Step-by-step explanation:
Let's say the position of the fire is point C.
Bearings are measured from the north-south line. So ∠BAC = 55°, and ∠ABC = 60°.
Since angles of a triangle add up to 180°, ∠ACB = 65°.
Using law of sine:
190 / sin 65° = a / sin 60° = b / sin 55°
Solving:
a = 181.6
b = 171.7
Station A is 181.6 miles from the fire and station B is 171.7 miles from the fire.
Buckle up, this one was a long one.
I set up 1 / 3(12 + x) as a fraction and set it equal to - 8(6 - x).
Get rid of the parentheses by distributing the integers on the outside. You get 1 / 36 + 3x = - 48 + 8x.
To get rid of the fraction, you multiply both sides by the (36 + 3x) polynomial to get 1 = (- 48 + 8x)(36 + 3x).
Now we do the FOIL method to get 1 = 24x^2 + 288x - 144x - 1728. Combine like terms to get 24x^2 + 144x - 1728 = 1.
Simply again by dividing each term the GCF of 24 to get 24(x^2 + 6x - 72) = 1.
Factor the inside of the parentheses to get 24(x + 12)(x - 6) = 1. Now divide both sides by 24 to isolate the x variables to get (x + 12)(x - 6) = 1/24.
Set each polynomial equal to 1/24 to get you possible answers for what x can be.
x + 12 = 1/24. Subtract 12 from both sides; you get x = - 12 + 1/24 to get x = - 11 23/24.
x - 6 = 1/24. Add 6 to both sides; you get x = 6 + 1/24 to get x = 6 1/24
x^2 + 4x + 4 is the perfect square of (x + 2)
so x^2 + 4x + 4 = (x+2)^2
Substitute x^2 + 4x + 4 with (x+2)^2 in the equations:
(x + 2)^2 = 25
Notice that 25 is also the perfect square of 5 so 5^2 = 25
Substitue 25 with 5^2 in the equation:
(x + 2)^2 = 5^2
Since both sides of the equation are being squared, we can square root both sides, and since we re doing this to both sides, both sides are still equal and the equation still holds true
This results in:
+-(x + 2) = +- 5
This means the 5 can be either postivie or negative, so there are 2 sollutions:
x + 2 = 5 x + 2 = -5
x = 3 x = -7
Its 3 or -7 so you must ve copied the wrong possible answers
Answer:
6 minutes
Step-by-step explanation:
The ant can crawl 40 cm per minute but is pushed back 5 cm every minute aswell. In total the ant will crawl 35 cm per minute (40 - 5 = 35).
In order to find how long it will take for the ant to reach the hole we <u>divide</u> 210 by 35 (210/35) to get the answer of 6, therefore it takes the ant 6 minutes to reach the hole.
Answer:
how would i solve this .u know how, i just wont
Step-by-step explanation: