Given:
To find:
The congruent angles and sides, then find the another valid congruency statement.
Solution:
We have,
We know that, corresponding parts of congruent triangles are congruent (CPCTC).
Using CPCTC, we get
Angles:
Sides:
The another congruent statement is 
.
Therefore, the required table is
Angles Sides
The another congruent statement is .
Let p(x) be a polynomial, and suppose that a is any real
number. Prove that
lim x→a p(x) = p(a) .
Solution. Notice that
2(−1)4 − 3(−1)3 − 4(−1)2 − (−1) − 1 = 1 .
So x − (−1) must divide 2x^4 − 3x^3 − 4x^2 − x − 2. Do polynomial
long division to get 2x^4 − 3x^3 − 4x^2 – x – 2 / (x − (−1)) = 2x^3 − 5x^2 + x –
2.
Let ε > 0. Set δ = min{ ε/40 , 1}. Let x be a real number
such that 0 < |x−(−1)| < δ. Then |x + 1| < ε/40 . Also, |x + 1| <
1, so −2 < x < 0. In particular |x| < 2. So
|2x^3 − 5x^2 + x − 2| ≤ |2x^3 | + | − 5x^2 | + |x| + | − 2|
= 2|x|^3 + 5|x|^2 + |x| + 2
< 2(2)^3 + 5(2)^2 + (2) + 2
= 40
Thus, |2x^4 − 3x^3 − 4x^2 − x − 2| = |x + 1| · |2x^3 − 5x^2
+ x − 2| < ε/40 · 40 = ε.
Step-by-step explanation:
Radius = 4 ft
Side of the square = 8 ft
Area of circle = πr² ≈ 3 × 4² = 48 ft²
Square area = a² = 8² = 64 ft²
area of composite shape = Square area - Area if circle = 64 - 48 = 16 ft²
Answer:
C.)
Step-by-step explanation:
cut the shape into a square and a triangle, find their area's and add. ^_^
The rectangle they give you is 12 units tall. This is the result of scaling by a factor of 1.5, ie it is 1.5 times taller than what the answer will be. Let the answer rectangle have a height of h. This means h*1.5 = 12, or 1.5h = 12
Divide both sides by 1.5 to find that h = 8. The answer rectangle's height is 8 units.
The width's will be treated in a similar manner. I picked on the height since it's easier to see that the height lines up with 12 (the width seems to be between 2 and 4, but its not clear if its at the midpoint).
