The sky appears blue because of Rayleigh scattering while water appears blue due to selective absorption and scattering of light.
Why does the sky appear blue and the water blue?The blue color of the sky is a result of Rayleigh scattering which occurs when the Earth's atmosphere scatters shorter wavelengths of light (blue and violet) more efficiently than longer wavelengths (red and orange).
When sunlight enters the atmosphere, the blue light is scattered in all directions by the molecules and tiny particles present in the air creating the blue appearance of the sky.
Similarly, water appear blue due to selective absorption and scattering of light. Water molecules selectively absorb colors from the visible light spectrum and absorb longer wavelengths (such as red) more effectively than shorter wavelengths (such as blue).
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a contractor is notified that 40% of the lumber shipment will be late. When the shipment arrives there are 50 stacks of lumber missing. How many stacks in total were supposed to be delivered?
The total number of stacks that were supposed to be delivered is 125.
In order to determine how many stacks of lumber were supposed to be delivered, we need to use a bit of algebra.
Let's start by assigning a variable to the total number of stacks. We can call this variable "x".
Now, we know that 40% of the lumber shipment will be late.
That means that only 60% of the shipment will arrive on time.
We can express this as an equation:0.60x = number of stacks that arrive on time
We also know that when the shipment arrives, there are 50 stacks of lumber missing.
This means that the total number of stacks delivered is 50 less than the number of stacks that were supposed to be delivered.
We can express this as another equation:x - 50 = number of stacks that were actually delivered
Now, we can set these two equations equal to each other, since they both represent the same thing:0.60x = x - 50
Solving for x, we can first subtract "0.60x" from both sides:x - 0.60x = 50
Simplifying the left side, we get:0.40x = 50
Finally, we can divide both sides by 0.40 to solve for x:x = 125
So, the total number of stacks that were supposed to be delivered is 125.
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of 25
Does this table represent a function? Why or why not?
X
2
4
6
8
10
y
1
3
4
6
A. Yes, because every x-value corresponds to exactly one y-value.
OB. No, because one x-value corresponds to two different y-values.
OC. Yes, because all of the x-values correspond to one or more
y-values.
OD. No, because two of the y-values are the same.
The statement "Yes, because every x-value corresponds to exactly one y-value" (A) is correct.
The given table represents a function. A function is a relationship where each input (x-value) is associated with exactly one output (y-value).
Looking at the table:
X | Y
2 | 1
4 | 3
6 | 4
8 | 6
10 | -
We can see that each x-value in the table corresponds to a unique y-value. There is no repetition or duplication of x-values, and each x-value has only one corresponding y-value.
Therefore, the statement "Yes, because every x-value corresponds to exactly one y-value" (A) is correct.
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in need of help
use the formula to find the hypotenuse of the right triangle below. Make sure you show your work. Round to the nearest tenth if needed.
The hypotenuse of the right triangle is 25
Finding the hypotenuse of the right triangleFrom the question, we have the following parameters that can be used in our computation:
The right triangle
The hypotenuse of the right triangle can be calculated using the following Pythagoras theorem
h² = sum of squares of the legs
Using the above as a guide, we have the following:
h² = 15² + 20²
Evaluate
h² = 625
Take the square roots
h = 25
Hence, the hypotenuse of the right triangle is 25
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A side of the triangle below has been extended to form an exterior angle of 76°. Find the value of x.
Set up the appropriate equation to solve for the missing angle.
Answer:
x = 23.6°
Step-by-step explanation:
The given diagram shows a right triangle with an unknown angle, x.
We have been given the measures of the hypotenuse of the triangle and the measure of the side opposite unknown angle. Therefore, we can use the sine trigonometric ratio to find the value of x.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
The unknown angle is x, so θ = x.
The side opposite the angle measures 6 units, so O = 6.
The hypotenuse of the triangle measures 15 units, so H = 15.
Substitute the values into the ratio and solve for x:
[tex]\sin x=\dfrac{6}{15}[/tex]
[tex]x=\sin^{-1}\left(\dfrac{6}{15}\right)[/tex]
[tex]x=23.5781784...[/tex]
[tex]x=23.6^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the value of x is 23.6°.
