The transformations which have made to produce the function
y₂ = 1+csc (x-π) from the <span>parent function y = csc x
</span>1. shift up one unit ⇒ shift one unit in the direction of positive y
2. shift to the left equal to π ⇒ shift π units in the direction of positive x
See the attached figure.
Blue graph represents the parent function
Red graph represents the produced function after transformation.
Answer:
(x+3), (y+9)
Step-by-step explanation:
Adding to x with translate the figure right (subtracting will translate it left), and adding to y will translate it up (subtracting will translate it down).
To get from a point on 
to the corresponding point on 
, you would move 3 to the right and 9 up, so it would be (x+3), (y+9)
The probability is 0.1429.
The probability that the first person chosen is a boy is 5/7. The probability that the second is a boy is 4/6; the third, 3/5; and the fourth, 2/4. Both the numerator and denominator decrease every time, because you lose a boy to choose from and you lose a student to choose from as well. This gives us:
5/7(4/6)(3/5)(2/4) = 120/840 = 0.1429.
Answer:
Step-by-step explanation:
Part 1.
The sine of an angle is defined as; Opposite side/the Hypotenuse. From the right angle triangle given; sin x =5/13.
The cosine of an angle is defined as; Adjacent side/Hypotenuse. From the right angle triangle given; cos x =12/13.
The tangent of an angle is defined as; Opposite side/Adjacent side. From the right angle triangle given; tan x =5/12.
Part 2.
We use the same definitions of the trigonometric ratios above;
sin y =12/13
cos y =5/13
tan y =12/5
Part 3.
The sin∠X and the cos∠Y are equal, their value is 5/13. The sine of angle is always equal to the cosine of its complement. In this case, ∠X+∠Y =90 hence ∠X is a complement of ∠Y.
Part 4.
The tangents of ∠X and ∠Y are inverses of each other. The tangent of an angle will always be equal to the inverse or reciprocal of the tangent of its complement.
