It is true, they are congruent by doing a proof. You have to divide the trapezoid into 2 equal triangles. Then you can prove it. They are congruent since corresponding parts of congruent triangles are congruent.
The volume of a prism is the product of the area of a the base and its height. Given the volume of the prism as 15x2 + x + 2 and the height as x2, the base can be expressed using this expressions. Volume = base x height. By substitution, <span>15x2 + x + 2 = (base) x (x2). Thus the answer is, base = (15x2 + x + 2)/x2 or base = 15 + (1/x) + (2/x2).</span>
Answer:
A = number of adult tickets
S = number of student tickets
1033 = total tickets sold
A + S = 1033
5A = money collected for adult tickets
S = money collected for student tickets
2265 = total money collected
5A + S = 2265
two equations and two unknowns:
5A + S = 2265
A + S = 1033
subtract 2nd equation from 1st and solve for A:
4A = 1232
A = 308
Plug in value for A in 1st equation and solve for S:
A + S = 1033
308 + S = 1033
S = 725
Answer:
x = 4 + sqrt(73) or x = 4 - sqrt(73)
Step-by-step explanation by completing the square:
Solve for x:
(x - 12) (x + 4) = 9
Expand out terms of the left hand side:
x^2 - 8 x - 48 = 9
Add 48 to both sides:
x^2 - 8 x = 57
Add 16 to both sides:
x^2 - 8 x + 16 = 73
Write the left hand side as a square:
(x - 4)^2 = 73
Take the square root of both sides:
x - 4 = sqrt(73) or x - 4 = -sqrt(73)
Add 4 to both sides:
x = 4 + sqrt(73) or x - 4 = -sqrt(73)
Add 4 to both sides:
Answer: x = 4 + sqrt(73) or x = 4 - sqrt(73)
