Answer:
False
Step-by-step explanation:
She worked as a carpenter for 12 hours and as a blacksmith for 18 hours.
Assuming you mean she earned $20 as a carpenter and $25 as a blacksmith per hour, with a total of 30 hours for $690,
let c represent carpenter hours and b for blacksmith hours.
20c + 25b = 690
c + b = 30
Subtract b from each side so that c = 30 - b
Plug this value into the first equation
20(30 - b) + 25b = 690
600 - 20b + 25b = 690
600 + 5b = 690
5b = 90
b = 18
To find c, plug this value of b into the other equation
c + 18 = 30
c = 12
Answer:
f(1) = 81
Step-by-step explanation:
f(n + 1) = 1/3 f(n)
⇔ f(n) = 3 × f(n + 1)
……………………………
if f(3) = 9 ⇒ f(2) = 3 × f(3) = 3 × 9 = 27
Then
f(1) = 3 × f(2) = 3 × 27 = 81
Given:
A plane flying a straight course observes a mountain at a bearing of 35° to the right of its course.
The distance between plan and mountain is 10 km.
A short time later, the bearing to the mountain becomes 45°.
Here NM is the distance between the plane from the mountain when the second bearing is taken.
We need to find the measure of NM.
![We\text{ know that }\angle INM\text{ and }\angle\text{XNM are supplementary angles.}](https://tex.z-dn.net/?f=We%5Ctext%7B%20know%20that%20%7D%5Cangle%20INM%5Ctext%7B%20and%20%7D%5Cangle%5Ctext%7BXNM%20are%20supplementary%20angles.%7D)
The sum of the supplementary angles is 180 degrees.
![\angle INM+\angle XNM=180^o](https://tex.z-dn.net/?f=%5Cangle%20INM%2B%5Cangle%20XNM%3D180%5Eo)
![\text{Substitute }\angle XNM=45^o\text{ in the equation.}](https://tex.z-dn.net/?f=%5Ctext%7BSubstitute%20%7D%5Cangle%20XNM%3D45%5Eo%5Ctext%7B%20in%20the%20equation.%7D)
![\angle INM+45^o=180^o](https://tex.z-dn.net/?f=%5Cangle%20INM%2B45%5Eo%3D180%5Eo)
![\angle INM=180^o-45^o](https://tex.z-dn.net/?f=%5Cangle%20INM%3D180%5Eo-45%5Eo)
![\angle INM=135^o](https://tex.z-dn.net/?f=%5Cangle%20INM%3D135%5Eo)
We know that the sum of all three angles of the triangle is 180 degrees.
![\angle INM+\angle NIM+\angle INM=180^o](https://tex.z-dn.net/?f=%5Cangle%20INM%2B%5Cangle%20NIM%2B%5Cangle%20INM%3D180%5Eo)
![\text{Substitute }\angle INM=135^o\text{ and }\angle NIM=35^o\text{ in the equation.}](https://tex.z-dn.net/?f=%5Ctext%7BSubstitute%20%7D%5Cangle%20INM%3D135%5Eo%5Ctext%7B%20and%20%7D%5Cangle%20NIM%3D35%5Eo%5Ctext%7B%20in%20the%20equation.%7D)
![135^o+35^o+\angle INM=180^o](https://tex.z-dn.net/?f=135%5Eo%2B35%5Eo%2B%5Cangle%20INM%3D180%5Eo)
![170^o+\angle INM=180^o](https://tex.z-dn.net/?f=170%5Eo%2B%5Cangle%20INM%3D180%5Eo)
![\angle INM=180^o-170^o](https://tex.z-dn.net/?f=%5Cangle%20INM%3D180%5Eo-170%5Eo)
![\angle INM=10^o](https://tex.z-dn.net/?f=%5Cangle%20INM%3D10%5Eo)
Consider the sine law.
![\frac{\sin N}{IM}=\frac{\sin M}{IN}=\frac{\sin I}{NM}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%20N%7D%7BIM%7D%3D%5Cfrac%7B%5Csin%20M%7D%7BIN%7D%3D%5Cfrac%7B%5Csin%20I%7D%7BNM%7D)
Take the equation to find the measure of NM.
![\frac{\sin N}{IM}=\frac{\sin I}{NM}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%20N%7D%7BIM%7D%3D%5Cfrac%7B%5Csin%20I%7D%7BNM%7D)
![\text{Substitute }\angle N=135^o,\angle I=35^o,\text{ and IM=10 in the equation.}](https://tex.z-dn.net/?f=%5Ctext%7BSubstitute%20%7D%5Cangle%20N%3D135%5Eo%2C%5Cangle%20I%3D35%5Eo%2C%5Ctext%7B%20and%20IM%3D10%20in%20the%20equation.%7D)
![\frac{\sin 135^o}{10}=\frac{\sin35^o}{NM}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csin%20135%5Eo%7D%7B10%7D%3D%5Cfrac%7B%5Csin35%5Eo%7D%7BNM%7D)
![NM=\frac{\sin 35^o}{\sin 135^o}\times10](https://tex.z-dn.net/?f=NM%3D%5Cfrac%7B%5Csin%2035%5Eo%7D%7B%5Csin%20135%5Eo%7D%5Ctimes10)
![NM=8.11](https://tex.z-dn.net/?f=NM%3D8.11)
Hence the measure of NM is 8.1 km.
The plane is 8.1 km far from the mountain when the second bearing is taken.
P/2 - l = w
perimeter divided by 2 minus the length