The points which represents the vertices of the given equation are; (15, −2) and (−1, −2).
<h3>Which points among the answer choices represents the vertices of the ellipse whose equation is given?</h3>
The complete question gives the equation of the ellipse as; (x-7)²/64+(y+2)²/9=1.
Since, It follows from convention that general equation of ellipse with centre as (h, k) takes the form;
(x-h)²/a² +(y-k)²/b² = 1.
Consequently, it follows from observation that the value of a and b in the given equation in the task content is; √64 = 8 and √9 = 3 respectively.
Since, 8 > 3, The vertices of the ellipse are given by; (h±a, k).
The vertices in this scenario are therefore;
(7+8, -2) and (7-8, -2).
= (15, -2) and (-1, -2).
Read more on vertices of an ellipse;
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Square
Rectangle
Rhombus
Trapezoid
Kite
They all have a four sides
The general form of the equation we need to find is (x - h)^2 = 4p(y- k).
The center is the distance between the directrix and focus.
So, center (h, k) = (3, 3/2) .
P = distance from center to the focus and it just so happens to be 1.5.
We now plug everything into the formula given above.
(x - 3)^2 = 4(1.5)(y - 3/2)
(x - 3)^2 = 6(y - 3/2)
Done!
The weight of each pie will be 6 and 8 pounds respectively if the ratio of the seeds in these piles 3:4
<h3>What is the ratio?</h3>
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We have:
A greedy hamster hoarded 2 piles of sunflower seeds. Yesterday the ratio of the seeds in these piles was 3:4
Let 3x and 4x are the seeds from the smaller and bigger pile.
= 4x + 2 (greedy hamster placed another 2 pounds of seeds in the bigger pile)
= 3x - 1/4 (ate 1/4 pound from the smaller pile)
4x + 2 = 5x
Because the quantities of seeds in those piles is in the ratio of 5:16
After solving:
x = 2
Smaller pile weight = 3x = 3(2) = 6
Bigger pile wieght = 4x = 4(2) = 8
Thus, the weight of each pie will be 6 and 8 pounds respectively if the ratio of the seeds in these piles 3:4
Learn more about the ratio here:
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Answer:
QR / SQ = SQ / TQ
Step-by-step explanation:
∠QST = 90 - ∠Q
∠R = 90 - ∠Q
∠QST = ∠R
ΔQST ~ ΔQRS
SQ / TQ = QR / SQ
