Answers
By means of relationship between powers and roots and algebra properties we conclude that radical expression ∛y · [2 · y · ∛(8 · y²) - ∛(y⁵) - 4∛(8 · y²)] is equivalent to 2 · y · ∛(8 · y⁵) - ∛(y⁶) - 4 ∛(8 · y³).
How to simplify a polynomial-like radical expression
In this problem we find a polynomial-like radical expression that must be simplified by algebra properties and by taking advantage of relationship between powers and roots. First, write the entire expression:
∛y · [2 · y · ∛(8 · y²) - ∛(y⁵) - 4∛(8 · y²)]
Second, apply distributive property:
2 · y · ∛(8 · y²) · ∛y - ∛(y⁵) · ∛y - 4∛(8 · y²) · ∛y
Third, use relationship between roots and powers:
2 · ∛(y³) · ∛(8 · y²) · ∛y - ∛(y⁵) · ∛y - 4∛(8 · y²) · ∛y
Fourth, apply multiplication of roots and multiplication of powers of equal base:
2 · y · ∛(8 · y⁵) - ∛(y⁶) - 4 ∛(8 · y³)
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Related Questions
Let f(x) = 2x+4 and g(x)=4x^2+4х.
After simplifying,
(f o g) (x)=
If looking at what I wrote is confusing I added a photo to help
Answers
The simplified form of (f o g)(x) = 8x² + 8x + 4.
What is differentiation?Differentiation is a process in calculus that is used to find the rate of change of a function at a specific point. It is the process of finding the derivative of a function.
To find (f o g)(x), we need to first find g(x) and then substitute that expression into f(x).
Given:
f(x) = 2x + 4
g(x) = 4x² + 4x
So:
(f o g)(x) = f(g(x)) = f(4x² + 4x) = 2(4x² + 4x) + 4
Now we can substitute the expression for g(x) into f(x) and simplify:
= 2(4x² + 4x) + 4 = 8x² + 8x + 4
Hence, (f o g)(x) = 8x² + 8x + 4
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h is defined by the rule
h(x)=2x-3
Answers
The complete function table using the defined function rule is as shown below.
How to solve function tables?We are given the function rule as;
h(x) = 2x - 3
From the function table attached, we will need to find the value of the function h(x) at x = -3, -2, 1, 3, 5
Thus;
Plugging in the value of -3 for x in the given function rule gives us the output as;
h(-3) = 2(-3) - 3
h(-3) = -9
Plugging in the value of -2 for x in the given function rule gives us the output as;
h(-2) = 2(-2) - 3
h(-2) = -7
Plugging in the value of 1 for x in the given function rule gives us the output as;
h(1) = 2(1) - 3
h(1) = -1
Plugging in the value of 3 for x in the given function rule gives us the output as;
h(3) = 2(3) - 3
h(3) = 3
Plugging in the value of 5 for x in the given function rule gives us the output as;
h(5) = 2(5) - 3
h(5) = 7
Thus, the complete function table is;
x h(x)
-3 -9
-2 -7
1 -1
3 3
5 7
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The surface area of an open-top box with length
L
, width
W
, and height
H
can be found using the formula:
A
=
2
L
H
+
2
W
H
+
L
W
Find the surface area of an open-top box with length 3 cm, width 5 cm, and height 7 cm.
Answers
The surface area of the open top box is 127 cm².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
Given that,
Surface area of the open-top box = 2LH + 2WH + LW, where L is the length, W is the width and H is the height.
L = 3 cm
W = 5 cm
H = 7 cm
Surface area = (2 × 3 × 7) + (2 × 5 × 7) + (3 × 5)
= 42 + 70 + 15
= 127 cm²
Hence the surface area of the given open top box is 127 cm².
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A contractor bought 8.2^2 ft of sheet metal. has used 3.7^2 ft so far and has $90 worth of sheet metal remaining. The equation 8.2x - 3.7x = 90 represents how much sheet metal is remaining and the cost of the remaining amount. How much does sheet metal cost per square foot?
Answers
Answer:
$20 per square foot
Step-by-step explanation:
[tex]8.2x-3.7x=90 \\ \\ 4.5x=90 \\ \\ x=20[/tex]
$20 per square foot?
0.056 divided by 4,939.0977
Answers
Answer: 0.00001134
I used a calculator then some mental math lol
10. Which of the following must be true?
Answers
Note that in the above mathematical scenario involving two similar triangles, the option that MUST be correct is AC < FH (Option C) This solution is arrived at using the Open Mouth Theorem.
