Answer:
$23.5Step-by-step explanation:
Gene is playing a game with a bag of marbles. If 3 of the marbles are blue, 4 are green, and 7 are yellow and awarded prices for the marbles are $2 green $0.5 yellow $4 blue, the expected payout for Gens game is expressed as shown;
If a blue marble costs $4, 3 blue marbles will cost 3*$4 = $12
If a green marble costs $2, 4 green marbles will cost 4*$2 = $8.0
If a yellow marble costs $0.5, 7 yellow marbles will cost 7*$0.5 = $3.5
Total payout for Gene's game will be the equivalent to $12+ $8 + $3.5 = $23.5.
Hence Gene expected cost will be $21.5
collen family plans to paint the window of their house. her father will paint twice as many window as her mother, and collen and her 2 brothers will paint an equal number of the rest of the windows
Answer:
21 windows
Step-by-step explanation:
colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?
Answer: Let the number of window Colleen father would paint be x while that of her mother be y. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father x = 2y
Let the number of windows each painted by Colleen and her 2 brothers be z since they would paint the same number of windows. The total number of windows to be painted = 2y + y + z + z + z = 3y + 3z = 3(y + z).
Then number of windows needed to be painted by Colleen and her mother is given as z + y. Since Colleen painted 7 windows as her share and her mother share i.e. y + z = 7
Therefore the total number of windows = 3(y + z) = 3(7) = 21 windows
Do the ratios 2/3 and 12/18 form a proportion?
yes
no
Answer:
Yes
Step-by-step explanation:
Because 12/18 = 2/3..(cancel 12 and 18 by 6)
Answer:
yes
Step-by-step explanation:
2x6=12
3x6=18
6 is the multiplying number
( the 2 equations are the same amount )
Graph y = tanx for -pi/4 ≤ x ≤ pi/4. What is the range?
Answer:
( -1, 1 )
Step-by-step explanation:
For f ( x ) = tan x ; Range = R (real no.)
Range in interval = ( -1, 1 )
Answer:
Step-by-step explanation:
The graph is below(picture)
● tan Pi/4 = 1
● tan -Pi/4 = -1
So the range is [-1;1]
A recipe needs two and one sixth cups of walnuts and eight and one eighth cups of peanuts. How many cups of nuts are needed for the recipe in all? please answer!!!
Answer:
10 and seven twenty-fourths (10 7/24)
Step-by-step explanation:
2 1/6 + 8 1/8 =
2 4/24 + 8 3/24 =
10 7/24
A ship sails 95 km on a bearing of 140 degrees,than further on 102km on a bearing of 260degrees,and than returns directly to its starting point.Find the length and bearing of the return journey
Answer:
1. 98.7 km
2. 303.5 degree
Step-by-step explanation:
Using the alternate angle, the angle at B will be 50 + 10 = 60 degree.
To calculate the length AC of the returning journey, use cosine formula to calculate it.
To find the bearing of the returning journey, use sine rule to calculate it.
Please find the attached file for the solution
PLEASE HELP ASAP! The quotient of two rational numbers is positive. What can you conclude about the signs of the dividend and the divisor?
Answer:
They either both have to be positive or negative.
Step-by-step explanation:
1 / 1 = 1
-1 / -1 = 1
This gets you positive, when both dividend and divisors are positive or negative.
-1 / 1 = -1
1 / -1 = -1
This gets you negative, when both dividend and divisors are different signs.
Answer:
Step-by-step explanation:
Both dividend and divisor have same sign -
(i) both have positive sign or
(ii) both have negative sign
Eg:
(i) [tex]\frac{10}{2}=5[/tex]
(ii)[tex]\frac{-10}{-2}=5[/tex]
BRAINLIEST, 5 STARS AND THANKS IF ANSWERED CORRECTLY.
How many real solutions does the equation 2p^2 + 9p - 7 = 0 have?