The appropriate equation to solve for the missing angle is sin(x) = 6/15
Setting up the appropriate equation to solve for the missing angle.From the question, we have the following parameters that can be used in our computation:
The right triangle
From the triangle, we have
Angle x
Also, we have the following sides in relation to x
Opposite = 6
Hypotenuse = 15
This means that we make use of the sine ratio
i.e. sin = opposite/hypotenuse
Using the above as a guide, we have the following:
sin(x) = 6/15
Hence, the equation is sin(x) = 6/15
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Simplify this expression.
a9 × a18 =
Answer:
[tex]a^{27}[/tex]
Step-by-step explanation:
assuming you mean
[tex]a^{9}[/tex] × [tex]a^{18}[/tex]
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
then
[tex]a^{9}[/tex] × [tex]a^{18}[/tex] = [tex]a^{(9+18)}[/tex] = [tex]a^{27}[/tex]
three and one quarter minus one and five eigths
Answer:
1 5/8
Step-by-step explanation:
3 1/4 - 1 5/8 = 3 2/8 - 1 5/8 = (2 + 1 + 2/8) - 1 5/8 = 2 + 8/8 + 2/8 - 1 5/8 =
= 2 10/8 - 1 5/8 = 1 5/8
Round 2445436 to the nearest million. Enter your answer in the box below.
Answer here
SUBMIT
Answer:2,000,000
Step-by-step explanation:
Given the value of 2,445,436, when we look at the hundred thousand place digit, we see that it is 4. Since 4 is less than 5, we will round down, making the rest of the digits zero.
Thus, 2,445,436 rounded off is 2,000,000 (2 million)
The difference of two numbers is 30. If the smaller number is two-third of the larger one, find the numbers
The difference of two numbers is 30. If the smaller number is two-third of the larger one, The smaller number is 60 and the larger number is 90.
Let's assume the smaller number is x and the larger number is y.
Two conditions exist given the information provided:
Between the two numbers, there is a 30 point difference:
y - x = 30
The smaller number is two-thirds of the larger number:
x = (2/3) * y
To find the values of x and y, we can solve this system of equations.
From equation 2, we can express y in terms of x:
y = (3/2) * x
Substituting this value of y in equation 1:
(3/2) * x - x = 30
(3/2 - 1) * x = 30
(1/2) * x = 30
x = (30 * 2) / 1
x = 60
Now, substituting the value of x in equation 2 to find y:
y = (3/2) * 60
y = 90
As a result, 60 is the smaller number while 90 is the larger number.
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Web de
-lane
GRAPHS OF TRIGONOMETRIC FUNCTIONS
6. Consider these two functions:
F(x)-2 cos(x)
G(x)-(2x)
Part I: What are the amplitudes of the two functions? (2 points)
what are the periods of the two functions? (2 points)
Part III: Draw sketches of at least two periods of the two graphs, labeling each of the graphs. You may
have to approximate the critical points of one of the graphs. (8 points)
Answer:
Part I:
The amplitude of the function F(x) is 2, since the coefficient of the cosine function is 2.
The amplitude of the function G(x) is not defined since it does not contain any trigonometric functions.
The period of the function F(x) is 2π since the period of the cosine function is 2π.
The period of the function G(x) is π since the function is a linear function with slope 2.
Part III:
To sketch the graph of F(x), we can start by plotting the maximum and minimum values of the cosine function, which are 2 and -2, respectively. Then, we can shift the graph downward by 2 units to obtain the graph of F(x). The resulting graph should look like a cosine graph with amplitude 2, but shifted downward by 2 units. We can repeat this pattern for one period of the function, which is 2π, to obtain the following sketch:
| /\
2 | / \
| / \
| / \
| / \
| / \
_____|_________________________
| 0 π 2π
To sketch the graph of G(x), we can start by plotting the y-intercept, which is 0. Then, we can use the slope of 2 to plot additional points on the graph. Since the period of G(x) is π, we can plot two periods by plotting points at x=0, π/2, π, 3π/2, and 2π. The resulting graph should look like a straight line with slope 2. Here is a sketch of the graph:
|
|
|
4 | /
| /
| /
|/________________________
| 0 π 2π
Note that the critical point of G(x) is at x=0, where the slope changes from positive to negative.
Si tengo dos papas y un kilo de arroz y me sale 500 pesos.
¿Cuánto valen dos kilos de arroz?
Dos kilos de arroz tiene un precio total de 533.332 pesos.
¿Cómo determinar el precio unitario de dos kilos de arroz?En este problema debemos determinar el precio total de dos kilos de arroz. Inicialmente, nosotros debemos construir el sistema de ecuaciones lineales correspondiente:
2 · x + y = 500
3 · x = 350
Donde:
x - Precio unitario de la papa.y - Precio unitario del arroz.Ahora determinamos los precios unitarios:
x = 350 / 3
x = 116.667
y = 500 - 2 · x
y = 500 - 2 · 116.667
y = 266.666
Finalmente, calculamos el precio total de los dos kilos de arroz:
C = 2 · 266.666
C = 533.332
ObservaciónEl enunciado está incompleto. La forma completa es la siguiente:
Si tengo dos papas y un kilo de arroz y me sale 500 pesos. Y si compro tres papas con 350 pesos. ¿Cuánto valen dos kilos de arroz?
