Answer:
See explanation
Step-by-step explanation:
You are given the equality
[tex](x^2+y^2)^2=(x^2-y^2)^2+(2xy)^2[/tex]
where x, y are two positive integers with x>y.
1. x=2,y=1, then
[tex]c=x^2+y^2=2^2+1^2=5\\ \\a=x^2-y^2=2^2-1^2=3\\ \\b=2xy=2\cdot 2\cdot 1=4[/tex]
First Pythagorean triple is (3,4,5)
2. x=3,y=1, then
[tex]c=x^2+y^2=3^2+1^2=10\\ \\a=x^2-y^2=3^2-1^2=8\\ \\b=2xy=2\cdot 3\cdot 1=6[/tex]
Second Pythagorean triple is (6,8,10)
3. x=3,y=2, then
[tex]c=x^2+y^2=3^2+2^2=13\\ \\a=x^2-y^2=3^2-2^2=5\\ \\b=2xy=2\cdot 3\cdot 2=12[/tex]
Third Pythagorean triple is (5,12,13)
4. x=4,y=1, then
[tex]c=x^2+y^2=4^2+1^2=17\\ \\a=x^2-y^2=4^2-1^2=15\\ \\b=2xy=2\cdot 4\cdot 1=8[/tex]
Fourth Pythagorean triple is (8,15,17)
5. x=4,y=2, then
[tex]c=x^2+y^2=4^2+2^2=20\\ \\a=x^2-y^2=4^2-2^2=12\\ \\b=2xy=2\cdot 4\cdot 2=16[/tex]
Fifth Pythagorean triple is (12,16,20)
6. x=4,y=3, then
[tex]c=x^2+y^2=4^2+3^2=25\\ \\a=x^2-y^2=4^2-3^2=7\\ \\b=2xy=2\cdot 4\cdot 3=24[/tex]
Sixth Pythagorean triple is (7,24,25)
7. x=5,y=1, then
[tex]c=x^2+y^2=5^2+1^2=26\\ \\a=x^2-y^2=5^2-1^2=24\\ \\b=2xy=2\cdot 5\cdot 1=10[/tex]
Seventh Pythagorean triple is (10,24,26)
8. x=5,y=2, then
[tex]c=x^2+y^2=5^2+2^2=29\\ \\a=x^2-y^2=5^2-2^2=21\\ \\b=2xy=2\cdot 5\cdot 2=20[/tex]
8th Pythagorean triple is (20,21,29)
9. x=5,y=3, then
[tex]c=x^2+y^2=5^2+3^2=34\\ \\a=x^2-y^2=5^2-3^2=16\\ \\b=2xy=2\cdot 5\cdot 3=30[/tex]
9th Pythagorean triple is (16,30,34)
10. x=5,y=4, then
[tex]c=x^2+y^2=5^2+4^2=41\\ \\a=x^2-y^2=5^2-4^2=9\\ \\b=2xy=2\cdot 5\cdot 4=40[/tex]
10th Pythagorean triple is (9,40,41)
If -2x²+5-8 is multiplied by 4x-9, what is the coefficient of x in the resulting polynomial?
A) -77
B) -45
C) -32
D) -13
Answer:
-77 assuming you meant to write -2x^2+5x-8 instead of -2x^2+5-8
Step-by-step explanation:
You could multiply it out and see...
(-2x^2+5x-8)(4x-9)
(-2x^2)(4x-9)+(5x)(4x-9)+(-8)(4x-9)
-8x^3+18x^2+20x^2-45x-32x+72
-8x^3+38x^2-77x+72
Coefficient of x^3 is -8
Coefficient of x^2 is 38
Coefficient of x is -77
Constant term is 72
NEED HELP WITH A MATH QUESTION WITH FINDING A SURFACE AREA OF A SQAURE PYRAMID
ANSWER
[tex]S.A = 125 {in}^{2} [/tex]
EXPLANATION
The total surface area of a square pyramid is the area of the 4 triangular faces plus the area of the square base.
