20pts please help me

which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1

lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. $y=\sec x$

B. $y= \tan x$

C. $y= \cot x$

D. $y= \csc x$

Answer:

A. $y=\sec x$

D. $y=\csc x$

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: $y=\sec x$

We know that, the $\sec x=\frac{1}{\cos x}$

The range of $\cos x$ is from -1 to 1 given as [-1, 1]. So,

$|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the secant function as:

$\sec x\leq -1\ or\ \sec x\geq 1\\$

Therefore, the range of $y=\sec x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

Choice B: $y= \tan x$

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: $y= \cot x$

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: $y=\csc x$

We know that, the $\csc x=\frac{1}{\sin x}$

The range of $\sin x$ is from -1 to 1 given as [-1, 1]. So,

$|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

$\csc x\leq -1\ or\ \csc x\geq 1\\$

Therefore, the range of $y=\csc x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

6 0

3 years ago

Multiply using FOIL or Table method (x + 4) (x + 5)

mylen [45]

Answer:

${x}^{2} + 9x + 20$

Step-by-step explanation:

1) Use FOIL method: (a + b) (c + d) = ac + ad + bc + bd.

${x}^{2} + 5x + 4x + 20$

2) Collect like terms.

${x}^{2} + (5x + 4x) + 20$

3) Simplify.

${x}^{2} + 9x + 20$

Therefor, the answer is x² + 9x + 20.

5 0

2 years ago

What is 4/20 as a percent? And how do I find it?

Reika [66]

Well u know 4/20 equals 0.2 as a decimal but as a percentage it is 20% so 4/20 as a percentage is 20%

4 0

2 years ago

Can someone help me on this Please

saul85 [17]

9514 1404 393

Answer:

11.6 cm

Step-by-step explanation:

As the page title tells you, the Pythagorean theorem must be applied more than once. As you know, it tells you the square of the hypotenuse is the sum of the squares of the two sides.

AD² = ED² +EA²

EA² = AD²-ED² = 7² -6² = 13

EA = √13 ≈ 3.606

__

CD² = ED² +EC²

EC² = CD² -ED² = 10² -6² = 64

EC = √64 = 8

__

The length of the horizontal diagonal is ...

AC = EA +EC = 3.6 +8 = 11.6 . . . cm

6 0

3 years ago

Doug took 180 photos during his vacation. He took 2/3 of photos during

pogonyaev

Answer:

66 pictures

Step-by-step explanation:

180 ÷ 3 = 60 60 x 2 = 120

120 = 2/3. He took 120 pictures on the first day of his vacation.

120 ÷ 4 = 30 30 x 1 = 30

30 = 1/4. He took 30 pictures of landscapes

120 ÷ 10 = 12 12 x 3 = 36

0.3 = 36. He took 36 pictures of people.

36 + 30 = 66 pictures.

He took 66 pictures of landscapes and people.

Hopefully this helps :3 sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3

-Bee~

7 0

2 years ago