Asimismo, el enunciado y la respuesta están escritos en español.
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What are the coordinates of the center of this hyperbola? (y+3)^2/25-(x-4^2/36=1
Answer:
Step-by-step explanation:
To determine the coordinates of the center of the hyperbola with the equation:
(y + 3)^2/25 - (x - 4)^2/36 = 1
We can compare it to the standard form equation of a hyperbola:
(y - k)^2/a^2 - (x - h)^2/b^2 = 1
In the given equation, we have (y + 3)^2/25 - (x - 4)^2/36 = 1. Comparing this to the standard form, we can identify the center as (h, k), where h = 4 and k = -3.
Therefore, the coordinates of the center of the hyperbola are (4, -3).
Betsy, a recent retiree, requires $6,000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 17% per year or in a certificate of deposit (CD) lying 7% per year. How much money should be invested in each to realize exactly $6,000 in interest per year
Betsy should invest $25,000 in B-rated bonds and $25,000 in the CD to generate exactly $6,000 in interest per year.
To solve the problem, Betsy needs to determine the amount of money she should invest in B-rated bonds and a certificate of deposit (CD) in order to generate exactly $6,000 in interest per year.
Let's assume Betsy invests x dollars in B-rated bonds and y dollars in a CD. The annual interest on B-rated bonds is 17% and the interest on the CD is 7%.
We can set up a system of equations:
Equation 1: 0.17x + 0.07y = 6,000 (represents the total interest earned per year)
Equation 2: x + y = 50,000 (represents the total amount invested)
To solve the system, we can use the method of substitution. Rearrange Equation 2 to solve for x: x = 50,000 - y.
Substitute the value of x in Equation 1:
0.17(50,000 - y) + 0.07y = 6,000
Simplifying the equation gives: 8,500 - 0.17y + 0.07y = 6,000
Combining like terms: -0.10y = -2,500
Solving for y: y = 25,000
Substituting the value of y back into Equation 2: x + 25,000 = 50,000
Solving for x: x = 25,000
Therefore, Betsy should invest $25,000 in B-rated bonds and $25,000 in the CD to generate exactly $6,000 in interest per year.
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How many minutes would you have to walk in November so that your mean for the 11 months would be 2 percentage points more than your mean for the 10 months?
The number of minutes you need to walk in November for the mean of 11 months to be 2 percentage points higher than the mean of 10 months, you would need to walk additional minutes that would make up for the desired increase.
To calculate the number of minutes you would have to walk in November, we need more information about the mean values for the 10 months and the desired mean for the 11 months. Please provide the mean values for both the 10 months and the desired mean increase.
To calculate the number of minutes you would have to walk in November, we need to understand the problem statement more clearly.
Let's say you have walked a certain number of minutes for 10 months, and you want to find out how many additional minutes you need to walk in November to increase the mean (average) for the 11 months by 2 percentage points compared to the mean for the 10 months.
Here are the steps to calculate the required number of minutes:
Determine the mean for the 10 months: Add up the total number of minutes you walked in the 10 months and divide it by 10 to calculate the mean.
Calculate the desired mean for the 11 months: Add 2 percentage points (0.02) to the mean for the 10 months to determine the desired mean for the 11 months.
Multiply the desired mean for the 11 months by 11: This will give you the total number of minutes you should have walked in the 11 months to achieve the desired mean.
Subtract the total number of minutes you have already walked in the 10 months from the result obtained in step 3: This will give you the additional number of minutes you need to walk in November.
By following these steps, you can determine the number of minutes you need to walk in November to achieve the desired increase in the mean for the 11 months compared to the mean for the 10 months.
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3 towns have a distance of a= 80km , b=90km and c =100 km and they form a triangle find angles for each of the towns and the area of the whole triangle
The angles of the triangle formed by the towns can be determined using the law of cosines with the given side lengths.
We may apply the rule of cosines to get the angles of the triangle the towns create. Assume that the towns are identified as A, B, and C and that their relative distances are 80 km, 90 km, and 100 km. These sides' opposing angles shall be designated as,, and, respectively.
We may determine the angles by using the law of cosines to calculate: cos() = (2bc)/(b2 + c2 - a2)
cos() is equal to (c2 + a2 - b2) / (2ca).
cos() is equal to (2ab) / (a2 + b2 - c2).
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34.8 divided by 0.02
Answer:
1740
Step-by-step explanation:
34.8/0.02 =
Multiply the numerator and denominator by 100.
