Answer:
Positive exponent
Step-by-step explanation:
Like x root 1 , 2 , 3 etc
If it said negative exponent then x root -1, -2 etc etc.
Answer:
Inside the triangle - Acute Triangle
Outside the triangle - Obtuse Triangle
On the hypotenuse - Right Triangle
Step-by-step explanation:
The <u>circumcenter</u> is the point where the perpendicular bisectors of a triangle intersect.
In the special case of a right triangle, the circumcenter lies exactly at the midpoint of the hypotenuse.
The circumcenter of an acute triangle lies inside the triangle.
The circumcenter of an obtuse triangle lies outside the triangle.
Answer: x=4, y=-2
Step-by-step explanation: 4x+y=14, x-2y=8
4x+y-y=14-y
4x/4=14/4-y/4
x=14-y/4-(2y)(4)/4
4(14-9y)/4=(8)(4)
14-9y-14=32-14
-9y/-9=18/-9
y=-2
(14)-(-2)/4
14+2/4
16/4
4
x=4
x=4, y=-2
Answer:
Part a) ![BC=10\ units](https://tex.z-dn.net/?f=BC%3D10%5C%20units)
Part b) ![AC=13.66\ units](https://tex.z-dn.net/?f=AC%3D13.66%5C%20units)
Step-by-step explanation:
step 1
Find the length side BC
Applying the law of sines
we know that
![\frac{AB}{sin(C)}=\frac{BC}{sin(A)}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7Bsin%28C%29%7D%3D%5Cfrac%7BBC%7D%7Bsin%28A%29%7D)
we have
![AB=5\sqrt{2}\ units](https://tex.z-dn.net/?f=AB%3D5%5Csqrt%7B2%7D%5C%20units)
![A=45^o](https://tex.z-dn.net/?f=A%3D45%5Eo)
![C=30^o](https://tex.z-dn.net/?f=C%3D30%5Eo)
substitute
![\frac{5\sqrt{2}}{sin(30^o)}=\frac{BC}{sin(45^o)}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7Bsin%2830%5Eo%29%7D%3D%5Cfrac%7BBC%7D%7Bsin%2845%5Eo%29%7D)
solve for BC
![BC=\frac{5\sqrt{2}}{sin(30^o)}(sin(45^o))](https://tex.z-dn.net/?f=BC%3D%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7Bsin%2830%5Eo%29%7D%28sin%2845%5Eo%29%29)
![BC=10\ units](https://tex.z-dn.net/?f=BC%3D10%5C%20units)
step 2
Find the measure of angle B
we know that
The sum of the interior angles in a triangle must be equal to 180 degrees
so
![m\angle A+m\angle B+m\angle C=180^o](https://tex.z-dn.net/?f=m%5Cangle%20A%2Bm%5Cangle%20B%2Bm%5Cangle%20C%3D180%5Eo)
substitute the given values
![45^o+m\angle B+30^o=180^o](https://tex.z-dn.net/?f=45%5Eo%2Bm%5Cangle%20B%2B30%5Eo%3D180%5Eo)
![75^o+m\angle B=180^o](https://tex.z-dn.net/?f=75%5Eo%2Bm%5Cangle%20B%3D180%5Eo)
![m\angle B=180^o-75^o](https://tex.z-dn.net/?f=m%5Cangle%20B%3D180%5Eo-75%5Eo)
![m\angle B=105^o](https://tex.z-dn.net/?f=m%5Cangle%20B%3D105%5Eo)
step 3
Find the length side AC
Applying the law of sines
we know that
![\frac{AB}{sin(C)}=\frac{AC}{sin(B)}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7Bsin%28C%29%7D%3D%5Cfrac%7BAC%7D%7Bsin%28B%29%7D)
we have
![AB=5\sqrt{2}\ units](https://tex.z-dn.net/?f=AB%3D5%5Csqrt%7B2%7D%5C%20units)
![A=45^o](https://tex.z-dn.net/?f=A%3D45%5Eo)
![B=105^o](https://tex.z-dn.net/?f=B%3D105%5Eo)
substitute
![\frac{5\sqrt{2}}{sin(30^o)}=\frac{AC}{sin(105^o)}](https://tex.z-dn.net/?f=%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7Bsin%2830%5Eo%29%7D%3D%5Cfrac%7BAC%7D%7Bsin%28105%5Eo%29%7D)
solve for AC
![AC=\frac{5\sqrt{2}}{sin(30^o)}(sin(105^o))](https://tex.z-dn.net/?f=AC%3D%5Cfrac%7B5%5Csqrt%7B2%7D%7D%7Bsin%2830%5Eo%29%7D%28sin%28105%5Eo%29%29)
![AC=13.66\ units](https://tex.z-dn.net/?f=AC%3D13.66%5C%20units)
$16,750 -$2,870 -$800 = $13,080
Biweekly means she is paid 26 times a year.
$13,080 ÷ 26 = 503.0769231
b. $503.08