Answer:
Step-by-step explanation:
We'll first clear a few points.
1. A hyperbola with horizontal axis and centred on origin (i.e. foci are centred on the x-axis) has equation
x^2/a^2-y^2/b^2=1
(check: when y=0, x=+/- a, the vertices)
The corresponding hyperbola with vertical axis centred on origin has equation
y^2/a^2-x^2/b^2=1
(check: when x=0, y=+/- a, the vertices).
The co-vertex is the distance b in the above formula, such that
the distance of the foci from the origin, c satisfies c^2=a^2+b^2.
The rectangle with width a and height b has diagonals which are the asymptotes of the hyperbola.
We're given vertex = +/- 3, and covertex=+/- 5.
And since vertices are situated at (3,0), and (-3,0), they are along the x-axis.
So the equation must start with
x^2/3^2.
It will be good practice for you to sketch all four hyperbolas given in the choices to fully understand the basics of a hyperbola.
Answer:
see below for a graph
Step-by-step explanation:
The first inequality does not include the "equal to" case, so its boundary is graphed with a dashed line. If we consider only the y term, we have y < ..., so the shading is below the line.
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The second inequality includes the "equal to" case, so its boundary line is solid. Again, considering only the y-term, we have y ≥ ..., so the shading is above the line.
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We find that points (-6, 0) and (0, 6) will satisfy both inequalities, as will any point in the doubly-shaded area.
To find the difference between two numbers, subtract.
405.87 - 379.5 = <span>26.37</span>
Answer:
7th
Step-by-step explanation:
63 - 58 = 5
68-63 = 5
She is adding 5 points each time
a1 = 58
d = 5
a2 = 63
a3 = 68
a4 = 58+5 = 73
a5 = 73+5 = 78
a6 = 78+5 = 83
a7 = 83+5 = 88
This is the first assessment greater then 85, so the 7th assessment