Answer:
work is shown and attached
Answer:
Question A)
Question B)
Question C)
Step-by-step explanation:
A)
We are given:
We can rewrite the expression:
The square root and square will cancel each other out. Thus:
B)
We are given:
Rewrite:
Note that the square root of 9 is simply 3. We can also factor the second part:
Rewriting:
Simplify:
C)
We are given:
Rewrite. Note that 50 = 25(2):
Simplify. We can rewrite the factor as:
The square and square root will cancel out. Thus:
Fun, geometry disguised as probability.
That's a pentagon, which we can view as 10 right triangles with legs a and s/2 (half of s) and hypotenuse r. So area of the pentagon is
P = 10 × (1/2) a (s/2) = 10 (1/2) (3.2) (4.7/2) = 37.6
The area of the circle is πr² so the circle area is
C = π (4²) = 50.265482
The white area is the difference, C-P, and the probability we seek is the fraction of the circle that's white, so (C-P)/C.
p = (C-P)/C =1-P/C = 1-37.6/50.265482 = 0.251971
Answer: 0.25
Higher than I would have guessed from the figure.
Answer- 45 degrees
Step-By-Step Explanation- You're welcome lol
Triangle ABC is an isosceles triangle.
Solution:
Given data:
∠ABC = 70° and ∠ACD = 55°
<em>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</em>
m∠BAC = m∠ACD
m∠BAC = 55°
<em>Sum of the angles in a straight line add up to 180°.</em>
m∠ACD + m∠ACB + m∠ABC = 180°
55° + m∠ACB + 70° = 180°
m∠ACB + 125° = 180°
Subtract 125° from both sides, we get
m∠ACB = 55°
In triangle ABC,
∠BAC = 55° and ∠ACB = 55°
∠BAC = ∠ACB
Two angles in the triangle are equal.
Therefor triangle ABC is an isosceles triangle.
