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3 years ago

Which conjunction or disjunction is equivalent to the open sentence |a – 9| ≤ 4.

Mathematics

1 answer:

xenn [34]3 years ago

3 0

The absolute value inequality is equivalent to
±(a - 9) ≤ 4
When the minus sign is chosen and the expression is multiplied by -1, the comparison operator is reversed and the expression becomes
a - 9 ≥ -4

The solution spaces of
a - 9 ≤ 4
a - 9 ≥ -4
overlap, so the solution is the conjunction of the two inequalities. This matches selection ...
D. a - 9 ≤ 4 and a - 9 ≥ -4

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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

A shopkeeper buys a dress for $40

DanielleElmas [232]

Answer:

48 - 40 = $8, there is a $8 dollar increase.

Formula for change of percentage;

changed price

___________ x 100% (100/100)

original amount

Replace those values with the values we found;

40/48 x 100/100 = 20% increase.

4 0

2 years ago

PLEASE HELP

katovenus [111]

<u>Answer:</u>

$593.26

<u>Step-by-step explanation:</u>

We know that the price of the laptop is $2500 and each year its resale value decreases by 25%. It means that 100 - 25 = 75% of the value is retained every year for the resale.

So, the resale value for 1st year = $\frac{75}{100} *2500 =$ $1875

for 2nd year = $\frac{75}{100} *1875 =$ $1406.25

for 3rd year = $\frac{75}{100} *1406.25 =$ $1054.7

for 4th year = $\frac{75}{100} *1054.7 =$ $791.01

for 5th year = $\frac{75}{100} *791.01 =$ $593.25

Or we can use the following formula to find its resale value after 5 years:

$2500*(0.75)^5 =$ $593.26

4 0

3 years ago

I need help completing this problem ASAP

Evgen [1.6K]

Answer:

8 sqrt(5)

Step-by-step explanation:

sqrt(45) + sqrt(125)

Rewriting

sqrt(9*5) + sqrt( 25 *5)

we know sqrt(ab) = sqrt(a) sqrt(b)

sqrt(9) sqrt(5) + sqrt(25) sqrt(5)

3 sqrt(5)+5 sqrt(5)

Add like terms

8 sqrt(5)

5 0

3 years ago

Read 2 more answers

Please help asap :( This is my "Final grade" My Teacher wants a full explanation included ! on how i got the answer. )

Mrac [35]

If the whole diameter of sphere is 6 inch(means radius is 3 inch) & thickness of material is 1 inch, so the radius of the hollow part should be 2 inch (3-1=2)

The total volume of the ball will be;

= Total volume - Volume of hollow part

= 4/3πr³ - 4/3πr³

= 4/3 × 3.14 × (3)³ - 4/3×3.14×(2)³

= 4 × 3.14 × 9 - 4/3 × 3.14 × 8

= 113.04 - 33.52

= 79.52

If the density of the material is 3.25 g/in3, then the density of 79.52 inch³ should be;

= 79.52 × 3.25

= 258.44 g

Now, if there are 8 spheres in one box, the weight if box will be;

= 258.44 × 8

= 2,067.52 g

_____________________________

Ahh! Finally done with this, if you have any doubt just do ask me :)

3 0

3 years ago