This is given by the formula!
[tex]S.A = 4 \times \frac{1}{2} bh + {l}^{2} [/tex]
From the diagram, the base is 5 inches and the height is 10 inches.
We substitute the values to get:
[tex]S.A = 4 \times \frac{1}{2} \times 5 \times 10 + {5}^{2} [/tex]
This simplifies to;
[tex]S.A = 100 + 25[/tex]
[tex]S.A = 125 {in}^{2} [/tex]
The number of fish in a lake can be modeled by the exponential regression equation y = 14.08 • 2.08x, where x represents the year. Which is the best prediction for the number of fish in year 5? Round your answer to the nearest whole number. A. 39 B. 548 C. 1464 D. 146
Answer: B. 548
Step-by-step explanation:
You know that the exponential regression equation [tex]y = 14.08* 2.08^x[/tex] models the number of fish in a lake.
You know that the variable "x" represents the year. Therefore, ir order to predict the number of fish in year 5, you need to substitute [tex]x=5[/tex] into the given exponential regression equation.
Then, you get:
[tex]y = 14.08* 2.08^x\\\\y = 14.08* 2.08^5\\\\y=548.17[/tex]
Rounded to the nearest whole number:
[tex]y=548[/tex]
Answer:
The correct answer option is C. 548.
Step-by-step explanation:
We are given that the number of fish in a lake can be modeled by the following exponential regression equation:
[tex] y = 1 4 . 0 8 \times 2 . 0 8 ^ x [/tex]
where [tex]x[/tex] represents the number of year.
We are to determine whether which of the given answer options best predict the number of fish in year 5.
[tex] y = 1 4 . 0 8 \times 2.08^5[/tex]
[tex]y = 548.17[/tex] ≈ 548
A group of friends go to the movies. The function h(x) represents the amount of money spent where x is the number of friends at the movies. Does a possible solution of (6.5,$95.25) make sense for this function?
Answer:
not really
Step-by-step explanation:
The number of friends (x) is expected to be an integer. 6.5 friends does not really make sense.
_____
There are all kinds of ways this might make sense, but none of them are supported by the information given in the problem statement.
No, the solution (6.5,$ 95.25) do not make a sense.
Since, the number of people going for a movie can't be in decimals.
Step-by-step explanation:The function h(x) represents the amount of money spent where x is the number of friends at the movies.
The domain of such a function has to be whole numbers.
Because the number of people that go for a movie must exist as a whole they can't exist in decimals.
( i.e. either no one will go.
1 will go.
2 friends will go and so on)
i.e. the domain is the set of all non-negative integers.
Why is MAE ≅ TON
HL
HA
LL
Answer:
HL
Step-by-step explanation:
HL (Hypotension-Leg) postulate of congruence : In two right triangles if the hypotenuses are equal and any two corresponding legs are equal in both triangles then the triangles are congruent.
In the given right triangles MAE and TON,
AM = OT,
EM = NT,
Thus, by the HL postulate,
Δ MAE ≅ Δ TON
First option is correct.
Read the passage and examine the text in bold. Then, answer the question.
I always loved my grandfather's explanations of our seasons, "This is the country of three seasons. From June on to November it lies hot, still, and unbearable, sick with violent and unrelenting storms; then on until April, it is chill, quiet, and drinks its scant rain and scanter snows. From April to the hot season again, it is blossoming, radiant, and a seductress." His months were only approximate, later or earlier the rain-laden wind may drift up the water gate of the Colorado River from the Gulf and bring to us our heat, chill, or radiance. In the desert, we see the land sets its seasons by the rain.
Does the bolded portion contain an error? Choose the correction if one is needed.
a) seasons; "This is the
b) seasons: "This is the
c) seasons; however, "This is the
d) No correction needed
Answer:
The correct option is:
a) seasons; "This is the
A semicolon is most commonly used to link (in a single sentence) two independent clauses that are closely related in thought.When a semicolon is used to join two or more ideas (parts) in a sentence, those ideas are then given equal position or rank.
