To simplify the expression (x+5)(x^2-25)(x+5)^2(x-5)^2, we can begin by factoring the expressions:
(x+5) = (x+5)
(x^2-25) = (x-5)(x+5)
(x+5)^2 = (x+5)(x+5)
(x-5)^2 = (x-5)(x-5)
Now, we can substitute these factorized expressions back into the original expression:
(x+5)(x^2-25)(x+5)^2(x-5)^2 = (x+5)(x-5)(x+5)(x-5)(x+5)(x+5)(x-5)(x-5)
Simplifying further, we can combine like terms:
(x+5)(x-5)(x+5)(x-5)(x+5)(x+5)(x-5)(x-5) = (x+5)^3(x-5)^3
Therefore, the simplified expression is (x+5)^3(x-5)^3.
As for the domain of this expression, it includes all real numbers because there are no restrictions or limitations on the values that x can take. Therefore, the domain is (-∞, ∞).
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Malik can spend no more than $24 to buy pecans and cashews. He will pay $6 per pound for pecans and $8 per pound for cashews. Which graph best represents the number of pounds of pecans and the number of pounds of cashews Malik can buy?
Answer:
Graph D
Step-by-step explanation:
We can look at the number of pounds of pecans and cashews, shown on the x- and y-axis, respectively.
All of the graphs have an x-intercept of (4, 0), meaning that the number of pecans being bought is 4 lbs.
Since pecans cost $6 per lb, we can multiply the cost by 4 in order to make sure that the total cost is not exceeding $24.
$6 · 4 lbs = $24
Let's look at the y-axis to see how many lbs of cashews Malik can buy. The y-intercept is (0, 3) for all graphs, meaning that 3 lbs of cashews are being bought.
Since cashews cost $8 per pound, we can multiply the cost by 4 in order to make sure that the total cost is not exceeding $24.
$8 · 3 lbs = $24
The shaded area represents the values that can be used in the problem. Since we want $24 or less, the shaded region has to be below the line.
Malik can spend no more than $24, so the line should be solid since this means that the values the line touches are inclusive. 4 lbs of pecans and 3 lbs of cashews should be inclusive.
The graph that has all of these properties is Graph D.
Can someone help me solve question number 14? I've tried to solve it and got 3426 while the answers in the book say it's 2,6. Can someone pls explain why it's wrong?
Answer:
x = 2, 6
Step-by-step explanation:
differentiate f(x) using the power rule
f'(a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex] and f'( constant) = 0
given
f(x) = x³ - 12x² + 6x - 8
f'(x) = 3x² - 24x + 6
equate f'(x) to - 30
3x² - 24x + 6 = - 30 ( add 30 to both sides )
3x² - 24x + 36 = 0 ( divide through by 3 )
x² - 8x + 12 = 0 ← in standard form
(x - 2)(x - 6) = 0 ← in factored form
equate each factor to zero and solve for x
x - 2 = 0 ⇒ x = 2
x - 6 = 0 ⇒ x = 6
solution is x = 2, 6
let g(x)=xe^-x+be^-x where b is a positive constant
The possible value of positive constant b for an absolute maximum value of function g(x), [tex]g(x) = xe^{-x} + be^{-x} [/tex] at x = [tex] \frac{2}{3} [/tex] is equals to the [tex] \frac{1}{3} [/tex].
An absolute maximum point is a point where the function acquires its largest possible value. To drive the max or min absolute value, we have to substitute the derivative value of function equals to zero. We have a function, [tex]g(x) = xe^{-x} + be^{-x} [/tex], where b is positive constant. We have to determine the possible value of b for absolute maximum of g at x= 2/3.
Differentiating the function g(x) with respect to x
=> [tex]g'(x) = - x e^{-x} + e^{-x} - be^{-x} [/tex]
[tex]= (1 - x - b )e^{-x}[/tex]
[tex]= \frac{1 - x - b }{e^{x}}[/tex]
For obtaining absolute maximum value put, g'(x) = 0
=> [tex]\frac{1 - x - b }{e^{x}} = 0[/tex]
Substitute x = 2/3, in above expression,
[tex] \frac{1 - \frac{2}{3} - b }{e^{\frac{2}{3}}} = 0[/tex]
=> [tex]1 - \frac{2}{3} - b = 0[/tex]
=> [tex] b = \frac{1}{3}[/tex]
Hence, the required value of b is [tex] \frac{1}{3} [/tex].
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Complete question:
Let g(x)=xe^(-x)+be^(-1), where b is a positive constant. For what positive value of b does g have an absolute maximum at x=2/3 .Justify your answer.
