Comment
In a 45 - 45 - 90 triangle the two smaller sides are =. So when you use
a^2 + b^2 = c^2, you need a and b both to find the area.
So call both of them = b^2.
Equation and solution
a^2 + b^2 = c^2
b^2 + b^2 = c^2
2b^2 = c^2
c = 24
b = ???
2 b^2 = 24^2
2 b^2 = 576 Divide by 2
b^2 = 288 I'm going to leave this as it is for the moment. You'll see what in a second.
Area of a triangle
Area of a triangle = 1/2 h * b
But the height and base are the 2 smaller equal sides of a 45_45_90 triangle
so h = b
base = b
Area of a triangle = 1/2 b^2 The equalities above tell you that. h and b of the triangle are equal.
Area = 1/2 288 feet^2
Area = 144 feet^2
Multiply denominator (in this case do 6x10)
Multiply the numerator (in this case do 1x1)
So the answer is 1/60
Answer:
b. 10
Step-by-step explanation:
Answer: a) x = 5 or -1 b) x = √3+2
c) x = -1/2 or -3/2
Step-by-step explanation:
a) (x − 2)² = 9
First step is to take the square root of both sides to eliminate the square
√ (x − 2)² = √9
x-2 = +-3
x = +3+2
x = 5 and;
x = -3+2
x = -1
x = 5 or -1
b) 3(x-2)² = 9
First we divide both sides by 3 to get;
(x-2)² = 9/3
(x-2)² = 3
Second step is to take the square root of both sides to eliminate the square
√(x-2)² = √3
x-2 = √3
x = √3+2
c) 6 = 24(x+1)²
Dividing both sides by 24, we have
6/24 = (x+1)²
1/4 = (x+1)²
Taking the square root of both sides we have
√1/4 = √(x+1)²
= +-1/2 = x+1
x = +1/2-1 = -1/2 and;
x = -1/2-1 = -3/2
x = -1/2 or -3/2
<h3>
Answers: Choice A and Choice C</h3>
Explanation:
Think of the vertical lines as train tracks (the metal rails).
Stuff between the rails are interior angles.
Angles 3 and 6 are one pair of alternate interior angles because they are on alternating sides of the transversal line. The other pair of alternate interior angles are angles 4 and 5.
Alternate interior angles are congruent when we have parallel lines like this.