What does the Open Mouth Theorem state?The above-stated Theorem in Geometry asserts that if two sides of two triangles are congruent and the included angle differs, then the greater angle is opposite the longer side.
This theorem is known as the Open Mouth Theorem because it is based on the idea that the two sides of a triangle are "pivoted" at their common vertex.
Please keep in mind that this theorem only works if we know two pairs of sides are congruent like this.
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A company sells snow globes made out of glass that are in the shape of hollow
spheres. Nolan measures the outer diameter of a snow globe to be 30 cm. If
the glass has a thickness of 0.5 cm, find the total volume of glass that makes
up the globe. Round your answer to the nearest hundredth if necessary.
(Note: diagram is not drawn to scale.)
Answers
The total volume of glass that makes up the globe to the nearest hundredth is equal to 12,771.71 cubic centimeters.
How to calculate the volume of a sphere?Mathematically, the volume of a sphere can be calculated by using this mathematical expression:
Volume = 4/3 × πr³
Where:
r represents the radius.
Based on the information provided about the globe, the diameter of the hollow sphere is given by;
Diameter of sphere = 30 cm
Radius = diameter/2 = 30/2 = 15 cm.
Actual radius = 15 cm - 0.5 cm = 14.5 cm.
Substituting the given points into the volume of a sphere formula, we have the following;
Volume of sphere = 4/3 × 3.142 × 14.5³
Volume of sphere = 12,771.71 cubic centimeters.
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Provide proof for following situation.
look above please to the attachment.
Answers
The proof for the side AB congruent to side ED is given below.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
Given that
C is the intersecting point of AD and EB.
Side AC is congruent to side EC.
Also ∠A = ∠E
By vertical angles theorem, a pair of intersecting lines form 2 pairs of vertically opposite angles which are equal.
Therefore, ∠ACB = ∠ECD
Also given that sides AC and EC are congruent.
By ASA congruence theorem, if two angles and an included side of a triangle is equal to the corresponding two angles and included side of another triangle, then the triangles are congruent.
So triangles ABC and CDE are congruent.
C is the common point for both the triangles.
So the side opposite to C are AB and ED.
So they are equal and thus congruent.
Hence the sides AB and ED are proved to be congruent.
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MARKING BRAINLIEST!!!!! The Sea Dragon, a pendulum ride at an amusement park, moves from its central position at rest according to the trigonometric function below, where t represents time, in seconds. F(t) = 20cos (2pi/5)t, how many seconds does it take the pendulum to complete one full cycle?
Answers
According to the trigonometric function, F(t) = 20 cos (2π/5)t where t represents time, in seconds. representing the pendulum ride of the sea dragon. It will take the pendulum 5 seconds to complete one full cycle.
What is a period in math?A period on a graph function is the distance between two repeating points.
The graph repeats itself as it advances along the x-axis, as you can see.
Periods are the cycles of this predictable repetition. Every 6.28 units, or 2 pi radians, this graph repeats.
The equation is F(t) = 20 cos (2π/5)t
The amplitude of the equation is 20 and the graph makes 2π/5 oscillations at every t seconds
the period to complete an oscillation which is 2π
2π/5 * t = 2π
t = 2π * 5/2π
t = 5 seconds
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Unsure how to do my Algebra homework!
Answers
On solving the exponential function 16000 = P(0.9455)^t, the original value of the car is obtained as $18,930.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The value of car in amount is A(t) = $16,000.
The rate of depreciation is x = 5.45% per year.
Rewriting the rate in exponential form - (1 - 0.0545) = 0.9455
The car is t = 3 years old.
Let P be the model that depicts the original cost of the car.
Then the exponential function will be -
16000 = P(0.9455)^t
Substituting the value of t in the equation -
16000 = P(0.9455)³
16000 = 0.8452P
P = 16000/0.8452486
P = 18,929.34 ≈ 18,930
Therefore, the original value of car was $18,930.
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Which graph matches the inequality y is greater than or equal to negative one third times x plus 1? The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line. The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line. The graph shows a dashed line, which crosses the y-axis at 1 and the x-axis at 3, with shading below the line.
Answers
The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.
What is the slope-intercept form of a line?The slope-intercept form of a line is represented by y=mx+c where m=slope and c is the y-intercept of the line
Given here: The inequality y≥ -x/3 +1
Now, To graph an inequality, treat the <, ≤, >, or ≥ sign as an = sign, and graph the equation. If the inequality is < or >, graph the equation as a dotted line. If the inequality is ≤ or ≥, graph the equation as a solid line.
