We have 2 denominators that we need to get rid of. Whenever there are the denominators, all we have to do is multiply all whole equation with the denominators.
Our denominators are both 2 and x+1. Therefore, we multiply the whole equation by 2(x+1)
![\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%5B2%28x%2B1%29%5D-%5Cfrac%7B2%7D%7Bx%2B1%7D%5B2%28x%2B1%29%5D%20%3D%201%5B2%28x%2B1%29%5D)
Then shorten the fractions.
![\frac{x}{2}[2(x+1)]-\frac{2}{x+1}[2(x+1)] = 1[2(x+1)]\\x(x+1)-2(2)=1(2x+2)](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%5B2%28x%2B1%29%5D-%5Cfrac%7B2%7D%7Bx%2B1%7D%5B2%28x%2B1%29%5D%20%3D%201%5B2%28x%2B1%29%5D%5C%5Cx%28x%2B1%29-2%282%29%3D1%282x%2B2%29)
Distribute in all.
We should get like this. Because the polynomial is 2-degree, I'd suggest you to move all terms to one place. Therefore, moving 2x+2 to another side and subtract.
We are almost there. All we have to do is, solving for x by factoring. (Although there are more than just factoring but factoring this polynomial is faster.)
Thus, the answer is x = 3, -2
Here are the steps.
In order to get the answer, first we need to get the x and y value of the center of the circle by using the equation of a circle (x^2 + y^2 = r^2)
<span>The center is (-9, -4)</span>
Once you get the center point, find the equation of the line (in a form of a radius) from the center point to point (2, -1). Get the slope.
The slope from center to point (2, -1) is 11/3
Finally, get the negative reciprocal of the slope from the previous step and form the equation using slope-intercept form ( y=mx + b). Then, that's the equation of the tangent line.
The slope of the tangent line is -3/11
The equation is y = -3/11x - 5/11
Shortest side (a) = 58
middle side (b) = 64
longest side (c) = 77
the 3 sides a + b + c = 199
b = a + 6
c = a + 19
substitute your new values for b & c into your original formula, so:
a + (a+6) + (a+19) = 199
3a + 25 = 199
3a = 174
a = 58
then substitute 58 into your b & c formulas to figure out the rest
b = a + 6 = 58 + 6 = 64
c = a + 19 = 58 + 19 = 77
Answer:
a. 96 square units
Step-by-step explanation:
The figure is a rectangle with width AB = (20-12) = 8 units and height BC = (20-8) = 12 units.
The area of the rectangle is (8 units)×(12 units) = 96 square units.
ANSWER
EXPLANATION
Since the directrix is
the axis of symmetry of the parabola is parallel to the y-axis.
Again, the focus being,
also means that the parabola will open upwards.
The equation of parabola with such properties is given by,
where
is the vertex of the parabola.
The directrix and the axis of symmetry of the parabola will intersect at
The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.
This implies that,
and
The equation of the parabola now becomes,
Thus, the distance between the vertex and the directrix.
This means that,
Since the parabola opens up, we choose
Our equation now becomes,
This simplifies to
or
This is the same as,
The correct answer is D .