Saturday Pizza Orders at Pizza Palace
Pepperoni 24
Beef 36
Sausage 21
Cheese 38
Mushroom 6
What percent
of orders were
for beef?
Round to the
nearest percent.
Answer: 28.8%
Step-by-step explanation:
First, add all the pizzas together. This gives us the total; 125
Next, put 36 over the total. 36/125.
Divide 36/125. Equals .288
When doing percentage, You multiply your decimal by 100, or bounce the decimal twice to the right. This gets you 28.8%
the difference between the roots of the equation 3x^2-5x+q=0 is 1/3. find q
Answer:
q = 2
Step-by-step explanation:
You want to find q such that the difference between the two roots of 3x²-5x+q is 1/3.
Sum of rootsIn quadratic ax²+bx+c, the sum of the roots is (-b/a). For roots p and s, this tells us ...
p + s = -(-5)/3 = 5/3
The problem statement tells us the difference is ...
p - s = 1/3
Adding these two equations gives ...
2p = (5+1)/3 = 2
p = 1 . . . . . . . . . . . . . divide by 2
s = p -1/3 = 2/3 . . . . find the smaller root
Product of rootsThe product of the two roots is (c/a) = (q/3):
ps = (1)(2/3) = q/3
q = 2 . . . . . multiply by 3
The value of q is 2.
#95141404393
find the general solution to the system x ' = ax where a is the given matrix.
The general solution to the system x' = Ax, where A is the given matrix, can be expressed as x(t) = Ce^(At), where C is a constant matrix and e^(At) is the matrix exponential of At. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.
To find the general solution to the system x' = Ax, we can express the solution in terms of the matrix exponential. The matrix exponential of At, denoted as e^(At), is defined as the power series expansion of the exponential function applied to the matrix At. It can be computed using various techniques, such as diagonalization, Jordan decomposition, or power series.
The general solution to the system x' = Ax can then be written as x(t) = Ce^(At), where C is a constant matrix. This solution represents a linear combination of exponential functions, where each component of x(t) is determined by the corresponding component of C and the matrix exponential of At.
The matrix exponential e^(At) has properties that are analogous to those of the scalar exponential function. It satisfies the initial condition e^(A * 0) = I, where I is the identity matrix, and it can be used to find solutions for different initial conditions by appropriately choosing the constant matrix C.
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help help helpppppppppppppppppppppppp
Answer:
B, D, F
Step-by-step explanation:
You want the diagrams that show lines through the center of enlargement, where the smaller triangle is enlarged to form the larger triangle.
EnlargementEach point in an enlarged figure is moved toward or away from the center of enlargement along a line through that center. That is, corresponding vertices of a triangle and its enlargement will lie on a line through the enlargement center.
The diagrams of interest are those that show lines through corresponding vertices of the triangles.
Diagrams B, D, F show lines through the center of enlargement.
__
Additional comment
The center of enlargement is marked in the attachment by a blue dot. Enlargement is by a factor of 3.
Points are moved away if the scale factor is greater than 1; toward the center of enlargement for a scale factor less than 1.
<95141404393>
find y. the number on the leg is 9.
The length of y of the triangle is y = 9√2 units
Given data ,
Let the Triangle be ΔABC , such that
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
On simplifying , we get
From the trigonometric relations , we get
sin θ = opposite / hypotenuse
sin 45° = 9 / y
Multiply by y on both sides , we get
y = 9 / sin 45°
On simplifying , we get
y = 9√2 units
Hence , the length is y = 9√2 units
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Note: Your teacher will review your response to ensure you receive proper credit for your answer.
18. Does the relation in the table represent direct variation, inverse variation, or neither? If it is
direct or inverse variation, write an equation to represent the relation. Explain your answer.
x
5
2
10
1
y
Its not direct variation or inverse
15
|2|3
20
1
2
an equation to represent the relation is,
⇒ y = 10/x
We know that,
Proportion is extensively explained. Proportion is mostly discussed using ratios and fractions. A fraction is written as a/b, while a ratio is represented as a:b, and a proportion states that two ratios are equal. In this case, a and b can be any two integers. The ratio and proportion are important foundations for understanding numerous ideas in mathematics and science.
Since, The relation represents an inverse variation because as the values of x is increasing the values of y is decreasing.
Hence, We can formulate;
y = k/x
Plug y = 5, x = 2;
5 = k/2
Solve for k;
k = 5 x 2
k = 10
Thus, The required equation is y = 10/x
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The complete question is :
does the relation in the table represent direct variation, inverse variation, or neither? if it is direct or inverse variation, write an equation to represent the situation. Explain your answer
x 5, 10, 15, 20
Y 2, 1, 2/3, 1/2
(k + 1 )(k - 5 ) = 0 solve equation for x
Answer:
solve for k or x?
because x isnt on the equation.
i solved for k though
k = -1, 5
Step-by-step explanation:
Solved by simplifying both sides of the equation, then isolating the variable.
