Which of the following correctly represents the set of numbers using interval notation?

Answers

Answer 1

Answer:

(-∞,-2) and [2,5) will be the correct representation of the given number line.

What is the range and domain of a function?

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

Given a number line with arrows.

If a number is included then it is given in the middle bracket [ ] while if it is not included then it is given in the small bracket ().

Since in the given number line,

The line is coming through -∞ and at 2 not up to

So,

(-∞,-2) will be correct.

Now,

The right-hand sideline is going from 2 to 5(not included)

So,

[2,5) will be correct.

Hence "(-∞,-2) and [2,5) will be the correct representation of the given number line".

For more details about the range and domain of the function,

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Answer 2

Answer:

Option 3

Step-by-step explanation:

-infinity < x< -2 , 5 > x ≥ 2

Round bracket for boundary excluded, and square bracket for boundary included

(-infinity, -2) or [2,5)

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in a two digit number the tens digit is 6 more than the units digit. if the digits are interchanged, the sum of the new and the original number is 132. Determine the original number.

Answers

Given:

In a two digit number the tens digit is 6 more than the units digit.

If the digits are interchanged, the sum of the new and the original number is 132.

To find:

The original number.

Solution:

Let the unit digit of the original number be x. So, the tens digit is (x+6) and the value of the number is:

$m=(x+6)* 10+x* 1$

$m=10x+60+x$

$m=11x+60$

If we interchange the digits, then the value of new number is:

$n=x* 10+(x+6)* 1$

$n=10x+x+6$

$n=11x+6$

The sum of the new and the original number is 132.

$m+n=132$

$11x+60+11x+6=132$

$22x+66=132$

$22x=132-66$

$22x=66$

Divide both sides by 22.

$x=(66)/(22)$

$x=3$

So, the unit digit of the original number is 3 and the tens digit is:

$x+6=3+6$

$x+6=9$

Therefore, the original number is 39.

Rays of light incident on a lens and parallel to the principal axis of the lens converge

Answers

So we want to know in which point do light rays that are incident on a lens and parallel to the principal axis converge. Rays parallel to the principal axis and are incident on a lens converge in the focal point of the lens. So the correct answer is focal point.

The correct answer is:

Focal point.

Explanation:

The focal point of a lens is the point in space where parallel light rays meet after they pass through the lens. A perfect" lens sends all light rays through one focal point, which result in the clearest image.

professor must randomly select 4 students to participate in a mock debate. There are 18 students in his class. In how many different ways can these students be selected, if the order of selection does not matter?

Answers

18 divided by 4 gives 4r2 so we could do 32 different ways

Yvette is trying to calculate the distance between point C(1, 2) and point D(7, 10). Which of the following expressions will she use? square root of the quantity of 10 minus 2 all squared plus 7 minus 1 all squared square root of the quantity of 10 minus 1 all squared plus 7 minus 2 all squared square root of the quantity of 10 minus 7 all squared plus 2 minus 1 all squared square root of the quantity of 7 minus 10 all squared plus 1 minus 2 all squared

Answers

So this can be solve using the distance formula: D = sqrt [ (x2 – x1)^2 + (y2 – y1)^2] So the expression she should use is: D = sqrt [ (7 – 1)^2 + (10 – 2)^2] Then the answer would be: D = sqrt [ (6)^2 + (8)^2] D = 10

Answer:

square root of the quantity of 10 minus 2 all squared plus 7 minus 1 all squared

Step-by-step explanation:

What is the exact value of the trigonometric ratio of tan-240 degrees?

Answers

Tan240=1.732050808
Tan^-1(240)=89.76126897

Which equation represents the line whose slope is 2 and whose y-intercept is 6

Answers

The basic format for questions like these are y=mx+b where m stands for the slope and the b stands for the y-intercept, and x and y stand for the coordinates of the equation. So if you fill it in, it would be y=2x+6.

slope of 2 means that the the x part is 2x

So when x is 0 y must equal 6

so the equation is y = 2x + 6

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