Step-by-step explanation:
Answer:
A. seasons: "This is the
Step-by-step explanation:
Skylar and Wyatt both play soccer. Wyatt scored 2 times as many goals as Skylar. Together they scored 15 goals. Could Skyler have scored 3 goals? Why or why not?
Answer:
No, he did not score 3,
Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.
Step-by-step explanation:
Let x be the score of Skylar,
Since, Wyatt scored 2 times as many goals as Skylar.
So, Wyatt's score = 2x
Thus, total scores = x + 2x = 3x
According to the question,
3x = 15
x = 5
Hence, Skyler have scored 5 goals.
Because, 2 times of 5 is 10 and the sum of 10 and 5 is 15.
Final answer:
Skylar could have scored 3 goals because, based on the information provided, they scored 5 goals after solving the equation that evaluates the total goals scored by both Skylar and Wyatt.
Explanation:
To determine if Skylar could have scored 3 goals, given that Wyatt scored 2 times as many goals as Skylar and together they scored 15 goals, we can set up a simple algebraic equation. Let's denote the number of goals Skylar scored as S, which means that Wyatt scored 2S goals.
The total number of goals is the sum of the goals scored by both Skylar and Wyatt, which is S + 2S = 15. This simplifies to 3S = 15. By dividing both sides of the equation by 3, we get S = 5.
Therefore, Skylar could have scored 3 goals because the calculations show that Skylar scored 5 goals.
Anna wants to rent movies from either Service A or Service B. Service A charges $37.92 as a subscription fee with a charge of $2.18 per movie.Service B charges $33.25 as a subscription fee plus $3.55 per movie. Service B is running a special offer where the first movie is free. Given that Anna always rents at least 1 movie in a given subscription period, how many movies would she have to rent for the average cost per movie to be equal at Service A or Service B?
Answer:
6 movies
Step-by-step explanation:
:Service A
1. $37.92 +&2.18=$40.1
2. $41.1+$2.18=$42.28
3....
4....
5....
6. $48.82+$2.18=$51
Service B
1. $33.25+free movie=$33.25
2. $33.25+$3.55=$36.8
3....
4....
5....
6. $47.45+$3.55=$51
Simply put, an equation shows A. a method for finding the value x. B. that one thing is equal to another. C. the value of an unknown quantity. D. a rule for finding an unknown quantity.
Answer:
B. that one thing is equal to another.
Step-by-step explanation:
An equation has a "left side", an "equal sign", and a "right side." It shows the left side is equal to the right side (one thing is equal to another).
___
An equation may or may not involve variables and unknown quantities.
Which products result in a difference of squares? Check all that apply.
(x – y)(y – x)
(6 – y)(6 – y)
(3 + xz)(–3 + xz)
(y2 – xy)(y2 + xy)
(25x – 7y)(–7y + 25x)
(64y2 + x2)(–x2 + 64y2)
Answer:
(x-y)(y-x)
Step-by-step explanation:
because x-y=y-x
what is the equation of the line that is perpendicular to -x+y=7 and passes through (-1,-1)
Answer:
x + y = -2
Step-by-step explanation:
When you are given the equation of a line in standard form (or close to it, as here), you can make the equation for a perpendicular line through a given point by ...
swap the coefficients of the variables and negate one of themsubstitute the variable values at the given point to find the new constantHere, if we make the left side of the equation be ...
x + y =
we have done the first part of the above recipe. For the second part, we put the point values in for the variables:
x + y = (-1) + (-1) = -2
The equation of the perpendicular line is ...
x + y = -2
3x = 729
Solve for x
plz help. it's urgent. Will mark brainly
Answer: x=243
Step-by-step explanation:
I really need some help please!
cos(a - B) + cos(a + B) = _____
A. 0
B. 2cosacosB
C. 2sinasinB
D. 2(cosacosB + sinasinB)
The answer is B.
