Answer:
![y=2sin[\frac{\pi}{4}(x+3) ]-5](https://tex.z-dn.net/?f=y%3D2sin%5B%5Cfrac%7B%5Cpi%7D%7B4%7D%28x%2B3%29%20%5D-5)
Step-by-step explanation:
The standard form for a sinusoidal function is given by:
y = Asin[B(x - C)] + D
Where A is the amplitude of the sine wave, the period is 2π/B, C is the phase shift and D is the vertical displacement / translation
Given:
A = 2, D = -5 (down), C = -3 (left).
8 = 2π/B; B = π/4
Therefore:
![y=2sin[\frac{\pi}{4}(x+3) ]-5](https://tex.z-dn.net/?f=y%3D2sin%5B%5Cfrac%7B%5Cpi%7D%7B4%7D%28x%2B3%29%20%5D-5)
Answer:
a) 3.8:1
b) 3.2:1
Step-by-step explanation:
80+15=95
95/25=3.8
80/25=3.2
Answer:
x=3
Step-by-step explanation:
Simplifying
9 + -2(x + -5) = x + 10
Reorder the terms:
9 + -2(-5 + x) = x + 10
9 + (-5 * -2 + x * -2) = x + 10
9 + (10 + -2x) = x + 10
Combine like terms: 9 + 10 = 19
19 + -2x = x + 10
Reorder the terms:
19 + -2x = 10 + x
Solving
19 + -2x = 10 + x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-1x' to each side of the equation.
19 + -2x + -1x = 10 + x + -1x
Combine like terms: -2x + -1x = -3x
19 + -3x = 10 + x + -1x
Combine like terms: x + -1x = 0
19 + -3x = 10 + 0
19 + -3x = 10
Add '-19' to each side of the equation.
19 + -19 + -3x = 10 + -19
Combine like terms: 19 + -19 = 0
0 + -3x = 10 + -19
-3x = 10 + -19
Combine like terms: 10 + -19 = -9
-3x = -9
Divide each side by '-3'.
x = 3
Simplifying
x = 3
Answer:
She spent $380 altogether and She had left $ 20
Answer:
Option (3)
Step-by-step explanation:
Given:
Horizontal side of a triangle ABC is side AC.
AB and BC are the perpendicular lines.
BD is perpendicular to side AC.
Solution:
Option (1).
Slopes of AB and BC are reciprocal.
False.
Option (2)
Angle DAB and BCD are equal.
False.
Option (3).
Since, sides AB and BC are perpendicular lines,
Slopes of AB and BC will be negative reciprocals.
True.
Option (4).
Triangles ABD and BCD are similar.
False.
Therefore, Option (3) will be the answer.