Solve your equation step-by-step.
3(x+1)=−2(x−1)−4
Simplify both sides of the equation.
3(x+1)=−2(x−1)−4
Simplify:
3x+3=−2x−2
Add 2x to both sides.
3x+3+2x=−2x−2+2x
5x+3=−2
Subtract 3 from both sides.
5x+3−3=−2−3
5x=−5
Divide both sides by 5.
5x/5 = −5/5
x=−1
The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
<h3>What is the equation of the ellipse associated with the coordinates of the foci?</h3>
By <em>analytical</em> geometry we know that foci are along the <em>major</em> axis of ellipses and beside the statement we find that such axis is parallel to the x-axis of Cartesian plane. Then, the <em>standard</em> form of the equation of the ellipse is of the following form:
(x - h)² / a² + (y - k)² / b² = 1, where a > b (1)
Where:
- a - Length of the major semiaxis.
- b - Length of the minor semiaxis.
Now, we proceed to find the vertex and the lengths of the semiaxes:
a = 10 units.
b = 8 units.
Vertex
V(x, y) = 0.5 · F₁(x, y) + 0.5 · F₂(x, y)
V(x, y) = 0.5 · (3, 2) + 0.5 · (- 9, 2)
V(x, y) = (1.5, 1) + (- 4.5, 1)
V(x, y) = (- 3, 2)
The equation of the ellipse in <em>standard</em> form is (x + 3)² / 100 + (y - 2)² / 64 = 1. (Correct choice: B)
To learn more on ellipses: brainly.com/question/14281133
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Answer:
the first equation
Step-by-step explanation:
97 is not a pefect square. You can obtain the square root of 97 using a calculator.
Using a calculator, square root of 97 is approximately 9.85
