ratio of perimeter is the same as ratio of sides so perimeter would be 1:4
since area is in square units you need to square the ratio (1:4)^2 which is 1:16
Answer: (b) The focus of an ellipse is always located precisely at the center of the ellipse.
Step-by-step explanation:
An ellipse is defined as <em>"a closed curve with two axes of symmetry (major axis and minor axis) that results in cutting the surface of a cone by an oblique plane to the axis of symmetry with an angle greater than that of the generatrix with respect to the axis of revolution"</em>. That is why the ellipse is considered a conic figure.
To understand it better: an ellipse has two points on its major axis that are equidistant from the center , which are called foci, being this distance constant. In addition, the eccentricity allows to know how far the foci are from the center of the ellipse.
Therefore, the statement that indicates an ellipse has only one focus located precisely at the center is incorrect.
Answer:
(x, y) = (-1, -3) or (4, 12)
Step-by-step explanation:
A graphing calculator can show the solutions to this system.
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You can equate expressions for y and solve for x.
3x = x^2 -4
x^2 -3x = 4 . . . . add 4-3x
x^2 -3x +2.25 = 6.25 . . . . complete the square by adding (-3/2)^2 where -3 is the coefficient of x.
(x -1.5)^2 = 2.5^2 . . . . . . rewrite as squares
x -1.5 = ±2.5 . . . . . . . . . . take the square root
x = 1.5 ± 2.5 = -1, +4
y = 3x = -3, +12, respectively
Solutions are ...
(x, y) = (-1, -3) . . . . and . . . . (4, 12)
Answer: yes?
Step-by-step explanation:
Answer:
<u>The value of the annuity in 10 years will be US$ 15,552.90</u>
Step-by-step explanation:
Let's use the ordinary simple annuity formula to calculate the value of the annuity in 10 years, this way:
FV = Future value of an annuity stream
PMT = Dollar amount of each annuity payment = US% 50
r = Interest rate = 3.5% compounded biweekly = 0.035/26
n = Number of periods in which payments will be made = 26 * 10 = 260
FV = PMT * [(1 + r)ⁿ − 1]/r
Now, replacing with the real values, we have:
FV = 50 * [(1 + 0.035/26)²⁶⁰ − 1]/(0.035/26)
FV = 50 * [(1.001346154)²⁶⁰ − 1]/0.001346154
FV = 50 * 0.41873217/0.001346154
FV = 50 * 311.058148
<u>FV = 15,552.90 </u>
<u>We only rounded the last product to the next cent, in all the other cases we used all the decimals for the calculations.</u>