Please answer quickly I need it asap ill give brainiest!!!
The correct matching of the items of math in the columns is:
a number that has more factors than just 1 and itself - composite numbersmallest number that all the given denominators divide into evenly - least common denominatordata grouped using non-numerical criteria - categorical datafractions with the same numerical value; fractions that are equal to each other - equivalent fractionsa line segment that goes through the center of the circle to connect two points on the circle - diametera plane figure that is one side of a solid figure - facethe measurement of the space inside a plane figure - areaa shape or object that has been transformed - imagehaving the same exact size and shape - congruentWhat are some terms in math ?A composite number is a number that possesses additional factors besides 1 and its own value. The smallest number that can be divided evenly by all the denominators given is known as the least common denominator.
Non-numeric criteria are used to group data in categorical data. Fractions that have identical numerical values are referred to as equivalent fractions. When a line segment passes through the center of a circle and joins two points on its circumference, it is known as the circle's diameter.
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please helppp question 13
The coordinates of vertices U(1 , -3) , V(4 , -3) , T(1 , -4) , W(4 , -4) becomes
U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4) after the reflection across x-axis occurs.
Solution:
When a point is reflected across the x-axis, the x-coordinate remains unchanged, but the y-coordinate is assumed to be the additive inverse. Point (x, y reflection )'s across the x-axis is (x, -y).
the point (x , y)→ (x , -y).
In the question given 4 coordinates,
U(1 , -3)
V(4 , -3)
T(1 , -4)
W(5 , -4)
the reflection across x-axis
U(1 , -3) →U' (1, 3)
V(4 , -3) → V'(4 , 3)
T(1 , -4) → T'(1 , 4)
W(5 , -4) → W'(5 , 4)
so after the reflection across the x axis the coordinates of the vertices becomes ,
U' (1, 3) , V'(4 , 3) , T'(1 , 4) , W'(5 , 4)
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complete question:
Find the coordinates of the vertices of each figure after the given transformation
3) reflection across the x-axis
Enter Question Text
A U'(1,3),V'(4,3), W'(5,4),T'(1,4)
B U'(3,1),V'(3,4,), W'(4,5),T'(4,1)
D U'(-1,3),V'(-4,3), W'(-5,4),T'(-1,4)
(3)(4-3);W(Sp-4)T(4)
U
T
X
Find the value of x in the figure.
Help me please! 45 points and brainliest will be given if the option is available.
Answer:
I think it should be -2.5,-4.5
Answer: Yes the answer is -2.5 , -4.5
Step-by-step explanation:
This is not only because the X axis is always first, but also because the lines are not perfectly centered. Hope this helps! Give the other person brainliest, they answered first and they have never gotten one.
Problem #2
Andy is supplying his class members with colored paper tomorrow. He has 4 times
as many orange papers as blue papers. There are a total of 37 students in his
class. How many blue papers and orange papers did Andy bring to class?
27
Answer:
what is 478/6 +7*25+78+123-568
if the population of san diego grows by 2.0% per year how long will it take the population to double?
It will take approximately 35 years for the population of San Diego to double if it grows at a rate of 2.0% per year.
To determine how long it will take for the population of San Diego to double, we can use the concept of exponential growth.
When a population grows by a fixed percentage, the formula to calculate the doubling time is given by:
Doubling Time = (log(2) / log(1 + growth rate))
In this case, the growth rate is 2.0% or 0.02 (expressed as a decimal). Plugging this value into the formula, we can calculate the doubling time.
Doubling Time = (log(2) / log(1 + 0.02))
Using a calculator, we can evaluate this expression:
Doubling Time ≈ 35 years
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The great pyramid in giza, Egypt is a square-based. The length of one side of the base is 755 feet, it has a height of 481 feet and a slant height of 610 feet. About how many cubic feet are inside the great pyramid
There are 98,087,770 cubic feet inside the Great Pyramid.
To calculate the approximate volume of the Great Pyramid in Giza, we can use the formula for the volume of a pyramid:
Volume = (1/3) × base area × height
Since the Great Pyramid is square-based, the base area is equal to the length of one side squared. Given that the length of one side of the base is 755 feet, the base area is [tex]755^2[/tex] square feet.
