Answer:
(8, - 2 )
Step-by-step explanation:
A translation of 4 units right means add 4 to the x- coordinate
A translation of 5 units up means add 5 to the y- coordinate
(x, y ) → (x + 4, y + 5 ) ← translation rule, then
(4, - 7 ) → A'(4 + 4, - 7 + 5 ) → A'(8, - 2 )
Sine (theta) = 5 / hypotenuse
We do not know the hypotenuse length, so let's use the tangent function.
tan (theta) = 5/7
arc tan (5/7) = 35.538 Degrees
Answer:
25.2
Step-by-step explanation:
Secant-Tangent Formula:
(whole secant) x (external part) = (tangent)^2
(41+12) * 12 = x^2
( 53) * 12 = x^2
636= x^2
Taking the square root of each side
sqrt(636) = x
25.2=x
<span>a.{x | x is a real number such that x^2 = 1}
x^2 = 1 => x = +/- 1
=> {-1, 1} <------ answer
b.{x | x is a positive integer less than 12}
1 ≤ x < 12 => {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} <------ answer
c.{x | x is the square of an integer and x < 100}
x = n^2 < 100 => n^2 - 100 < 0
=> (n - 10) (n + 10) < 0
=> a) n - 10 > 0 and n + 10 < 0 => n > 10 and n < - 10 which is not possible
b) n - 10 < 0 and n + 10 > 0 => n < 10 and n > - 10 => - 10 < n < 10
=> n = { - 9, - 8, - 7, - 6, - 5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
=> x = {0, 1, 4, 9, 16, 25, 36, 49, 64, 81} <---- answer
d.{x | x is an integer such that x^2 = 2}
</span>
x = {∅ } because x is √2 which is not an interger but an irrational number
=> Answer: { ∅ }