I tried putting 9 for a and 7 for B. cos(9-7)+cos(9+7) = 2cos(9)cos(7)
[tex]\bf \textit{Product to Sum Identities} \\\\ cos(\alpha)cos(\beta)=\cfrac{1}{2}\left[\cfrac{}{}cos(\alpha-\beta)\quad +\quad cos(\alpha+\beta)\right] \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ cos(a)cos(B)=\cfrac{1}{2}\left[\cfrac{}{}cos(a-B)+cos(a-B) \right] \\\\\\ 2cos(a)cos(B)=cos(a-B)+cos(a-B)[/tex]
What is the range of the following function:
y = 2(5^x) - 1
The answer is:
The range of the function is:
Range: y>2
or
Range: (2,∞+)
Why?To calculate the range of the following function (exponential function) we need to perform the following steps:
First: Find the value of "x"
So, finding "x" we have:
[tex]y=2(5^{x}-1)\\\frac{y}{2}=5^{x}-1\\\\\frac{y}{2}-1=5^{x}\\\\Log_{5}(\frac{y}{2}-1)=Log_5(5^{x})\\\\x=Log_{5}(\frac{y}{2}-1)[/tex]
Second: Interpret the restriction of the function:
Since we are working with logarithms, we know that the only restriction that we found is that the logarithmic functions exist only from 0 to the possitive infinite without considering the number 1.
So, we can see that if the variable "x" is a real number, "y" must be greater than 2 because if it's equal to 2 the expression inside the logarithm will tend to 0, and since the logarithm of 0 does not exist in the real numbers, the variable "x" would not be equal to a real number.
Hence, the range of the function is:
Range: y>2
or
Range: (2,∞+)
Note: I have attached a picture (the graph of the function) for better understanding.
Have a nice day!
Avery has a total of $12.50 in her piggy bank at home. Each week she takes out $1.25 to ride the city bus. Write an equation representing the balance, c, in the piggy bank, where w, represents weeks.
Answer:
1.25(w)-12.50=C
Which is one of the transformations applied to the graph of [tex]f(x)=x^2[/tex] to produce the graph of [tex]p(x)=-50+14x-x^2[/tex]?
A. a shift down 1 unit
B. a shift left 7 units
C. a shift right 1 unit
D. a shift up 7 units
Could you explain your answer?
If it's wrong it should be report called "improper answer."
No need to spamming answers! If you spamming and that's going to mark your answer report.
Thank you!
-Charlie
Answer:
A
Step-by-step explanation:
Write each parabola in standard form.
f(x) = x²
f(x) = (x − 0)² + 0
For p(x), complete the square.
p(x) = -50 + 14x − x²
p(x) = -(x² − 14x + 50)
p(x) = -(x² − 14x + 49 + 1)
p(x) = -(x² − 14x + 49) − 1
p(x) = -(x − 7)² − 1
The transformation from f(x) to p(x) includes a reflection about the x-axis, a shift right 7 units, and a shift down 1 unit.
The answer is A.
a country has a population of about 124 million people and an area of about 1.95km^2.
what is the population density of the country?
round to the nearest whole number
64 people/km^2
82 people/km^2
122 people/km^2
242 people/km^2
Answer:
64 people/m^2
Step-by-step explanation:
The population density can be found by diving the number of people by the amount of area
I assume that the answer should be in metre squares or the area should be 1.95 million km^2
124000000/(1.95*1000000)
=63.5897...
=64 people/m^2
Answer:
64M people/km^2
Step-by-step explanation:
To calculate the density of population you just have to divide the population by the area of the country or region that you are calculation, in this case it wouldbe like this:
Density of population= [tex]\frac{124 M}{1.95 km^{2} }[/tex]
D= [tex]\frac{124 M}{1.95 km^{2} }[/tex]= 63,58 M[tex]\frac{M}{km^{2} }[/tex]
So rounded to the neares whoel number would be 64 M people per squared kilometer.