Therefore y=-x/3 +1 is a line in slope-intercept form with slope=-1/3 and y-intercept 1
Thus the line should intersect the y-axis at y=1 and the x-axis at x=3
∴ The graph of this equation is plotted in attached file.
Hence, The graph shows a solid line, which crosses the y-axis at 1 and the x-axis at 3, with shading above the line.
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Answer:
A
Step-by-step explanation:
i took the test xx
there is a line that includes the point(1,17) and has a slope of 1. What is its equation in slope-intercept form
Answers
An equation of the line in slope-intercept form that passes through the point (1, 17) and has a slope of 1 is equal to y = x + 16.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.Given the following parameters:
Point (x, y) = (1, 17)Slope = 1Substituting the given parameters into the point-slope formula, the equation of the line in is slope-intercept form given by;
y - y₁ = m(x - x₁)
y - 17 = 1(x - 1)
y = x - 1 + 17
y = x + 16
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The 11 students in the Environmental Club represent 5% of the students in the seventh grade. How many students are in the seventh grade?
Answers
Answer: 220
Step-by-step explanation:
Create ratios using fractions, one for the students, and one for the percent
students: [tex]\frac{11}{x}[/tex] percents: [tex]\frac{5}{100}[/tex]
Then cross multiply 1. [tex]11 *100 = 1100[/tex], 2. [tex]1100 / 5 = 220[/tex]
So [tex]x = 220[/tex], this means there are a total of 220 students in 7th grade
An animal shelter has 1008 cats, dogs and rabbits. The ratio of the number of dogs to the number of cats in the animal shelter is 3:7. The ratio of the number rabbits to the number of dogs is 2:5. How many rabbits are in the shelter
Answers
There are 108 rabbits in the shelter.
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
We have to given that;
An animal shelter has 1008 cats, dogs and rabbits.
And, The ratio of the number of dogs to the number of cats in the animal shelter is 3 : 7. The ratio of the number rabbits to the number of dogs is 2 : 5.
Here, The ratio of the number of dogs to the number of cats in the animal shelter is 3:7. The ratio of the number rabbits to the number of dogs is 2:5.
So, We can formulate;
Number of dogs : Number of cats = 3 : 7
Number of rabbits : Number of dogs = 2 : 5
Hence, We get;
Number of rabbits : Number of dogs : Number of cats = 6 : 15 : 35
Since, An animal shelter has 1008 cats, dogs and rabbits.
Hence, We get;
⇒ 6x + 15x + 35x = 1008
⇒ 56x = 1008
⇒ x = 18
Thus, Number of rabbits = 6x
= 6 × 18
= 108
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Which of the following points satisfies y < 3x - 6?
(2, -4)
(1,0)
Answers
The point (2,-4) satisfies y < 3x - 6
Explanation: The coordinates are in the form (x,y) so 2 is the x value, and -4 is the y value. You substitute these values into the equation:
y<3x-6
-4<3(2)-6
-4<6-6
-4<0
Now let’s substitute (1,0) into the inequality:
y<3x-6
0<3(1)-6
0<3-6
0<-3
This is false as 0 is greater than -3, not less than. Hope this helps :)
Solve the following question:
|p+2|=5
Answers
Select the correct answer. What is the equation of a line passing through (-6, 5) and having a slope of 1 3 ? A. y = 1 3 x − 23 3 B. y = 1 3 x − 3 C. y = 1 3 x + 7 D. y = 3x + 7 Reset Next
Answers
Answer:
C
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given m = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
to find c substitute (- 6, 5 ) into the partial equation
5 = [tex]\frac{1}{3}[/tex] (- 6) + c = - 2 + c ( add 2 to both sides )
7 = c
y = [tex]\frac{1}{3}[/tex] x + 7 ← equation of line
Which ordered pairs are solutions to the system of equations (-2,1.6)(0,3 3/5)(2,5 3/5) y=-0.5x+0.6
Y=x+3 3/5
Answers
The ordered pairs are solutions to the system of equations are (-2,1.6)
How to determine which ordered pairs are solutions to the system of equations?In order to determine which ordered pairs are solutions to the system of equations, you need to equate the two equations and solve for x:
y = -0.5x+0.6 and y= x+3 3/5
-0.5x+0.6 = x+3 3/5
-0.5x+0.6 = x+3.6
x+3.6 + 0.5x-0.6 = 0
1.5x + 3 = 0
1.5x = -3
x = -3/1.5
x = -2
y =-0.5x+0.6
y = -0.5(-2) + 0.6
y = 1.6
y = x + 3.6
y = -2 + 3.6
y = 1.6
Thus, the ordered pairs are (-2, 1.6)
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Edgar works in the shipping department of a toy manufacturer. Toy cars weigh 6 pounds apiece and are shipped in a container that weighs 5 pounds when empty. Toy trucks, which weigh 3 pounds apiece, are shipped in a container weighing 20 pounds. When packed with toys and ready for shipment, both kinds of containers have the same number of toys and the same weight. What is the number of toys?
