You use the for a cos(bx - c) + d to find your answer.
Amplitude = 5
Period = 2pi / 3
Phase shift = pi / 3 (moving to the right)
Midline or Vertical shift = 2
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Answer:
7 months
Step-by-step explanation:
To find the amount the gym memberships will be the same, write a system of equations and find their intersection point. The intersection point will be the two equations equal to each other.
Gym 1 charges a one time joining fee of $245 and then adds to that $40 a month or 40m. So together the cost is 245 + 40m.
Gym 2 charges $0 or no joining fee. Then adds $75 per month or 75m.
So to find when they are equal, then 75m = 245 + 40m. Solve for m.
75m = 245 + 40m
35m = 245
m = 7
Answer: third choice (4 - 9).
Explanation:
1) The first reflection, Ry = - 5, means a reflection is across the line y = - 5
2) Since the point P has y-coordinate - 1, its discance to the line y = - 5 is 4 units (P is located 4 units upper the line y = - 5).
Then, the reflection of the y-coordinate will be 4 units below the line y = - 5, which is -5 - 4 = - 9,
Therefore, the y-coordinate of the image is - 9.
3) The second reflection, Rx = 1, means a reflection across the line x = 1.
4) Since the point P has x-coordinate - 2, its distance to the line x = 1 is 3 units (P is located 3 units to the left of the line x = 1).
Then, the reflection of P will be 3 units to the right of the line x = 1.
That is 1 + 3 = 4.
Therefore, the x-coordinate of the image is 4.
5) You have obtained the x and y - coordinates of the image, x = 4 and y = -9, that is (4, - 9) which is the third choice.
The area of the shape is 35 square units
<h3>How to determine the area of the shape?</h3>
The given shape is a trapezoid, and it has the following side lengths
Parallel bases = 6 and 8
Height = 5
The area of the shape is then calculated as:
A = 0.5 * (sum of parallel bases) * height
Substitute the known values in the above equation
A = 0.5 * (6 + 8) * 5
Evaluate the product
A = 35
Hence, the area of the shape is 35 square units
Read more about areas at:
brainly.com/question/24487155
#SPJ1
Let the side length of the original square be x, then
1/4 x^2 = (x - 3)^2
x^2 = 4(x^2 - 6x + 9) = 4x^2 - 24x + 36
3x^2 - 24x + 36 = 0
3(x^2 - 8x + 12) = 0
x^2 - 8x + 12 = 0
x^2 - 2x - 6x + 12 = 0
x(x - 2) - 6(x - 2) = 0
(x - 6)(x - 2) = 0
x - 6 = 0 or x - 2 = 0
x = 6 or x = 2
but x cannot be 2 since the side length of the smaller square will be negative.
Therefore, the side length of the original square is 6 inches.