A. 0
B. 1
C. 2
D. 3
Answer:
C
Step-by-step explanation:
Determine the nature of the solutions using the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 then 2 real and distinct solutions
• If b² - 4ac = 0 then 2 real and equal solutions
• If b² - 4ac < 0 then no real solutions\
Given
2p² + 9p - 7
with a = 2, b = 9, c = - 7 , then
b² - 4ac = 9² - (4 × 2 × - 7) = 81 +56 = 137
Since b² - 4ac > 0 then there are 2 real solutions → C
Answer:
C. 2
Step-by-step explanation:
2p² + 9p - 7 = 0
p = {-9±√((9²)-(4*2*-7))} / (2*2)
p = {-9±√(81+56)} / 4
p = {-9±√137} / 4
p = {-9±11.7} / 4
p₁ = {-9-11.7} / 4 = -20.7/4 = -4.55 aprox.
p₂ = {-9+11.7} / 4 = 2.7/4 = 0.67 aprox.
This equation have 2 real solutions:
-4.55 aprox.
0.67 aprox.
A teacher is experimenting with a new computer-based instruction and conducts a study to test its effectiveness. In which situation could the teacher use a hypothesis test for matched pairs?
The teacher gives each student in the class a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a post-test. The teacher wants to see if the difference in scores will show an improvement.
The teacher randomly divides the class into two groups. One of the groups receives computer-based instruction. The other group receives traditional instruction without computers. After instruction, each student takes a test and the teacher wants to compare the performance of the two groups.
The teacher uses a combination of traditional methods and computer-based instruction. She asks students which they liked better. She wants to determine if the majority prefer the computer-based instruction.
Answer:
The teacher gives each student in the class a pretest. Then she teaches a lesson using a computer program. Afterwards, she gives each student a post-test. The teacher wants to see if the difference in scores will show an improvement.
Step-by-step explanation:
In hypothesis testing, there is a premise or a claim where an analyst want to test or to investigate in an experiment. In this study, different sampling methods are being carried out.
In hypothesis testing, we usually have the null hypothesis and the alternative hypothesis.
The null hypothesis is an established hypothesis which is usually denoted by [tex]H_o[/tex] and it is a currently accepted value or default for a parameter.
On the other hand the alternative hypothesis or the research hypothesis denoted by [tex]H_a[/tex] came into place to challenge the study to be tested.
In the given question , the teacher wants to see the difference in the outcome of the test scores if there will be an improvement. The same is true for hypothesis testing, we tends to see the difference in the test statistics result maybe it is significant or not in order to determine the conclusion on the null hypothesis.
f(x) = x^2. What is g(x)?
pls help
Answer:
A. g(x)= 1/3x²
Step-by-step explanation:
The graph of the function g(x) has a point (3,3) on it.
So
g(3) = 3Let's check which of the answer choices is correct:
A. g(x)= 1/3x²g(3) = 1/3*3² = 3g(3) = 3This is correctB. g(x)= (1/3x)²
g(3) = (1/3*3)² = 1g(3) = 1 ≠ 3IncorrectC. g(x) = 1/9*x²
g(3)= 1/9*3²= 1g(3) = 1 ≠ 3IncorrectD. g(x)= 3x²
g(3)= 3*3²= 27g(3) = 27 ≠ 3IncorrectCorrect choice is A. g(x)= 1/3x²
I have no idea how to solve this
Answer:
9
Step-by-step explanation:
Consider the polygon to consist of 2 rectangles, rectangle X (The bigger rectangular) and Y(the smaller rectangle), as shown in the diagram attached below.
To find DE + EF, let's find each lengths as follows:
DE = BC - FA
DE = 9 - 5 = 4
EF = AB - DC
EF = 8 - DC (we don't know DC)
Let's find out DC by considering the area of the entire polygon to derive an equation that will enable us to find DC.
Area of a rectangle = L*B
Therefore:
Area of the polygon = Area of rectangle X + Area of rectangle Y
Area of Polygon = (AB*FA) + (DE*DC)
52 = (8*5) + (4*DC)
52 = 40 + (4*DC)
Subtract 40 from both sides
52 - 40 = 4*DC
12 = 4*DC
Divide both sides by 4 to make DC the subject.
