
Fourth, simplify.
x=50/115=10/23 or 0.435
1) The expressions are not equivalent. When you expand and multiply 2(x + 3) it becomes 2x + 6. This is not equal to 3x + 5
2) They are equivalent. Again, expand and multiply the second expression. 2(3n + 4) becomes 6n + 8. This makes both sides equal.
3) They are equivalent. In the parentheses, you are adding 3 y's and a 2. This gives you 3y + 2. Now add the additional 3y that follows the closed parentheses. You'll have 6y + 2. Now both sides are equivalent.
If shapes are congruent, then they are mathematically equal (same dimensions, angles etc.). So just locate where the angle x is on both triangles, it should have a value on or a calculable value on the other. If you provide us with the actual sheet I could walk you through it.