Answers
The number of toys is 5 in each container.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Let x be the number of toys in each container.
Weight of one toy car = 6 pounds
Weight of the container in which toy cars shipped = 5 pounds
Weight of x toy cars = 6x
Total weight of the container when toy cars are placed = 6x + 5
Weight of one toy truck = 3 pounds
Container weight = 20 pounds
Weight of x toy trucks = 3x
Total weight of the container when toy trucks are place = 3x + 20
Given that both containers have same weight.
6x + 5 = 3x + 20
6x - 3x = 20 - 5
3x = 15
x = 5
Hence the number of toys in each container is 5.
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Classify the variables in the data if it’s (qualitative, nominal, ordinal, quantitative, discrete, or continuous etc)
Answers
Answer:
Like
Step-by-step explanation:
1. Nominal
2. Discrete
3. Quantitative
4. discrete
5. discrete
6. Qualitative
write an equation of the line that passes through (4,3) and is parallel to the line y=1/4x+10
Answers
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
[tex]y=\stackrel{\stackrel{m}{\downarrow }}{\cfrac{1}{4}}x+10\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]
so we're really looking for the equation of a line whose slope is 1/4 and that it passes through (4 , 3)
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{4} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{ \cfrac{1}{4}}(x-\stackrel{x_1}{4}) \\\\\\ y-3=\cfrac{1}{4}x-1\implies {\Large \begin{array}{llll} y=\cfrac{1}{4}x+2 \end{array}}[/tex]
A baker makes 60 muffins. He sells 24 of the muffins.
He put the rest of the muffins in boxes. Each box can hold 4 muffins.
Which equation can be used to find b, the number of boxes the baker will need?
OA.
B.
OC.
OD. (60
60+ 24 ÷ 4 = b
60 24 ÷ 4 = b
-
(60+24) ÷ 4 = b
24) = 4 = b
-
Answers
Answer:c
Step-by-step explanation:
c
Answer:b
Step-by-step explanation:
Please help. I'm really confused on how to solve this.
Answers
Explanation
556/650 is the original price over the new one, because it was bumped up from the original. 100/p means 100 percent of the price = 556, p, the new percentage, = 650
Which of the following is an equivalent expression to 7.5+s using commutative property?
Answers
An equivalent expression to 7.5 + s using commutative property is; s + 7.5
How to use the commutative property of algebra?
The commutative property under addition is an algebra property that states that the change in the order of numbers in an addition operation does not change the sum.
This means that for any real numbers x, y, we have;
x + y = y + x
The commutative property under multiplication states that the change in the order of numbers in multiplication operation does not change the product.
This means that for any real numbers c, d we have;
c × d = d × c
We want to find n equivalent expression to 7.5 + s using commutative property. Thus, we will apply the commutative property of addition as followd; 7.5 + s = s + 7.5
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how much did bleep blair receive in royalties last year
Answers
One batch of brownies calls for 1 box of brownie mix and the ingredients shown.
Fudge-like brownie
2 eggs
1/4 cup of water
1/2 cup of oil
Cake-like brownie
3 eggs
1/4 cup of water
1/2 cup of oil
a. What amounts of eggs, water, and oil would you need for 2 batches of fudge-like brownies?
b. What amounts of eggs, water, and oil would you need for 3 batches of cake-like brownies?
Sorry if it's all confusing. If you don't know, then don't answer. Please answer if you know ASAP.
Answers
a) The amounts needed for 2 batches of fudge-like brownies are of:
Eggs: 4.Water: 1/2 cup.Oil: 1 cup.b) The amounts needed for 3 batches of cake-like brownies are of:
Eggs: 9.Water: 0.75 cups.Oil: 1.5 cups.How to obtain the needed amounts?The needed amounts for each case are obtained applying the proportions in the context of this problem.
