Simplify: -5g + 2h - 3g + g -2h
2 answers:
-7g+h you have to simplify by adding and subtracting same values so h’s together and g’s together
Answer: The answer is -7g
Step-by-step explanation:
-5g+2h-3g+g-2h
-5g+2h-3g+g-2h
=-7g+2h-2h
=-7g
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Answer: 5 sides
Step-by-step explanation:
Helloo:)
it’ll be loge (100) because ln = loge
(I’m not sure how to explain this, but I hope it helps:)!
The value of 4 is in the ones place
First, note that
Then
![m\angle A=90^{\circ}-m\angle C \text{ and } m\angle C=90^{\circ}-m\angle A.](https://tex.z-dn.net/?f=m%5Cangle%20A%3D90%5E%7B%5Ccirc%7D-m%5Cangle%20C%20%5Ctext%7B%20and%20%7D%20m%5Cangle%20C%3D90%5E%7B%5Ccirc%7D-m%5Cangle%20A.)
Consider all options:
A.
![\tan A=\dfrac{\sin A}{\sin C}](https://tex.z-dn.net/?f=%5Ctan%20A%3D%5Cdfrac%7B%5Csin%20A%7D%7B%5Csin%20C%7D)
By the definition,
![\tan A=\dfrac{BC}{AB},\\ \\\sin A=\dfrac{BC}{AC},\\ \\\sin C=\dfrac{AB}{AC}.](https://tex.z-dn.net/?f=%5Ctan%20A%3D%5Cdfrac%7BBC%7D%7BAB%7D%2C%5C%5C%20%5C%5C%5Csin%20A%3D%5Cdfrac%7BBC%7D%7BAC%7D%2C%5C%5C%20%5C%5C%5Csin%20C%3D%5Cdfrac%7BAB%7D%7BAC%7D.)
Now
![\dfrac{\sin A}{\sin C}=\dfrac{\dfrac{BC}{AC}}{\dfrac{AB}{AC}}=\dfrac{BC}{AB}=\tan A.](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin%20A%7D%7B%5Csin%20C%7D%3D%5Cdfrac%7B%5Cdfrac%7BBC%7D%7BAC%7D%7D%7B%5Cdfrac%7BAB%7D%7BAC%7D%7D%3D%5Cdfrac%7BBC%7D%7BAB%7D%3D%5Ctan%20A.)
Option A is true.
B.
![\cos A=\dfrac{\tan (90^{\circ}-A)}{\sin (90^{\circ}-C)}.](https://tex.z-dn.net/?f=%5Ccos%20A%3D%5Cdfrac%7B%5Ctan%20%2890%5E%7B%5Ccirc%7D-A%29%7D%7B%5Csin%20%2890%5E%7B%5Ccirc%7D-C%29%7D.)
By the definition,
![\cos A=\dfrac{AB}{AC},\\ \\\tan (90^{\circ}-A)=\dfrac{\sin(90^{\circ}-A)}{\cos(90^{\circ}-A)}=\dfrac{\sin C}{\cos C}=\dfrac{\dfrac{AB}{AC}}{\dfrac{BC}{AC}}=\dfrac{AB}{BC},\\ \\\sin (90^{\circ}-C)=\sin A=\dfrac{BC}{AC}.](https://tex.z-dn.net/?f=%5Ccos%20A%3D%5Cdfrac%7BAB%7D%7BAC%7D%2C%5C%5C%20%5C%5C%5Ctan%20%2890%5E%7B%5Ccirc%7D-A%29%3D%5Cdfrac%7B%5Csin%2890%5E%7B%5Ccirc%7D-A%29%7D%7B%5Ccos%2890%5E%7B%5Ccirc%7D-A%29%7D%3D%5Cdfrac%7B%5Csin%20C%7D%7B%5Ccos%20C%7D%3D%5Cdfrac%7B%5Cdfrac%7BAB%7D%7BAC%7D%7D%7B%5Cdfrac%7BBC%7D%7BAC%7D%7D%3D%5Cdfrac%7BAB%7D%7BBC%7D%2C%5C%5C%20%5C%5C%5Csin%20%2890%5E%7B%5Ccirc%7D-C%29%3D%5Csin%20A%3D%5Cdfrac%7BBC%7D%7BAC%7D.)
