It's an isosceles triangle so angles A and BCA are congruent.
Angle BCA is the supplement of BCD, so 180-109 = 71.
Angle A is congruent to that, so A=71 degrees.
Let's see if we can get that in the format they want, kind of as a proof.
1. ∠BCD=109° Reason: Given
2. AB ≅ BC Reason: Given
3. ∠BCA = 71° Reason: Linear pairs are supplementary
4. ΔABC is isosceles. Reason: Definition of isosceles
5. ∠A ≅ ∠BCA Reason: Isoceles triangle theorem
6. ∠A = 71° Reason: Def congruent
Answer: 71 degrees
Answer:
see explanation
Step-by-step explanation:
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x ), thus
P(1, - 1 ) → P'(1, 1 )
Q(3, - 2 ) → Q'(2, 3 )
R(3, - 4 ) → R'(4, 3 )
Since the tank is 66.06% full, it is (100 - 66.06) = 33.94% empty.
Its capacity is 6,000L. So, in order to fill it to capacity, the service station
must order 33.94% of 6,000L .
33.94% = 0.3394
"of" means "times"
0.3394 x 6,000L = <em>2,036.4 liters</em> needed, to fill the tank to the rim.
Question: What value of c will complete the square below (
) and make the expression a perfect square trinomial?
Answer: c = 225
Step-by-step explanation:
Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)². In the presented trinomial, we can immediately identify that <u>a = x, and b² = c</u>, but we need to find the numerical value of 
.
To do this, note that the middle term, or <u>2ab, corresponds with (is equal to) 30x</u>. We know that a = x, and thus, <u>2ab = 2bx</u>. Now, 2bx and 30x are corresponding terms; thus, <u>2bx = 30x</u>.
Dividing by 
on both sides gives us <u>b = 15</u>. Therefore, c = b² = 15² = 225. (As a squared binomial, this would be (x + 15)² as a = x and b = 15.)
