Answer:
0.8181818
Step-by-step explanation:
3/11×3 = 0.8181
Answer:
A
Step-by-step explanation:
The volume of a pyramid is one third the height times the area of the base.
V = ⅓ h A
The base is a square, so the area is the width times length.
V = ⅓ h wl
Problem is, we don't know the height, only the slant length. But we can use this to find the height.
If we cut a cross section down the middle of the pyramid, we get an isosceles triangle. The base of the triangle is 24, and the legs are 37.
If we cut this triangle in half, we get two right triangles. Each right triangle has a base of 12 and a hypotenuse of 37.
Now we can use Pythagorean theorem to find the height of the triangle, which is also the height of the pyramid.
c² = a² + b²
37² = 12² + h²
h = 35
Now we can find the volume. h = 35, w = 24, and l = 24:
V = ⅓ h wl
V = ⅓ (35) (24) (24)
V = 6720
So the volume is 6720 ft³, or answer A.
Answer: 55
Step-by-step explanation: There is one simple theorem we need to know in order to solve for this.
Triangle Angle-Sum Property: All three angles interior angles of a triangle add up to 180°.
Thus, we could label the points A, B, and C, and set up an algebraic expression.
Let A = 27, B = 98, and C = x.
A + B + C = 180°.
Substituting A, B, and C we get:
27 + 98 + x = 180°.
Adding, we get:
125 + x = 180°
Subtracting 125 by 180, we get:
x = 55°
Thus, the angle X is 55°.
We could have simply solved this by just doing 180 - 98 - 27 = 55 in the first place, but I wanted to show you how I got such results.
Given:
The function, f(x) = -2x^2 + x + 5
Quadratic equation: 0 = -2x^2 + x +5
where a = -2
b = 1
c = 5
The discriminate b^2 - 4ac = 41
To solve for the zeros of the quadratic function, use this formula:
x = ( -b +-√ (b^2 - 4ac) ) / 2a
x = ( 1 + √41 ) / 4 or 1.85
x = ( 1 - √41 ) / 4 or -1.35
Therefore, the zeros of the quadratic equation are 1.85 and -1.35.
