Answer:
b^2 = 5, a^2 = 4 and k= -2.
Step-by-step explanation:
In this case we have the first focus (-2, -2), the center (1, -2) and from the graph we can deduce that the distance between the vertices 2a is 4. So 2a=5 then a=2, thus, a^2 = 4.
The hyperbola is centered at the point (h, k) = (1, -2) thus we can conclude that h=1 and k = -2.
We can deduce from the graph that the distance from the center to each focus is 3, so c=3. (c represents de distance from center to focus).
We know that c^2 = a^2 + b^2
Solving for b^2, we have that:
b^2 = c^2 - a^2 = 3^2 - 2^2 = 5
Then b^2 = 5
D. It is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.
Problem
Solution
For this case we can take common factor in the denominator 2x and we got:
![\frac{1}{2x}(\frac{3}{1}-\frac{1}{4x})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2x%7D%28%5Cfrac%7B3%7D%7B1%7D-%5Cfrac%7B1%7D%7B4x%7D%29)
Then we can solve the fractions with this operation:
![\frac{1}{2x}(\frac{3\cdot4x-1\cdot1}{1\cdot4x})=\frac{1}{2x}(\frac{12x-1}{4x})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2x%7D%28%5Cfrac%7B3%5Ccdot4x-1%5Ccdot1%7D%7B1%5Ccdot4x%7D%29%3D%5Cfrac%7B1%7D%7B2x%7D%28%5Cfrac%7B12x-1%7D%7B4x%7D%29)
then we can simplify on this way:
Hey there! :)
-(3x)² + 3 = -6
Simplify.
-(9x²) + 3 = -6
Simplify.
-9x² + 3 = -6
Subtract 3 from both sides.
-9x² = -6 - 3
Simplify.
-9x² = -9
Divide -9 from both sides.
-9x² ÷ -9 = -9 ÷ -9
Simplify.
x² = 1
So, x = 1 OR x = -1
~Hope I helped!~
Proportion A
The first thing you should know in this case is what the rate of change means.
The rate of change in a linear equation is given by the slope of the line.
For a linear equation, the rate of change is constant.
So we have to:
y = 9x
The slope is:
m = 9
Proportion B
The slope of the line will be:
m = (y2-y1) / (x2-x1)
Substituting values:
m = (57.5-34.5) / (5-3)
m = 11.5
Answer:
The rate of change in proportion A is 2.5 less than in proportion B.