x + y = 3.36 --> the boys are splitting $3.36
x = 3y - .12 --> one boy received $.12 less than 3 times as much as the other
--> substitute the second equation for the x in the first equation
(3y - .12) + y = 3.36 --> combine like terms
4y - .12 = 3.36 --> add .12 to both sides of the equation
4y = 3.48 --> divide both sides by 4
y = .87
the other boy gets $0.87
substitute into x = 3y - 12
x = 3(.87) - .12
x = 2.61 - .12
x = 2.49
the first boy gets $2.49
3
We found the factors and prime factorization of 9 and 12. The biggest common factor number is the GCF number. So the greatest common factor 9 and 12 is 3.
Answer:
v=9
Step-by-step explanation:
x=23
Simplifying
(3x + -50) + (7x)
Reorder the terms:
(-50 + 3x) + (7x)
Remove parenthesis around (-50 + 3x)
-50 + 3x + (7x) =
Combine like terms: 3x + (7x)
-50 + 10x
Solving
-50 + 10x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '50' to each side of the equation.
-50 + 50 + 10x = 180 + 50
Combine like terms: -50 + 50 = 0
0 + 10x = 180 + 50
10x = 180 + 50
Combine like terms: 180 + 50 = 230
10x = 230
Divide each side by '10'.
Simplifying
x = 23
We have the base measurement for the triangles composing the sides. We need their altitude.
Imagine a right triangle with these sides:
(1) from the apex of the pyramid to the point on the base directly underneath it (471 ft);
(2) from the middle of base edge to the point underneath the apex (half of 708 ft = 354 ft);
(3) the hypotenuse, the altitude of a triangular side.
Using the Pythagorean Theorem, we find the hypotenuse to be
√(471^2 + 354^2) = about 589.2 feet
Now we add up the four triangles' areas. Each is base * altitude / 2, so:
4 x 708 x 589.2 / 2
= 2 x 708 x 589.2
= 834,307.2 square feet, the lateral area.