= 3480/2
= 3000/2 + 480/2
= 1500 + 240
= 1740
Answer:
1740
Step-by-step explanation:
I just used a calculator which gave me 1740
Use the equation of the line to identify a point the line passes through and the slope of the line. Then, graph the line.
y+3=3/2(x+4)
A point on the line is (0, 3).
Given equation of the line:y + 3 = 3/2 (x + 4)
It can be rewritten in slope-intercept form as: y = 3/2x + 6 - 3
Slope of the line can be determined by comparing with y = mx + b, where m is the slope and b is the y-intercept.
Therefore, comparing given equation with y = mx + b, we get Slope (m) = 3/2
To find a point on the line, we can substitute any arbitrary value of x or y and solve for the other variable.
Let's take x = 0:y + 3 = 3/2 (0 + 4)y + 3 = 6y = 3
Therefore, a point on the line is (0, 3).
Now, to graph the line, we need to plot this point and use the slope to find other points. We know that slope is rise over run, which means for every increase of 2 units in x, there is an increase of 3 units in y.
So, we can use this to find other points as follows:Starting from (0, 3), move 2 units to the right and 3 units up to get another point, say (2, 6).Then, move 2 units to the left and 3 units down to get another point, say (-2, 0).
Join all the points on the graph to get the line.
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In the diagram below, which distance represents the distance from point Qto RS?
The distance that represents the distance from point Q to RS is: QT.
How to find the line distance?The distance between a point and a line, is usually defined as the shortest distance that exists between a fixed point and any point on the line. It is the length of the line segment that is perpendicular to the line and passes through the point.
In the given figure attached, we can see that among the lines drawn from point Q to line RS ,the line QT is perpendicular to RS and as such, it means that is represents the distance between the point and the line.
Therefore, we conclude that the distance that represents the distance from point Q to RS is: QT.
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Enter the number that belongs in the green box 9 103 6
9
This seems to be an isosceles triangle, which means that 2 sides are equal. In this case, that would be 9.
I NEED HELP FAST!!!!!!!
Answer: answer is C
Step-by-step explanation: If you take the value of greeting cards and divide by the amount of greeting cards you will get the rate per greeting card.
A pharmaceutical company is experimenting with an alternative drug to aid in
depression symptoms. An initial 729 mg of the drug is administered on the first
treatment and uses 1/3 of the previous dosage for each subsequent treatment. How
much of the drug is needed to administer 5 treatments?
As per the pharmaceutical company is experimenting with an alternative drug to aid in depression symptoms total amount of the drug used in all 5 treatments is 1089mg.
The pharmaceutical company wants to experiment with an alternative drug to help relieve symptoms of depression.
On the first treatment, 729mg of the drug is administered.
The company uses 1/3 of the previous dosage for each subsequent treatment.
The amount of the drug needed to administer 5 treatments is 123.375 mg.
The solution to the problem:
The given details in the problem can be tabulated as shown below:
To determine the amount of drug needed to administer 5 treatments, the information that each subsequent treatment consumes 1/3 of the previous dose can be used.
Let's calculate the dosage for each treatment:
Treatment 1: 729 mg (starting dose)
Treatment 2: 1/3 * 729 mg = 243 mg
Treatment 3: 1/3 * 243 mg = 81 mg
Treatment 4: 1/3 * 81 mg = 27 mg
Treatment 5: 1/3 * 27 mg = 9 m
Therefore, to perform 5 treatments a total of 729 mg + 243 mg + 81 mg + 27. mg + 9 mg = 1089 mg of drug required.
The amount of the drug required for the 5th treatment is 123.375mg.
The total amount of the drug used in all 5 treatments is729 + 243 + 81 + 27 + 9 = 1089mg
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What is the measure of the unknown angle?
A full circle divided into a three hundred twenty four degree angle and an unknown angle.
36°
37°
40°
42°
Answer:
36°
Step-by-step explanation:
A full circle is 360° so you subtract 324° from 360° which gets you 36°
Which inequality in standard form represents the shaded region ?
Ximena pays a flat cost of $44.50 per month and $4 per gigabyte. She wants to keep her bill at $50.10 per month. How many gigabytes of data can she use while staying within her budget?
Answer:
Ximena can use 1 gigabytes of data
Step-by-step explanation:
The first thing you want to do is subtract
51.10 - 44.50 = 5.6
5.6 is the amount of money she will have to spend on data
With each gigabyte costing 4 dollars and only 5 dollars to spend
she can only use one gigabyte
Jack's father has recorded the amount of time his son has played video games for the last 7 days. The corresponding scatterplot is shown below. Using the best-fit line, which of the following predictions is TRUE? a.) Jack devoted 38 minutes to playing video games after 1 day. b.) Jack devoted 50 minutes to playing video games after 6 days. c.) Jack devoted 64 minutes to playing video games after 8 days. d.) Jack devoted 41 minutes to playing video games after 2 days.
