Step-by-step explanation:
Surface area of a square pyramid is the area of the square base plus the area of the four triangles made from the base and the slant height.
SA = s² + 4(sh/2)
which reduces to:
SA = s² + 2sh
You are told that s = 11 and SA = 319. You can now solve for h:
319 = 11² + 2(11)h
319 = 121 + 22h
198 = 22h
h = 9 ft (answer C)
I hope it's helpful!!
Answer:
y = 14
Step-by-step explanation:
Plug in 4 as x into the equation:
y = 2 + 3x
y = 2 + 3(4)
Simplify:
y = 2 + 12
y = 14
So, when x = 4, y = 14.
Answer:
When we have 3 numbers, like:
a, b and c.
Such that:
a < b < c.
These numbers are a Pythagorean triplet if the sum of the squares of the two smaller numbers, is equal to the square of the larger number:
a^2 + b^2 = c^2
This is equivalent to the Pythagorean Theorem, where the sum of the squares of the cathetus is equal to the hypotenuse squared.
Now that we know this, we can check if the given sets are Pythagorean triples.
1) 3, 4, 5
Here we must have that:
3^2 + 4^2 = 5^2
solving the left side we get:
3^2 + 4^2 = 9 + 16 = 25
and the right side:
5^2 = 25
Then we have the same in both sides, this means that these are Pythagorean triples.
2) 8, 15, 17
We must have that:
8^2 + 15^2 = 17^2
Solving the left side we have:
8^2 + 15^2 = 64 + 225 = 289
And in the right side we have:
17^2 = 17*17 = 289
So again, we have the same result in both sides, which means that these numbers are Pythagorean triples
Answer:
y + 2 = -2(x - 3)^2
Step-by-step explanation:
We can see immediately that the vertex is at (3, -2).
The vertex form of the equation of a parabola is
y - k = a(x - h)^2.
If the parabola opened upward, the equation would be y + 2 = 2(x - 3)^2. But seeing that this particular parabola opens downward, the equation is
y + 2 = -2(x - 3)^2.
Check: Does the point (2, -4) satisfy this equation?
-4 + 2 = -2(2 - 3)^2 becomes -2 = -2(-1)^2, which is true.
