For E2020 Users, The answer is A, B, D.
Answer:
Equation of the Ellipse
Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given that the equation
x² + 2 x + 2y² - 12 y +11 = 0
⇒ x² + 2 x + 1 - 1 + 2(y² - 6 y )+ 11 = 0
x² + 2 x + 1 - 1 + 2(y² - 2(3) y+9-9 )+ 11 = 0
⇒ x² + 2 x + 1 - 1 + 2(y² - 2(3 y ) + 3²- 3² ) + 11 = 0
By using (a +b)² = a² + 2 a b + b²
(a -b)² = a² - 2 a b + b²
<u><em>Step(ii):-</em></u>
x² + 2 x + 1 - 1 + 2(y² - 2(3 y ) + 3²- 3² ) + 11 = 0
⇒ ( x+1)² +2( y-3 )² - 1 - 2(9) +11 =0
⇒ ( x+1)² +2( y-3 )² - 8 =0
( x+1)² +2( y-3 )² = 8
Dividing '8' on both sides , we get
This equation represents the Ellipse
Answer:
Isabella borrowed money to start a business.
at a rate of 4% simple interest. After 10
years, she had accumulated $800 in interest.
How much did she initially
borrow?
Yes
Answer:
D. Sum of Interior angles; Converse of opposite angles theorem.
Step-by-step explanation:
Solution:
Statement Reasons
1. m∠A =50°,m∠B= 130°,m∠C = 50° Given
Now we know that;
"Sum of all interior angles is 360°."
2. m∠A + m∠B + m∠C + m∠D =360° Sum of all Interior angles
3. 50°+ 130° + 50° + m∠D =360° Substitution
4. m∠D =130° Subtraction property of equality.
5. m∠A Congruent m∠C Angles with equal measure are congruent m∠B Congruent m∠D
Now By Converse of opposite angle theorem which states that;
"If the opposite angles of a quadrilateral are congruent, then the figure is a parallelogram."
6. ABCD is Parallelogram Converse of opposite angle theorem