12/4 = DC
3 = DC
DC = 3
Thus,
DE + EF = (BC - FA) + (AB - DC)
= (9 - 5) + (8 - 3)
= 4 + 5
= 9
Find m∠A.
A. 32
B. 26
C. 27
D. 30
============================================
Use law of cosines to find angle A
a^2 = b^2 + c^2 - 2*b*c*cos(A)
9^2 = 6^2 + 14^2 - 2*6*14*cos(A)
81 = 36 + 196 - 168*cos(A)
81 = 232 - 168*cos(A)
81 - 232 = -168*cos(A)
-151 = -168*cos(A)
-168*cos(A) = -151
cos(A) = (-151)/(-168)
cos(A) = 0.8988095
A = arccos(0.8988095)
A = 25.9979801
A = 26 degrees approximately
The angle m∠A will be 27. so option C is correct.
What is a cosine law?Cosine law is a formula relating the length of the sides of a triangle to the cosine of one angle of the triangle.
u² = s² + t² - 2(s)(t)·cos U
Use law of cosines to find angle A
a^2 = b^2 + c^2 - 2*b*c*cos(A)
9^2 = 6^2 + 14^2 - 2*6*14*cos(A)
81 = 36 + 196 - 168*cos(A)
81 = 232 - 168*cos(A)
81 - 232 = -168*cos(A)
-151 = -168*cos(A)
-168*cos(A) = -151
cos(A) = (-151)/(-168)
cos(A) = 0.8988095
A = 25.9979801
A = 26 degrees approximately
Therefore, the angle m∠A will be 27. so option C is correct.
Learn more about sine to cosine conversion here:
https://brainly.com/question/1421592
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Ayuda es para mañana El estudiante 1 y el estudiante 2 están a 53 metros, uno del otro. El estudiante 1, desde su posición, ve una caja fuerte, e inmediatamente mide el ángulo que el mismo forma con el estudiante 2, resultando de 37°. El estudiante 2, al advertirlo , mide enseguida el ángulo que forma la caja fuerte con el estudiante 1, resultando de 43°. ¿cual de los dos se halla más cerca de la caja fuerte?
A. El estudiante 2, ya que está aproximadamente a 32,29 metros.
B. El estudiante 1, ya que está aproximadamente a 32,29 metros.
C. El estudiante 2, ya que está aproximadamente a 37,28 metros.
D. El estudiante 1, ya que está aproximadamente a 37,28 metros.
Answer:
La opción correcta es;
Estudiante 2, ya que está aproximadamente a 32,39 metros de distancia
Step-by-step explanation:
Los parámetros dados son;
La distancia entre los dos estudiantes = 53 metros
El ángulo medido entre la línea del Estudiante 1 a la caja fuerte y el Estudiante 1 y el Estudiante 2 = 37 °
El ángulo medido entre la línea del Estudiante 2 a la caja fuerte y el Estudiante 2 y el Estudiante 1 = 43 °
Dado que los dos estudiantes y la caja fuerte forman los vértices de un triángulo, tenemos;
Sea θ el ángulo del triángulo opuesto a la distancia entre los dos estudiantes
Por lo tanto;
θ + 43 ° + 37 ° = 180 ° (teorema de suma de ángulos)
θ = 180 ° - (43 ° + 37 °) = 100 °
Por regla del seno, tenemos;
a / (sin (A) = b / sin (B)
Por lo tanto;
53 / (sin (100 °)) = b / (sin (37 °)) = c / (sin (43 °))
Lo que da;
b = (sin (37 °)) × 53 / (sin (100 °)) = 32,39 metros
c = (sin (43 grados)) × 53 / (sin (100 grados)) = 36,7 metros
Por lo tanto, el Estudiante 2 está más cerca, ya que está aproximadamente a 32,39 metros de distancia.
We can calculate E, the amount of euros that has the same value as D U.S. dollars, using the equation e=17/20d. How many U.S. dollars have the same value as 1 euro?
