What is the slope between the points (4,-2) and (-1,0)
1 answer:
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Answer:
4 + (or -) 3i
Step-by-step explanation:
Hi!
Alright, so we're going to move all of the variables and constants to one side. Then, using the quadratic formula, we'll find the answer.
1. Move 12x-5 to the left side of the equation by
a. Subtracting 12x from both sides
b. adding 5 to both sides.
1: x^2+4x+20-12x+5
2. Group the common terms
x^2+4x-12x+20+5 --> x^2-8x+25
3. Look at the problem. We can't factor this.
Explanation for why this isn't factorable (you can skip this)
(1) 25 is positive, so its two factors will both be either positive or negative. We're looking for a negative 8, so let's go with negative.
(2) Factors of 25: 1 & 25, 5 &5
Seeing the problem? Ya, none of the factors of 25 sum to eight. So, instead, we're going to use the quadratic formula.
4. So, the quadratic formula:
Our equation is x^2-8x+25=0
a is the constant in front of the x^2
b is the constant in front of the x
c is the term without any x values
so, a=1, b=-8, and c= 25
Into equation:
=
=
8/2 = 4
sqrt(-36) = 6i
6i/2 = 3i (remember, we still have the two in the denominator)
4 + (or -) 3i
Given:
A right prism has height 7½ and triangular bases with sides of length 5, 12, and 13.
To find:
The total surface area of the prism.
Solution:
We have,
Height of prism = 7½ = 7.5
Sides of triangular base are 5, 12, 13. These sides of Pythagorean triplets because
So, the base of the prism is a right triangle.
Area of a triangle is
The area of the base is equal to the area of the top, i.e., sq units.
Perimeter of the base is
The curved surface area of the prism is
Now, the total area of the prism is
Therefore, the total surface area of the triangular prism is 285 square units.