Answer:
Yes
Step-by-step explanation:
To see if (2,0) works as a solution to the systems of equations, we plug in the values of x and y and simplify. If the results are equal, then (2,0) is a solution.
3x + y = 6:
- (2,0) is a solution to this equation.
3x - y = 6:
-
- (2,0) is a solution to this equation.
Therefore, the answer is yes, it does work as a solution.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
A polar coordinate is that which can be written as (r, θ) where r is the radius and θ is the angle.
The radius, r, is also the hypotenuse of the right triangle that can be formed. Hence, it can be calculated through the equation,
r² = x² + y²
If we are to simplify this for the r alone, we have,
r = sqrt (x² + y²)
Substituting the known values,
r = sqrt ((4)² + (-4)²) = 4√2
The x and y can be related through the trigonometric function, tangent.
tan θ = y/x
To solve for θ
θ = tan⁻¹(y/x) = tan⁻¹(-4/4) = -45° = 315°
Hence, the polar coordinate is <em>(4√2, 315°)</em>
Answer: The length of the rectangle is 15 inches
Step-by-step explanation:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
The perimeter of a rectangle is expressed as 2 length + 2 width
Perimeter = 2(L + W)
The rectangle has a perimeter of 52 inches. It means that
2(L + W) = 52
L + W = 52/2 = 26 - - - - - - - 1
The length of the rectangle is 4 inches more than its width. It means that
L = W + 4
Substituting L = W + 4 into equation 1, it becomes
W + 4 + W = 26
2W = 26 - 4 = 22
W = 22/2 = 11
L = W + 4 = 11 + 4 = 15
Answer/Step-by-step explanation:
Part A:
Evidence 1: the line passes through the point of origin, (0, 0)
Evidence 2: it has a unit rate or constant of proportionality, k = y/x = 5/3
Part B:
When extended, if the ray passes through the point, (18, 30), then y/x of this point, should give us the same unit rate (k) of 5/3 of the graph.
Thus:
y/x = 30/18
Simplify
= 5/3
Thus, it has the same unit rate of the graph, therefore, the ray passes through the point (18, 30).