Find the slope of a line given the following points
Answer:
-6/5
Step-by-step explanation:
Slope = (y2 - y1)/(x2 - x1)
Plug in
Slope = (4 + 2)/(-2 - 3)
Slope = -6/5
Answer:
m = -6 / 5
Step-by-step explanation:
If you are given 2 points (x1, y1) and (x2,y2)
the slope is simply
m = (y2-y1) / (x2-x1)
m = (-2 - 4) / [3 - (-2)]
m = -6 / 5
At a snack bar, 3 hamburgers and a small drink cost $8.75. The cost of 2 hamburgers and 2 small drinks is $7.50. What is the cost of 4 hamburgers and 3 small drinks?
Answer:
13.75
Step-by-step explanation:
3b + d = 8.75
2b + 2d = 7.50
(3b + d = 8.75) times 2
(2b + 2d = 7.50) times -3
6b + 2d = 17.5
-6b + (-6d) = -22.5
the b's cancel out, 2d - 6d = -4d and 17.5 - 22.5 = -5
-4d = -5 Divide it and d = 1.25
then plug in 1.25 for d.
2b + 2(1.25) = 7.50
2b + 2.5 = 7.50
2b = 5
b= 2.5
3(2.5) + 1.25 = 8.75 ? Yes.
2(2.5) + 2(1.25) = 7.50 ? Yes.
4(2.5) + 3(1.25) = 13.75.
what is the measure of xyz
Answer:
The correct answer is option B. 65
Step-by-step explanation:
To find the measure of <VYX
Central angle of arc VW = 44°
Therefore m<VXY = 44/2 = 22°
And central angle of arc XZ = 86° therefore <XVY = 86/2 = 43
To find the mesure of <XYZ
m<XYZ = m<VXY + m<XVY
= 22 + 43
= 65°
Therefore the correct answer is option B. 65°
Find the area of the trapezoid .
Answer:
303.66 in²
Step-by-step explanation:
The area (A) of a trapezoid is
A = [tex]\frac{1}{2}[/tex] h (a + b)
where h is the perpendicular height and a, b the parallel bases
here h = 12.6, a = 19 and b = 29.2, so
A = 0.5 × 12.6 × (19 + 29.2)
= 0.5 × 12.6 × 48.2 = 303.66 in²
Answer: THIRD OPTION.
Step-by-step explanation:
The area of a trapezoid can be calculated with this formula:
[tex]A=\frac{h}{2}(B+b)[/tex]
Where "h" is the height, "B" is the long base and "b" is the short base.
You can identify that:
[tex]h=12.6in\\B=29.2in\\b=19in[/tex]
Therefore, you need to substitute these values into the formula [tex]A=\frac{h}{2}(B+b)[/tex] to calculate the area of that trapezoid. This is:
[tex]A=\frac{12.6in}{2}(29.2in+19in)\\\\A=303.66in^2[/tex]
This matches with the third option.
If the system of the linear equations above has infinitely many solutions, and c is a constant, what is the value of c?
A) - 6
B) - 3
C) - 2
D) - 1
1. For the system of linear equations to have an infinite number of solutions, the two lines must cross over an infinite number of times, ie. they would be the same line.
Now, if they are the same line and we were to write out both equations in the form y = mx + c, this would mean that the m value (the gradient) and the c value (the y-intercept) would be the same. Thus, the first step is to write out both equations in the form y = mx + c.
a) Equation 1:
3x - 9y = -6
3x = -6 + 9y (Add 9y to both sides)
3x + 6 = 9y (Add 6 to both sides)
(1/3)x + 2/3 = y (Divide both sides by 9)
Thus, the first equation may be written as y = (1/3)x + 2/3
b) Equation 2:
(1/2)x - (3/2)y = c
(1/2)x = c + (3/2)y (Add (3/2)y to both sides)
(1/2)x - c = (3/2)y (Subtract c from both sides)
(1/3)x - (2/3)c = y (Multiply both sides by 2/3)
Thus, the second equation may be written as y = (1/3)x - (2/3)c.
