Answer:
M = (Y2 - Y1) / (X2 - X1)
Step-by-step explanation:
First, look at a graph of a line and find two points, 1 and 2. You can use any two points on a line. The slope will be the same between any two points on a straight line.
Note the X and Y value for each of the points.
Now we'll designate the X and Y value for points 1 and 2. We'll use subscripts to identify them in the slope formula.
Hope this helps!
If the center is (0, 0), then there is no side to side or up or down motion. The center is at the origin. The standard form of a circle is (x-h)^2 + (y-k)^2 = r^2. Your h and your k are both 0's, so just fill in and square the radius:
x^2 + y^2 = 64
Answer:
a) one solution(x = 9)
b) no solution
c) infinite solutions
Step-by-step explanation:
a) To solve this equation, we can add 4 on both sides in order to isolate x:
x - 4 =5
+ 4 + 4
x = 9
Since x equals 9, that counts as only one solution, as there is only one value of x that makes the equation true.
b) We start by subtracting 2x from both sides to combine the variable terms:
2x - 6 = 2x + 5
-2x -2x
-6 = 5
The statement, -6 = 5 is never true and it is not dependent on the value of x. This means there are no solutions to this equation.
c) We can start by subtracting 3x from both sides to combine the terms with x:
3x + 12 = 3x + 12
-3x -3x
12 = 12
The statement above is always true, and no matter the value of x, it will always be true. This means there are infinite solutions to the equation.
1)
∠BAC = ∠NAC - ∠NAB = 144 - 68 = 76⁰
AB = 370 m
AC = 510 m
To find BC we can use cosine law.
a² = b² + c² -2bc*cos A
|BC|² = |AC|²+|AB|² - 2|AC|*|AB|*cos(∠BAC)
|BC|² = 510²+370² - 2*510*370*cos(∠76⁰) =
|BC| ≈ 553 m
2)
To find ∠ACB, we are going to use law of sine.
sin(∠BAC)/|BC| = sin(∠ACB)/|AB|
sin(76⁰)/553 m = sin(∠ACB)/370 m
sin(∠ACB)=(370*sin(76⁰))/553 =0.6492
∠ACB = 40.48⁰≈ 40⁰
3)
∠BAC = 76⁰
∠ACB = 40⁰
∠CBA = 180-(76+40) = 64⁰
Bearing C from B =360⁰- 64⁰-(180-68) = 184⁰
4)
Shortest distance from A to BC is height (h) from A to BC.
We know that area of the triangle
A= (1/2)|AB|*|AC|* sin(∠BAC) =(1/2)*370*510*sin(76⁰).
Also, area the same triangle
A= (1/2)|BC|*h = (1/2)*553*h.
So, we can write
(1/2)*370*510*sin(76⁰) =(1/2)*553*h
370*510*sin(76⁰) =553*h
h= 370*510*sin(76⁰) / 553= 331 m
h=331 m