Hence:
The amounts needed for 2 batches of fudge-like brownies are obtained multiplying the amounts given for 1 box of fudge-like brownie (2 eggs, 1/4 of a cup of water and 1/2 of a cup of oil) by 2.The amounts needed for 3 batches of cake-like brownies are obtained multiplying the amounts given for 1 box of cake-like brownie (3 eggs, 1/4 of a cup of water and 1/2 of a cup of oil) by 3.More can be learned about proportions at https://brainly.com/question/24372153
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The amounts of eggs, water, and oil needed for 2 batches of fudge-like brownies are:
eggs = 4cup of water = 2/4cup of oil = 1The amounts of eggs, water, and oil needed for 3 batches of cake-like brownies are:
eggs = 9cup of water = 3/4cup of oil = 3/2What is the ingredients needed for 2 batches?One batch of Fudge-like brownies:
2 eggs
1/4 cup of water
1/2 cup of oil
One batch of Cake-like brownie
3 eggs
1/4 cup of water
1/2 cup of oil
The amounts of eggs, water, and oil needed for 2 batches of fudge-like brownies can be determined by multiplying each ingredients by 2
eggs = 4
cup of water = 2/4
cup of oil = 1
The amounts of eggs, water, and oil needed for 3 batches of cake-like brownies can be determined by multiplying each ingredients by 3
eggs = 9
cup of water = 3/4
cup of oil = 3/2
Therefore, the ingredients needed for the other batches is determined by multiplying each ingredients by the number of required batches.
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Write an equation of the ellipse with foci (0,+-4) and co-vertices at (±4,0).
Answers
When the ellipse has co-vertices at (4,0) and foci at (0,+-4), the equation is y2/32+x2/16=1.
what is equation ?The algebraic equation y=mx+b is known as a linear equation. M serves as the y-intercept, and B serves as the slope. The previous clause has two variables, y and x, and is sometimes referred to as a "linear equation with two variables". Bivariate linear equations are those with two independent variables. The following are a few examples of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation takes the form y=mx+b, with m denoting the slope and b denoting the y-intercept, it is referred to as being linear. The term "linear" refers to an equation having the form y=mx+b, where m stands for the slope and b for the y-intercept.
given
The center is
=(0,0)
The equation is
y2/a2+x2/b2=1
b=4
c=4
a2=b2+c2
=16+16=32
When the ellipse has co-vertices at (4,0) and foci at (0,+-4), the equation is y2/32+x2/16=1.
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x
A
B
C
Number of Cars
4x D
300
Based on the information in this chart, which statement is true?
200
100
0
li
8-10am 10am-12pm 12-2pm
2-4pm
Time of Day
6-8pm
8-10pm
Around the same number of cars are on the busy street between 10 am -12 pm and 6-8 pm.
Around the same number of cars are on the busy street between 10 am - 12 pm and 2-4 pm.
Around the same number of cars are on the busy street between 10 am - 12 pm and 2 - 6 pm.
Around the same number of cars are on the busy street between 10 am- 12 pm and 12 - 2 pm.
Answers
Answer:
between 10 am - 12 pm and 2-4 pm.
Multiply: (x + 3) (x2 + x – 2)
Answers
Answer:
x3+4x2+x-6
Step-by-step explanation:
do it your selve
Let f(x) and g(x) be polynomials as shown below f(x)=a 0 +a 1 x+a 2 x^ 2 ...+a n x^ n; g(x)=b 0 +b 1 x+b 2 x^ 2 ...+b m x^ m Which of the following is true about f(x) and g(x) ? . f(x) and g(x) are not closed under addition because when added, the result will be a polynomial B. f(x) and g(x) are not closed under addition because when added, the result will not be a polynomial_ f(x) and g(x) are closed under addition because when added, the result will not be a polynomial . D. f(x) and g(x) are closed under addition because when added , the result will be a polynomial
Answers
Considering the closure under property the polynomials f(x) = a 0 + a 1 x + a 2 x^ 2 ... + a n x^ n; and g(x) = b 0 + b 1 x + b 2 x^ 2 ... + b m x^ m
D. f(x) and g(x) are closed under addition because when added , the result will be a polynomialWhat is closure under property?In mathematics, a set is considered closed if we are able to apply and complete an operation on its components while consistently receiving a component from the same set.
A set therefore either possesses closure for a given mathematical operation or it does not.
Use of real numbers is the closure property of addition. Addition of two real numbers results in areal number
In the given problem, the set considered is polynomial addition and the addition of the two polynomial will give a sum which is a polynomial hence we say it is closed under addition.
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