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3 years ago

Write the explicit equation for the sequence 5,8,11,14

1 answer:

4 0

Consecutive terms differ by 3, so

$a_n=a_{n-1}+3=a_{n-2}+2\times3=a_{n-3}+3\times3=\cdots=a_1+(n-1)\times3$

Since the first term is $a_1=5$ , the formula for the sequence is

$a_n=5+3(n-1)=3n+2$

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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

The value of -7 + 24 ÷ (-3)(2) is _____.<br><br> Show work

densk [106]

Answer:

$\boxed{=-23}$

Explanation: You had to used pemdas stands for: p-parenthesis, e-exponents, m-multiply, d-divide, a-add, and s-subtracting that came from left to right.

First you had to multiply and divide from left to right.

$24/(-3)=-8(2)$

$8*2=16$

$-7-16$

Then you add and subtract from left to right.

$-7-16=-23$

$=-23$

Final answer: $\boxed{=-23}$

Hope this helps!

And thank you for posting your question at here on brainly, and have a great day.

-Charlie

3 0

3 years ago

Given f(x)=-8x+5 And g(x)=10x+2what is g(x) - f(x)

lidiya [134]

G(x)-f(x)=10x+2- (-8x+5)
=10x+2+8x-5
=18x-3

5 0

3 years ago

There are three consecutive integers such that the sum of the two smallest integers is 17 less than three times the largest.What

abruzzese [7]

ANSWER:

Let the smallest integer = x

x + x + 1 = 3 ( x + 2 ) - 17

2x + 1 = 3x + 6 - 17

2x - 3x = 6 - 17 - 1

- x = - 12

x = 12

FINAL ANSWER:

Therefore, the smallest integer is 12.

Please mark as brainliest if you found this helpful! :)
Thank you and have a lovely day! <3

6 0

3 years ago

Which symbol makes the following number sentence true? 546, 322. 540, 997

Reil [10]

The answer is:
545>322
540 <997

8 0

3 years ago

Read 2 more answers