2. Now that we have both equations in the form y = mx + c, we can look at their gradients and y-intercepts:
Equation 1: gradient = 1/3, y-intercept = 2/3
Equation 2: gradient = 1/3, y-intercept = -(2/3)c
As we can see above, the gradients of the two lines are the same, however for them to be the same line their y-intercepts must also be equal. Thus, we must equate the two y-intercepts to find c:
2/3 = -(2/3)c
1 = -c (Multiply both sides by 3/2)
-1 = c (Multiply both sides by -1)
Thus, if the system of linear equations has infinitely many solutions, and c is a constant, the value of c is -1 (answer D).
The value of 'c' for the given system of the linear equations with infinitely many solutions is - 1.
What is a linear equation?"A linear equation is an equation in which the highest power of the variable is always 1."
Given system of linear equations are
1. [tex]3x - 9y=-6[/tex]
⇒ [tex]x - 3y = - 2[/tex]
Therefore, [tex]a_{1} = 1, b_{1} = -3, c_{1} = -2[/tex]
2. [tex]\frac{x}{2}-\frac{3y}{2} =c[/tex]
⇒ [tex]x - 3y = 2c[/tex]
Therefore, [tex]a_{2} = 1, b_{2} = -3, c_{2} = 2c[/tex]
For the system of the linear equations with infinitely many solutions,
[tex]2c = -2[/tex]
⇒ [tex]c = -1[/tex]
Learn more about linear equation here: https://brainly.com/question/2263981
#SPJ2
Anthony deposited $14,000 with a bank in a 5-year certificate of deposit yielding 6% compounded daily. Find the compound amount
A) $18,897.56
B) $32,897.56
C) $17,976.05
D) $16,542.10
Answer:
Total = 14,000 * 1 + (.06 / 365) ^365*5
Total = 14,000 * 1.0.000164383561643836^1,825
Total = 14,000 * 1.3498255274
Total = 18,897.56
Step-by-step explanation:
I could really use help with this!!!!
Answer:
Hi
Step-by-step explanation:
Please make sure you have posted all the information. i will be glad to help however it doesnt seem that all the instructions aare there
Write an equation of a line in point-slope form that has a slope of -2 and passes through (5, -1).
A. y + 1 = -2(x – 5)
B. y – 1 = -2(x – 5)
C. y – 5 = -2(x + 1)
D. y -5 = -2(x – 1)
Answer:
A. y + 1 = -2(x – 5)
Step-by-step explanation:
For a line with slope m through point (h, k), the equation is ...
y -k = m(x -h)
Fill in your values of m=-2, h=5, k=-1 and you have ...
y -(-1) = -2(x -5)
y +1 = -2(x -5) . . . . . . simplify. Matches selection A.
Yoda purchases a light saber for $1,678 with an installment loan that has an APR of 12%. The store financing requires a 15% down payment for 12 monthly payments. What is the finance charge?
Answer:$2,000
Step-by-step explanation:
What is the name of the thick, lower end of the digestive tract where solid waste is gathered and leaves the body?
The lower end of the digestive tract that gathers and expels solid waste from the body is called the rectum. The process involves the colon, where digestion occurs, water is reabsorbed, and waste is turned into feces, which is then eliminated through the anus.
The thick, lower end of the digestive tract where solid waste is gathered and leaves the body is called the rectum. After digested food passes through the small intestine, it enters the large intestine, or colon, where it undergoes further digestion and water reabsorption. The colon is home to a diverse microbiota that aids in digestion. The waste material, now known as feces, is then moved to the rectum. The rectum stores the feces until it triggers neural signals that lead to the urge to eliminate this waste through the anus.
What are the zeros of f(x) = (x − 7)(x − 3)(x − 2)?