Based on the best-fit line, the prediction that is TRUE is option d.) Jack devoted 41 minutes to playing video games after 2 days.
1. Look at the scatterplot and identify the best-fit line, which represents the trend or pattern in the data points.
2. Locate the point on the x-axis corresponding to 2 days.
3. Follow the vertical line from that point until it intersects with the best-fit line.
4. From that intersection, move horizontally to the y-axis to find the predicted value for the amount of time Jack devoted to playing video games after 2 days.
5. Based on the best-fit line, the predicted value is approximately 41 minutes.
6. Compare the predicted value with the given options.
7. Among the options, option d.) states that Jack devoted 41 minutes to playing video games after 2 days, which matches the prediction from the best-fit line.
8. Therefore, the TRUE prediction is option d.) Jack devoted 41 minutes to playing video games after 2 days.
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Answer:
Step-by-step explanation:
The line of best fit can be used to get predictions. So if we look at a particular day, we can get a predicted time based on the corresponding value on the best-fit line. If we look at Day 8, then the predicted time looks to be about 64 minutes.
If a/25 = 5b, what is the value of b when a=1
Solve the complex number X ⁴ + 2²x + 2 =0
The solutions to the equation x⁴ + 2x² + 2 = 0 are
x = ±√(-1 ± i).How to solve the equationTo solve the equation x⁴ + 2x² + 2 = 0, we can use a substitution to simplify the equation. Let's substitute y = x²:
Now, the equation becomes y² + 2y + 2 = 0.
We can solve this quadratic equation for y using the quadratic formula:
y = (-b ± √(b² - 4ac)) / (2a)
In this case, a = 1, b = 2, and c = 2. Plugging these values into the quadratic formula, we get:
y = (-2 ± √(2² - 4 * 1 * 2)) / (2 * 1)
= (-2 ± √(4 - 8)) / 2
= (-2 ± √(-4)) / 2
Since we have a square root of a negative number, the equation has complex solutions. Simplifying further:
y = (-2 ± 2i) / 2
= -1 ± i
Now, we substitute y back into the equation y = x²:
x² = -1 ± i
To solve for x, we take the square root of both sides:
x = ±√(-1 ± i)
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Mr. and Mrs. Doran have a genetic history such that the probability that a child being
born to them with a certain trait is 5/6. If they have three children, what is the
probability that exactly zero of their three children will have that trait? Round your
answer to the nearest thousandth.
Using the binomial distribution, it is found that there is a 0.056 = 5.6% probability that exactly one of their three children will have that trait.
For each children, there are only two possible outcomes, either they have the trait, or they do not. The probability of a children having the trait is independent of any other children, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X=\text{x})=C_{n,\text{x}}\times p^{\text{x}}\times(1-p)^{\text{n}-\text{x}}[/tex]
[tex]C_{n,\text{x}}=\dfrac{n!}{\text{x}!(n-\text{x})!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
5/6 probability of a children having the trait, hence [tex]p=0.83[/tex].They have three children, hence [tex]n=3[/tex]The probability is P(X = 1), hence:
[tex]P(X=\text{x})=C_{n,\text{x}}\times p^{\text{x}}\times(1-p)^{\text{n}-\text{x}}[/tex]
[tex]P(X=1)=C_{3,1}\times(0.83)^1\times(0.15)^2=0.056[/tex]
0.056 = 5.6% probability that exactly one of their three children will have that trait.
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What is the average rate of change for this quadratic
function for the interval from x=2 to x = 4?
A. 12
B. -6
C. -12
D. 6
-10-
Click here for long description
SUBMIT
The average rate of change of the function over the interval is -6
Finding the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
The graph
The interval is given as
From x = 2 to x = 4
The function is a quadratic function
This means that it does not have a constant average rate of change
So, we have
f(2) = -3
f(4) = -15
Next, we have
Rate = (-15 + 3)/(4 - 2)
Evaluate
Rate = -6
Hence, the rate is -6
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Absolute vale of x+2 if x is less than 2
Answer: The expression for the absolute value of x+2 when x is less than 2 is -(x+2).
Step-by-step explanation: When x is less than 2, x+2 is a negative number. The absolute value of a negative number is its opposite with the negative sign, so the absolute value of x+2 is -(x+2). Therefore, when x is less than 2, the expression for the absolute value of x+2 is -(x+2).