Then
![\dfrac{\tan (90^{\circ}-A)}{\sin (90^{\circ}-C)}=\dfrac{\dfrac{AB}{BC}}{\dfrac{BC}{AC}}=\dfrac{AB\cdot AC}{BC^2}\neq \dfrac{AB}{AC}.](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctan%20%2890%5E%7B%5Ccirc%7D-A%29%7D%7B%5Csin%20%2890%5E%7B%5Ccirc%7D-C%29%7D%3D%5Cdfrac%7B%5Cdfrac%7BAB%7D%7BBC%7D%7D%7B%5Cdfrac%7BBC%7D%7BAC%7D%7D%3D%5Cdfrac%7BAB%5Ccdot%20AC%7D%7BBC%5E2%7D%5Cneq%20%5Cdfrac%7BAB%7D%7BAC%7D.)
Option B is false.
3.
![\sin C = \dfrac{\cos A}{\tan C}.](https://tex.z-dn.net/?f=%5Csin%20C%20%3D%20%5Cdfrac%7B%5Ccos%20A%7D%7B%5Ctan%20C%7D.)
By the definition,
![\sin C=\dfrac{AB}{AC},\\ \\\cos A=\dfrac{AB}{AC},\\ \\\tan C=\dfrac{AB}{BC}.](https://tex.z-dn.net/?f=%5Csin%20C%3D%5Cdfrac%7BAB%7D%7BAC%7D%2C%5C%5C%20%5C%5C%5Ccos%20A%3D%5Cdfrac%7BAB%7D%7BAC%7D%2C%5C%5C%20%5C%5C%5Ctan%20C%3D%5Cdfrac%7BAB%7D%7BBC%7D.)
Now
![\dfrac{\cos A}{\tan C}=\dfrac{\dfrac{AB}{AC}}{\dfrac{AB}{BC}}=\dfrac{BC}{AC}\neq \sin C.](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ccos%20A%7D%7B%5Ctan%20C%7D%3D%5Cdfrac%7B%5Cdfrac%7BAB%7D%7BAC%7D%7D%7B%5Cdfrac%7BAB%7D%7BBC%7D%7D%3D%5Cdfrac%7BBC%7D%7BAC%7D%5Cneq%20%5Csin%20C.)
Option C is false.
D.
![\cos A=\tan C.](https://tex.z-dn.net/?f=%5Ccos%20A%3D%5Ctan%20C.)
By the definition,
![\cos A=\dfrac{AB}{AC},\\ \\\tan C=\dfrac{AB}{BC}.](https://tex.z-dn.net/?f=%5Ccos%20A%3D%5Cdfrac%7BAB%7D%7BAC%7D%2C%5C%5C%20%5C%5C%5Ctan%20C%3D%5Cdfrac%7BAB%7D%7BBC%7D.)
As you can see
and option D is not true.
E.
![\sin C = \dfrac{\cos(90^{\circ}-C)}{\tan A}.](https://tex.z-dn.net/?f=%5Csin%20C%20%3D%20%5Cdfrac%7B%5Ccos%2890%5E%7B%5Ccirc%7D-C%29%7D%7B%5Ctan%20A%7D.)
By the definition,
![\sin C=\dfrac{AB}{AC},\\ \\\cos (90^{\circ}-C)=\cos A=\dfrac{AB}{AC},\\ \\\tan A=\dfrac{BC}{AB}.](https://tex.z-dn.net/?f=%5Csin%20C%3D%5Cdfrac%7BAB%7D%7BAC%7D%2C%5C%5C%20%5C%5C%5Ccos%20%2890%5E%7B%5Ccirc%7D-C%29%3D%5Ccos%20A%3D%5Cdfrac%7BAB%7D%7BAC%7D%2C%5C%5C%20%5C%5C%5Ctan%20A%3D%5Cdfrac%7BBC%7D%7BAB%7D.)
Then
![\dfrac{\cos(90^{\circ}-C)}{\tan A}=\dfrac{\dfrac{AB}{AC}}{\dfrac{BC}{AB}}=\dfrac{AB^2}{AC\cdot BC}\neq \sin C.](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ccos%2890%5E%7B%5Ccirc%7D-C%29%7D%7B%5Ctan%20A%7D%3D%5Cdfrac%7B%5Cdfrac%7BAB%7D%7BAC%7D%7D%7B%5Cdfrac%7BBC%7D%7BAB%7D%7D%3D%5Cdfrac%7BAB%5E2%7D%7BAC%5Ccdot%20BC%7D%5Cneq%20%5Csin%20C.)
This option is false.