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3 years ago

What is the Product of x-3 and x-9

Mathematics

1 answer:

Serggg [28]3 years ago

4 0

Answer:

x^2-12x+27

Step-by-step explanation:

(x-3)(x-9)=x^2-3x-9x+27=x^2-12x+27

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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

Mrs.Stone is three times older than her younger daughter, Joyce, but only two times older than her older daughter, Alex. How old

olchik [2.2K]

Answer:

54 years

Step-by-step explanation:

Joyce age = x

Alex age = y

3x = 2y - - - (1)

y - 9 = 2(x - 9)

y - 9 = 2x - 18

-9 + 18 = 2x - y

9 = 2x - y

y = 2x - 9 - - (2)

3x = 2y

3x = 2(2x - 9)

3x = 4x - 18

18 = 4x - 3x

18 = x

Hence,

Mrs stone is 3 * 18 = 54 years

5 0

3 years ago

Find the measure of angle C

KiRa [710]

65 degrees
90-25 = 65

5 0

3 years ago

Which equation has an a-value of 1, a b-value of –3, and a c-value of –5?

ANTONII [103]

Answer:

answer is first option

${x}^{2} -3x - 5 = 0$

wherein, a = 1, b = -3, c = -5

8 0

3 years ago

Read 2 more answers

Suppose you cut along a diagonal of a rhombus, a rectangle, or a square. Would you get two triangles that have the same shape an

stich3 [128]

I believe the answer to your question is

Yes, you would get two triangles that have the same shape and size

3 0

3 years ago

What is the Product of x-3 and x-9​

What is the Product of x-3 and x-9