2x + y = 20
-5y = -6x + 12
To use the substitution method, first isolate one of the variables in one of the equations.
Isolate the "y" in the first equation (because it is the easiest to isolate), and substitute it into the second equation:
2x + y = 20 Subtract 2x on both sides
y = 20 - 2x
-5y = -6x + 12 (since y = 20 - 2x, you can substitute 20 - 2x into y)
-5(20 - 2x) = -6x + 12 Multiply -5 into (20 - 2x)
-100 + 10x = -6x +12 Add 100 on both sides
10x = -6x + 112 Add 6x on both sides
16x = 112 Divide 16 on both sides
x = 7
Now that you have found x, you can substitute 7 into x for one of the original equations:
2x + y = 20
2(7) + y = 20
14 + y = 20 Subtract 14 on both sides
y = 6
-5y = -6x + 12
-5y = -6(7) + 12
-5y = -42 + 12
-5y = -30 Divide -5 on both sides
y = 6
x = 7, y = 6
Answer:
12x+4
Step-by-step explanation:
To find the perimeter of any shape you just have to take the sum of all the sides.
In this case you would write:
4x+2 (side 1) +2x (side 2) +4x+2 (side 3) +2x (side 4)
Now you just have to simplify the expression which would give you:
12x+4 (after collecting like terms)
So the final answer will be 12x+4
Answer:
Step-by-step explanation:
The equation of a circle with center (a,b) and radius r, is
From the question, the center of the circle is located at (-6,2) and the radius is
We substitute the center and radius to get:
Simplify to obtain:
Answer:
(A)The northern lighthouse is 8.2 miles closer than the southern lighthouse.
Step-by-step explanation:
The triangle attached represents the given problem.
First, let us determine the distance of the Boat from each of the lighthouse.
In Triangle ABC,
∠A+∠B+∠C=180 degrees
21+∠B+16=180
∠B=180-37=143 degrees.
Using Law of Sines
Similarly
Difference in Distance =35.73-27.48=8.25 miles
Therefore, the northern lighthouse is 8.2 miles closer than the southern lighthouse.