Answer: 1.18 dollars
Step-by-step explanation:
Given that:
E = Euros
D = US dollars
If the equation showing the relationship between Euros and Dollar
is E = 17/20D
To find the equivalent amount of dollars for 1 euros, substitute E for 1 in the formula and make D the subject of formula
1 = 17/20 D
Cross multiply
17D = 20
D = 20/17
D = 1.18 dollars approximately
Therefore, 1.18 dollars have the same value as 1 euro.
A set of furniture was sold for GH cedis 3000 at a profit of 25%. Find the cost price.
Answer:
2400GH CedisStep-by-step explanation:
[tex]Selling \:price = 3000gh Cedis\\Profit \% = 25\%\\Cost\:price =?\\\\CP =\frac{ ( Selling\:price \times 100 )}{ ( 100 + percentage profit)} \\\\C.P = \frac{3000\times 100 }{100+25}\\\\ C.P = \frac{300000}{125} \\\\Cost\: Price = 2400gh Cedis[/tex]
Bill is building a staircase for his new home. He has measured several three-foot bars to support the handrail. If Bill nails the support bars to the handrail and to the edge of the staircase (a 2-inch-by-12-inch board attached parallel to the slope of the stairs) at 12-inch intervals, will the handrail be parallel to the staircase?
Answer:
6
Step-by-step explanation:
78
What is the answer!!
Answer:
∠ G = 121°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180
x + 3x + 25 + x - 5 = 180 , that is
5x + 20 = 180 ( subtract 20 from both sides )
5x = 160 ( divide both sides by 5 )
x = 32
Thus
∠ G = 3x + 25 = 3(32) + 25 = 96 + 25 = 121°
Answer:
121
Step-by-step explanation:
x/t+m=b need to make x the subject
Answer:
x=(t+m)/b is the answer
Step-by-step explanation:
Hope it will help :)
Answer:
x = t(b-m)
Step-by-step explanation:
x/t + m =b
subtract m from each side
x/t +m-m = b-m
x/t =b-m
Multiply each side by t
x/t *t = t(b-m)
x = t(b-m)
A limo is rented at a fixed cost for an evening. It is rented by 12 people, the average cost for each person will be $2 less than if it is rented by 10 people. How much does the limo cost for the evening?
Answer:
$120
Step-by-step explanation:
According to the information in the statement and taking into account that the price for renting the limo is fixed, you can say that the cost of renting the limo for 12 people is equal to the cost of renting it for ten. Then, the cost for 12 people is 12 for the cost per person which is equal to 10 for the cost per person and you can express it as follow:
x is the cost per person when the limo is rented by 10 people.
12*(x-2)=10*x
You can solve for x:
12x-24=10x
12x-10x=24
2x=24
x=24/2
x=12
Now that you have the cost per person when the limo is rented by 10 people, you can multiply this value for 10 to find the cost of renting the limo for the evening:
12*10=120
The answer is that the limo cost $120 for the evening.
Apply the distributive property to create an equivalent expression. ( 1 -2g +4h)\cdot 5 =(1−2g+4h)⋅5=left parenthesis, 1, minus, 2, g, plus, 4, h, right parenthesis, dot, 5, equals
Answer:
5 - 10g + 20hStep-by-step explanation:
Given three elements A, B and C related together according to the expression A(B+C), according to distributive property, the element A will be distributed to the rest of the element as shown;
A(B+C) = A(B)+A(C)
A(B+C) = AB + AC (Law of distributivity)
Given the expression according to the question (1−2g+4h)⋅5, in order to use the distributive law to find the equivalent expression, we will use the concept above as shown;
= (1−2g+4h)⋅5
= 5.(1−2g+4h)
= 5(1)-5(2g)+5(4h)
= 5 - 10g + 20h
Hence the equivalent expression using the distributive property is 5 - 10g + 20h
Answer:
5 - 10g + 20h
Compute the value of each expression: −4|−3−3|
Answer:-24
Step-by-step explanation:
Answer:
-24
Step-by-step explanation:
−4|−3−3|
First find the value inside the absolute value
−4|-6|
Absolute value means take the non-negative value
-4 * 6
Multiply
-24
The addition formula for cosine is shown below.