For this case we must find the zeros of the following function:
[tex]f (x) = (x-7) (x-3) (x-2)[/tex]
If we equate each term to 0 and we clear the variable "x", we will find the values that make the function equal to zero. So:
[tex]x-7 = 0\\x = 7[/tex][tex]x-3 = 0\\x = 3[/tex][tex]x-2 = 0\\x = 2[/tex]Thus, the zeros of the function are:
7,3,2
Answer:
Option C
The zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2
From the question,
We are to determine the zeros of the given function
The given function is
f(x) = (x - 7)(x - 3)(x - 2)
To determine the zeros of this function, we will set f(x) = 0
That is ,
f(x) = (x - 7)(x - 3)(x - 2) becomes
0 = (x - 7)(x - 3)(x - 2)
∴ (x - 7)(x - 3)(x - 2) = 0
Then,
We can write that
x -7 = 0 OR x - 3 = 0 OR x - 2 = 0
∴ x = 7 OR x = 3 OR x = 2
Hence, the zeros of the function f(x) = (x - 7)(x - 3)(x - 2) are 7, 3, 2. The correct option is the third option 7, 3, 2
Learn more here: https://brainly.com/question/12488960
need help with this question.
Answer:
distributive propertycommutative propertyassociative propertyStep-by-step explanation:
The distributive property lets you multiply each term inside parentheses by a factor outside parentheses. Here, we've gone from 4(x -1) to 4x -4.
The commutative property lets you change the order of elements of a sum or product. Here, we've gone from 3 + ( ) to ( ) + 3.
The associative property lets you move the parentheses from one group of elements of a sum or product to a different group of elements of the same sum or product. Here, we moved the parentheses from the first two terms to the last two terms of the sum.
_____
Comment on these properties in relation to the Order of Operations
The order of operations for evaluating an expression virtually ignores all of these properties, with the possible exception of the distributive property.
For evaluation of numerical expressions, any sum inside parentheses is evaluated to a single number before the multiplication implied by the parentheses is done. Hence the distributive property is not needed. (The distributive property must be used to remove parentheses when literal or mixed expressions are being evaluated.)
Likewise, the associative and commutative properties are ignored, because operations of addition or multiplication are always carried out left-to-right according to the order of operations. In actual practice, the associative and commutative properties can be used to simplify the evaluation of expressions, provided they are used properly and the meaning of the expression is not altered.
Determine whether the function shown in the graph is even or odd.
Answer:
D. The function is odd because it is symmetric with respect to the origin.
Step-by-step explanation:
We have been given a graph of a function. We are asked to determine whether our given function is odd or even.
We know that a function is even, when it is symmetric with respect to the y-axis.
We also know that a function is odd, when it is symmetric with respect to the origin.
Upon looking at our given graph, we can see that it is symmetric about the origin, therefore, option D is the correct choice.
The function is odd because it is symmetric with respect to the origin.
(Option D)
Further explanationWe will determine whether the function is shown in the graph is even or odd.
Let us recall how to distinguish whether the function graph is included in an even or odd function.
Even Functions
A function f is even if, for each x in its domain, [tex]\boxed{ \ f(-x) = f(x) \ }[/tex].The graph of an even function is symmetric with respect to the y-axis. In order to complete the graph for an even function just imagine the y-axis as a mirror and draw the reflection of each point on the other side.Examples: [tex]\boxed{ \ f(x) = x^2 \ } \boxed{ \ f(x) = 2x^4 - 4 \ } \boxed{ \ f(x) = sin \ x \ for \ -360^0 \leq x \leq 360^0 \ }[/tex]Odd Functions
A function f is odd if, for each x in its domain, [tex]\boxed{ \ f(-x) = -f(x) \ }[/tex].The graph of an odd function is symmetric with respect to the origin.In order to complete the graph for an odd function connect each point with the origin and extend that line to the other side of the origin until we have the same distance.Examples: [tex]\boxed{ \ f(x) = x^3 \ } \boxed{ \ f(x) = 2x^3 - 4x \ } \boxed{ \ f(x) = \frac{x^2 + 1}{2x} \ } \boxed{ \ f(x) = tan \ x \ }[/tex]Generally, the functions that we face are neither even nor odd.
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