Answer:
p > 0
Step-by-step explanation:
x² = p
x² - p = 0
A = 1, B = 0, C = -p
For 2 real roots:
B² - 4AC > 0
0² - 4(1)(-p) > 0
4p > 0
p > 0
Answer:
4√2 + 2√10
Step-by-step explanation:
Finding the perimeter here involves finding three point-to-point distances and then adding them up.
From (2, 2) to (6, -2) we have a change in x of 4 and a change in y of -4. We use the Pythagorean Theorem to determine the distance, which is the hypotenuse of a right triangle:
√( [4]² + [-4]² ) = 4√2. This is the length of the side connecting (2, 2) and (6, -2).
From (6, -2) to (5, 1), the distance is √( [-1]² + 3² ), or √10.
From (5, 1) to (2, 2), the distance is √( [-3]² + 1² ), or √10.
The perimeter is the sum of these three distances and is:
4√2 + √10 + √10, or 4√2 + 2√10
The base of the triangle ABC is 12 units.
Step-by-step explanation:
Step 1; First we need to identify which side is the base of the triangle. In this given triangle side CB is the base. So we plot points C and B on the graph. Coordinates for C are (-4, -3) and for B are (8, -3). We need to find the distance between the 2 edges of the triangle.
Step 2; To find the distance of CB, we use the formula;
Distance = √ (x2 - x1)² + (y2 - y1)².
Distance between C (-4, -3) and B (8, -3) where C is (x1, y1) and B is (x2, y2).
Distance = √(8 - (-4))² + (-3 -(-3))² = √12² + 0² = √12² = 12 units.
Similarly, triangle ABC's height equals 10 units.
Answer:
C
Step-by-step explanation:
Well you can see that the triangle is a 45°45°90° triangle.
The ratio from the leg to the hypotenuse is x : x√2
X = 10√2
Y = 10