Answer:
Step-by-step explanation:
Sin(A) = 8/10
Cos(A) = 6/10
Sin(B) = 15/17
Cos(B) = 8/17
Cos(A+B) = 6/10 * 15/17 - 8/10 * 8/17
Cos(A +B) = 90/170 - 64/170
Cos(A + B) = 26/170
15 decreased by twice a number
Answer:
Hello! I hope I am correct! (Picture below)
Step-by-step explanation:
Function:
Y=15-2x
The word “decreased” means subtraction & The word “twice” means 2x (2 times)
Therefore, the answer is 15-2x.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Look at picture.
Brainliest would be appreciated!
Hope this helps!
By: BrainlyAnime
Please help me I promise I will mark you brainliest if you are correct!!!!!!!!!!!!!!!!!!!!!!!!!! Use the graph of f to estimate the local maximum and local minimum. A quadratic graph is shown. The graph intercepts the x axis at approximately -2.8 and 1.2. A). No local maximum; local minimum: approx. (1,-7.67) B). Local maximum: (-2,8); local minima: (-3,0) and (3,3) C). Local maximum: approx. (1,8.08); local minima: approx. (-2,-7.67) and (3,2.75) D). Local maximum: ∞ local minima: (-3,0) and (3,3)
Answer:
Local Maximum Approx.: (1,8.08)
Local Minima Approx.: (-2,-7.67) and (3,2.75)
Step-by-step explanation:
Local maximums and minima there the highest and lowest points, respectively, on a graph in a specific region. (This is different from absolute maximum and minimum, which are the highest and lowest points overall.)
These are pretty clear to see on a curve, as they are the "turns" or the points where the curve switches direction from up to down or down to up.
On your graph, we have two local minima and one local maximum. The local minima are at x= -2 and x=3. The local maximum is at x=8. Because of the way the graph is, we have to approximate the y-values of each point.
The answer option which best describes this is the third option, so that is your answer.
HELP SOMEONE PLEASE!!!!! Factor completely 10x2 + 2x − 8. 2
(5x − 1)(x + 4) 2(5x − 4)(x + 1) 2(5x + 2)(x − 2) 2(5x − 2)(x + 2)
Answer:
2(5x - 4)(x + 1)
Step-by-step explanation:
10x^2 + 2x − 8 =
First, factor out the GCF of all terms which is 2.
= 2(5x^2 + x - 4)
5x^2 factors into 5x and x.
= 2(5x )(x )
-4 factors into -4 and 1, -1 and 4, and -2 and 2. Use the set of two factors in the proper positions that will give the middle term.
= 2(5x - 4)(x + 1)
Answer:
[tex]\large \boxed{2(5x-4)(x+1)}[/tex]
Step-by-step explanation:
[tex]10x^2 + 2x - 8[/tex]
Rewrite 2x as 10x - 8x.
[tex]10x^2 + 10x-8x - 8[/tex]
Factor out the two groups.
[tex]10x(x+1)-8(x+1)[/tex]
Take x+1 as a common factor.
[tex](10x-8)(x+1)[/tex]
Factor 10x - 8.
[tex]2(5x-4)(x+1)[/tex]
PLEASE HELP ME I GIVE 5 STARS !
Answer:
It's the 2nd option 2*2*3*3*5
Step-by-step explanation:
Answer:
b.
Step-by-step explanation:
you find a square root that goes into 180. i did 4 times 45. when you break apart 4 you get two times two. when you break apart 45 to get another square root, you get 9 times 5. when you break down 9 you get 3 and 3. so it is 2 times 2 times 3 times 3 times 5
Four students are verifying that x2 + x– 12 = (x – 3)(x + 4). Their conclusions are presented in the table. A 4-column table with 1 row. First column is labeled Damien with entry 3(negative 4) = negative 12, so the factors are correct. Second column is labeled Lauryn with entry negative 4 + 3 = negative 1, so the factors are correct. Third column is labeled Rico with entry negative 4(3) = negative 12 and negative 4 + 3 = negative 1, so the factors are correct. Fourth column is labeled Latisha with entry 4(negative 3) = negative 12 and negative 3 + 4 =1, so the factors are correct. Which student correctly verified that x2 + x – 12 = (x – 3)(x + 4)? Damien Lauryn Rico Latisha
Answer:
Latisha correctly verified that x² + x - 12 = (x - 3)(x + 4)
Step-by-step explanation:
In the problem, each student was to give their explanation of why the statement above is correct. In order to know if this statement is correct, you can also simply multiply the terms after the equal sign.
