An equation of the circle that will pass through the four (4) vertices of the square is (x + 2)² + y² = 2².
<h3>How to find the equation of this circle?</h3>
Mathematically, the general form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
- h and k represents the coordinates at the center.
- r is the radius of a circle.
<u>Note:</u> The center of a circle lies on the midpoint of the diagonal of a square, which is formed by joining its endpoints (opposite).
Midpoint on x-coordinate is given by:
Midpoint = (-2 - 2)/2
Midpoint = -4/2 = -2.
Midpoint on y-coordinate is given by:
Midpoint = (-2 + 2)/2
Midpoint = 0/2 = 0.
Thus, the center (h, k) = (-2, 0).
For the radius, we have:
r = √(-2)² + 0²
r = √4 = 2.
Substituting the parameters into the general equation, we have;
(x - (-2))² + (y - 0)² = 2²
(x + 2)² + y² = 2²
Read more on circle here: brainly.com/question/1615837
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Answer:
x = -8
m∠BDC = 68°
General Formulas and Concepts:
<u>Pre-Algebra
</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Geometry
</u>
- Definition of a Line: A line is 180°
Step-by-step explanation:
<u>Step 1: Set up Equation</u>
m∠BDC + m∠CDA = 180°
(-7x + 12)° + (-8x + 48)° = 180°
<u>Step 2: Solve for x
</u>
- Combine like terms: -15x + 60 = 180
- Isolate x term: -15x = 120
- Isolate x: x = -8
<u>Step 3: Find m∠BDC
</u>
- Define: m∠BDC = (-7x + 12)°
- Substitute in x: m∠BDC = (-7(-8) + 12)°
- Multiply: m∠BDC = (56 + 12)°
- Add: m∠BDC = 68°
Answer: 40:80:80
Step-by-step explanation:
The ratio is 1:2:2. This means, for every 5, the money is split in a ratio of 1:2:2. Let’s calculate how many 5s there are in 200. 200 / 5 = 40. So, the money will be split in 1:2:2 every 5 dollars 40 times.
Excellent. So, we can easily find out the ratio by multiplying the ratio 1:2:2 by 40. 1*40:2*40:2*40 = 40:80:80. Let’s add these up, and see if they result in 200. 40 + 80 + 80 = 200. So, our answer is correct.
Hope this helps!
Answer:
Step-by-step explanation: If Professor Lam grades 4 papers per hour, in 11 hours he will graded 44 papers. (11 x 4= 44). He had previously graded 6 papers giving him a total of 50 papers graded. His assistant can grade 5 papers per hour, thus it would take him 10 hours to grade the same amount of papers as Professor Lam. (10 x 5= 50) Thus: 11 hours Professor Lam 50 papers graded; 10 hours his assistant 50 papers graded.
Answer:
n = -12/11
Step-by-step explanation:
4n = -7n - 12
4n + 7n = -7n - 12+7n
11n = -12
11n/11 = -12/11
