Solution:
<u>Note that:</u>
- Triangle = 180°
- 5x + 130 + 3x + 2 = 180
<u>Simplify the equation to find x.</u>
- 5x + 130 + 3x + 2 = 180
- => 8x + 130 + 2 = 180
- => 8x + 2 = 180 - 130
- => 8x = 50 - 2
- => 8x = 48
- => x = 48/8 = 6
The value of x is 6.
$599*1.05 = $628.95
just times it by 1.05
1.
has a horizontal asymptote at ![y=-4](https://tex.z-dn.net/?f=y%3D-4)
This means that
![\displaystyle\lim_{x\to\pm\infty}f(x)-(-4)=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%5Cpm%5Cinfty%7Df%28x%29-%28-4%29%3D0)
(for at least one of these limits)
2.
has a vertical asymptote at ![x=3](https://tex.z-dn.net/?f=x%3D3)
This means that
has a non-removable discontinuity at
. Since
is some rational function, there must be a factor of
in its denominator.
3.
has an
-intercept at (1, 0)
This means
.
(a) With
![f(x)=\dfrac{ax+b}{x+c}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Bax%2Bb%7D%7Bx%2Bc%7D)
the second point above suggests
. The first point tells us that
![\displaystyle\lim_{x\to\pm\infty}\frac{ax+b}{x-3}+4=0=\lim_{x\to\pm\infty}\frac{ax+b+4x-3}{x-3}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Clim_%7Bx%5Cto%5Cpm%5Cinfty%7D%5Cfrac%7Bax%2Bb%7D%7Bx-3%7D%2B4%3D0%3D%5Clim_%7Bx%5Cto%5Cpm%5Cinfty%7D%5Cfrac%7Bax%2Bb%2B4x-3%7D%7Bx-3%7D%3D0)
In order for the limit to be 0, the denominator's degree should exceed the numerator's degree; the only way for this to happen is if
so that the linear terms vanish.
The third point tells us that
![f(1)=\dfrac{a+b}{1-3}=0\implies a=-b\implies b=4](https://tex.z-dn.net/?f=f%281%29%3D%5Cdfrac%7Ba%2Bb%7D%7B1-3%7D%3D0%5Cimplies%20a%3D-b%5Cimplies%20b%3D4)
So
![f(x)=\dfrac{-4x+4}{x-3}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7B-4x%2B4%7D%7Bx-3%7D)
(b) Since
![f(x)=\dfrac{rx+s}{2x+t}=\dfrac12\dfrac{rx+s}{x+\frac t2}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cdfrac%7Brx%2Bs%7D%7B2x%2Bt%7D%3D%5Cdfrac12%5Cdfrac%7Brx%2Bs%7D%7Bx%2B%5Cfrac%20t2%7D)
we find that
, and
and
.
Answer:
Use a compass to draw two equal arcs ...
Step-by-step explanation:
The attached diagram shows the construction of an angle bisector. First you draw arc DE, then arcs from D and E with the same radius that cross at F.
So, the step on your list is, "use a compass to draw two equal arcs from the intersection points of a previous arc and the legs."
Answer:
The answer is 12
Step-by-step explanation:
7+7 =14
38-14 = 24
24= 2 lengths so 24/2 gives you 12