(x - 3)(x + 4)
Use foil method to multiply.
x² - 3x + 4x - 12
Combine like terms.
x² + x - 12
You can also find out if the statement is correct is multiplying and adding the numbers together.
-3 * 4 = -12
-3 + 4 = 1
So, Latisha is correct because her explanation verified the statement above.
Answer:
Latisha
Step-by-step explanation:
Correct on edg
Solve the system of linear equations by graphing.
9x + 3y = -3
2x - y = -4
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
( -Screen Shot 1 is for (A) and Screen Shot 2 is for (B) - )
A) [tex]9x + 3y = -3[/tex]
= [tex]y = -3x -1[/tex]
Xmin: -10
Xmax: 10
Ymin: -10
Ymax: 10
~~~~~~~~
B) [tex]2x - y = -4[/tex]
= [tex]y = 2x + 4[/tex]
Xmin: -10
Xmax: 10
Ymin: -10
Ymax: 10
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
If this helped you, could you maybe give brainliest..?
Also Have a great day/night!
❀*May*❀
Answer:
y= -3x-1 and y=2x+4
Step-by-step explanation:
1. Rearrange the equations to the proper format which would be y=mx+b.
2. You can do this by adding or subtracting on both sides
- start with the first equation. subtract 9x on both sides.
- than divide 3 on both sides
- next equation subtract 2x on both sides
- divide -1 on both sides
which would get you y=-1-3x and y= 4+2x.
3. reagrange this equation again ( this step isn't always necessary)
you will get y= -3x-1 and y=2x+4
Remember M stand for the slope so your slopes for these two equations would be -3/1 and 2/1. Think about rise over run when you use slope. B is the y-intercept which means it will touch the y-axis.
Hope this helped!
Directions: Using the digits 0 to 9, fill in the boxes so that the chart is accurate. Use each digit only once per blue box and once per red box. Logs are base 10. Please help me out with this would really appreciate it, thanks.
Step-by-step explanation:
log 10 = 1. So if log x < 1, then x < 10. And if log x > 1, then x > 10.
The upper left number is the smallest, and can't be smaller than 1. If the exponent is 0, we can put any number in the red box.
The fractions in the upper right and lower left need to be as large as possible. The denominators will be small, and the numerators will be large.
From there, a little trial and error does the rest. The are many possible answers. I've included one.
Find the value of a.
a = 18°
Step-by-step explanation:we have opposite angles =>
=> 6a + 11 = 2a + 83
6a - 2a = 83 - 11
4a = 72
a = 72 : 4
a = 18°
what does |x| mean? like what do the | | 'bars' symbolize or represent?
Answer: Absolute Value
Step-by-step explanation:
The | | is a symbol for absolute value. This signifies that the number inside would be positive. Now, this doesn't mean it will always be a number inside absolute value bars. It can also be expressions.
Examples:
|1|: Even though the number inside is a positive 1, we know that it cannot be negative under any circumstances. The only exception would be if there was a negative sign on the outside of the absolute value.
|-1|: We see that there is a -1 in the absolute value. This means that it is actually a 1, not -1. The absolute value is what makes everything inside positive.
|1-5|: To solve this, we know that 1-5=-4. Without the absolute value, the answer -4 would be correct. In this case, we have absolute value, so the answer is actually 4.
|x+2|: x+2 can easily be negative. This would happen is x was a negative number that is smaller than -2. x+2 can also be positive, but the absolute value guarantees that the ending result must be positive.
