Given:
The center of the circle is at (0,0).
The circle passes through the point A(4,-3).
To find:
The radius and the equation of the circle.
Solution:
Distance formula:
The radius of the circle is the distance between the points (0,0) and (4,-3).
So, the radius of the circle is 5 units.
The standard form of a circle is
Where, (h,k) is center of circle and r is the radius.
Putting h=0, k=0, r=5, we get
Therefore, the radius of the circle is 5 units and the equation of the circle is .
Step-by-step explanation:
20.
In each proof, start by looking at what you're trying to prove. We want to prove that two triangles are congruent. To do that we use one of the following: SSS, SAS, ASA, or AAS.
To decide which one to use, look at the information given. We're given two pairs of congruent sides, so we can narrow the strategy down to either SSS or SAS. We aren't told anything about the third pair of sides, but we <em>can</em> see that ∠JNK and ∠MNL are vertical angles. We'll use this to show the triangles are congruent by SAS.
1. JN ≅ MN, Given
2. ∠JNK ≅ ∠MNL, Vertical angles
3. NK ≅ NL, Given
4. ΔJNK ≅ ΔMNL, SAS
21.
Repeat the same steps as 20. Again, we're trying to prove two triangles are congruent, so we have 4 strategies to choose from. Just like before, we're given two pairs of congruent sides, so we'll use either SSS or SAS. And again, we aren't told anything about the third pair of sides, but we can see that both triangles are right triangles. So we'll use SAS again.
1. MN ≅ PQ, Given
2. ∠LMN ≅ ∠NQP, Right angles are congruent
3. LM ≅ NQ, Given
4. ΔNML ≅ ΔPQN, SAS
Answer:
X=2
Step-by-step explanation:
Answer:
22.4
Step-by-step explanation:
using altitude theorem, the height of the triangle is 20
let y = height
10/y = y/40
y² = 400
y = 
or 20
Now we can us the Pythagorean Theorem to find 'x':
10² + 20² = x²
100 + 400 = x²
x=
≈ 22.4
Answer:
D. 5
Step-by-step explanation:
Heather runs 5 miles in 1 hour.
average speed = distance/time = 5 miles / 1 hour = 5 miles per hour
Answer: D. 5
