Answer:
g(x) = (x + 1)^2 + 3
Step-by-step explanation:
When x is replaced by x - h, it results in a horizontal translation of h units.
When y is replaced by y - k, it results in a vertical translation of k units.
f(x) = x^2 is the original function.
Rewrite it as
y = x^2
To translate it 1 unit left, you need h = -1.
x - h = x - (-1) = x + 1. Replace x with x + 1.
Now you have y = (x + 1)^2.
To translate 3 units up, you have k = 3.
y - k = y - 3. Replace y with y - 3.
y - 3 = (x + 1)^2
Solve for y.
y = (x + 1)^2 + 3
Replace y with g(x).
g(x) = (x + 1)^2 + 3
Answer:
see explanation
Step-by-step explanation:
(5)
Using the trigonometric identity
sin²x + cos²x = 1 ⇒ cos²x = 1 - sin²x
Given
3sin²Θ + 2cos²Θ - 2
= 3sin²Θ + 2(1 - sin²Θ) - 2
= 3sin²Θ + 2 - 2sin²Θ - 2
= sin²Θ
(6)
Using the trigonometric identity
secx = 
Consider the left side

= 
=
= secx = right side ⇒ verified
(7)
Using the trigonometric identity
1 + cot²x = csc²x
Given
sin²x. cot²x + sin²x ← factor out sin²x from each term
= sin²x(cot²x + 1)
= sin²x. csc²x
= sin²x ×
= 1
Answer:Sorry, but I don't know ;(
Step-by-step explanation:
The area of a regular hexagon with an apothem 18.5 inches long and a side 21 inches is 1, 165. 5 In²
<h3>
How to calculate the area of a regular hexagon</h3>
The formula is given thus;
Area of hexagon = (1/2) × a × P
where a = the length of the apothem
P = perimeter of the hexagon
Given a = 18. 5 inches
Note that Perimeter, p = 6a with 'a' as side
p = 6 × 21 = 126 inches
Substitute values into the formula
Area, A = 1 ÷2 × 18. 5 × 126 = 1 ÷2 × 2331 = 1, 165. 5 In²
Thus, the area of the regular hexagon is 1, 165. 5 In²
Learn more about the area of a hexagon here:
brainly.com/question/15424654
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Un parallelogramma è un quadrilatero avente i lati opposti paralleli (lato a = 10 cm, lato b = 12 cm);
La distanza tra i due lati paralleli si può considersre come l'altezza h (h=6)
L'area del parallelogramma é:
A= b×h = 12 cm × 6 cm = 72 cmq