Using the given height of 481 feet, we can substitute these values into the formula:
Volume = (1/3) × [tex]755^2[/tex] × 481
Calculating this expression, we find that the approximate volume of the Great Pyramid is:
Volume ≈ 98,087,770 cubic feet
There are approximately 98,087,770 cubic feet inside the Great Pyramid.
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100 points pls hurry and mark brainly
Each pail of plaster covers 95 square feet of ceiling. How many pails of
plaster would you need to buy to cover the ceiling of a room with walls 15
feet long?
Answer:
2.02
Explanation:
Each pail of plaster covers 97 Square feet of ceiling
The ceiling of the room is 14 ft long
= 14×14
= 196
Therefore the pail of plaster that will be needed to cover the rooms can be calculated as follows
= 196/97
= 2.02
please help me, I don't understand this...
Answer:
Down below
Step-by-step explanation:
2)(-6,3)
where h=-6&k=3
(x-h)²+(y-k)²=R²
(x-(-3)²+(y-6)²=11²
(x+3)²+(y²-6²)=11²
3)(x-3)²+(y+4)²=25
(x-h)²+(y-k)²=R²
h=3
k=-4
(
C(3,-4)
4)(x+1)²+(y-6)²=361
(x-h)²+(y-k)²=R²
R²=361
√R²=√361
R=19
the actual car is 8 feet long and 4 feet wide. grace wants her model to be 12 inches in length. which proportion could be used to find the width of her model?
The proportion that could be used to find the width of Grace's model car is 1/2 = Model width / 12 inches.
To find the width of Grace's model car, a proportion can be set up using the lengths of the actual car and the desired model:
Proportion: Actual width / Actual length = Model width / Model length
Given values:
Actual length = 8 feet
Actual width = 4 feet
Model length = 12 inches
Converting the units:
12 inches = 1 foot (since 1 foot = 12 inches)
Substituting the values into the proportion:
4 feet / 8 feet = Model width / 12 inches
Simplifying the proportion:
1/2 = Model width / 12 inches
To find the model width, cross-multiply and solve for the unknown:
Model width = (1/2) * 12 inches = 6 inches
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Transform the equation x-3y=15 to express it in slope-intercept form
Answer:
y = (1/3)x - 5
Step-by-step explanation:
x - 3y = 15
x - 15 = 3y
3y = x -15
y = (1/3)x - 5
Hello !
Answer:
[tex]\boxed{y=\frac{1}{3}x-5}[/tex]
Step-by-step explanation:
An equation in slope-intercept form is [tex]y=mx+b[/tex].
Let's isolate y in our equation :
[tex]x-3y=15\\-3y=-x+15\\3y=x-15\\y=\frac{1}{3}x-5[/tex]
Our equation is in the form [tex]y=mx+b[/tex] with [tex]m=\frac{1}{3}[/tex] and [tex]b=-5[/tex].
Have a nice day
The function models the cost in dollars, c(x) = 72(1.04)X, of 1 ounce of a certain chemical used in
a laboratory. & represents the number of years since 2010.
Part a: By What percer tage does the cost of the chemical increase per year?
An ounce of the chemical cost in 2018 is $98.54.
Given:
The function c(x) = 72 ⋅ (1.04)ˣ models the cost in dollars, c, of 1 ounce of a certain chemical used in a laboratory.
Exponential function, involves exponents. an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.
In mathematics, an exponential function is a function of form f (x) = a^x, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
x represents the number of years since 2010.
An ounce of the chemical cost in 2018 is,
= 72 × (1.04)⁸
= $98.54
Therefore, the cost is $98.54.
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kyra coverted some australian dollars to pounds she received £67.50
kyra coverted some australian dollars to pounds she received £67.50
Kyra will receive $125 USD when she converts £67.50 to USD.
Given that, Kyra wants to convert some Australian dollars to pounds she received £67.50.
Exchange rate =
Exchange rates are typically quoted as currency pairs, where one currency is the base currency and the other is the counter currency.
To convert £67.50 into USD using the exchange rate of $1 = £0.54, you can multiply the amount in pounds by the exchange rate.
Here's the calculation:
£67.50 x $1/£0.54 = $125
Therefore, Kyra will receive $125 USD when she converts £67.50 to USD.
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a recent study found that 30% of all opioid prescriptions are missing a documented medical justification for use. a hospital administrator wonders if a smaller proportion of patients at her hospital are missing a medical justification for their opioid prescriptions. suppose the hospital administrator conducts a review of a random sample of 25 opioid-prescribed patient files at her hospital and 5 of those files are missing a documented medical justification for the opioid prescription. a statistician carries out a significance test of the null hypothesis versus the alternative hypothesis. what is the value of the standardized test statistic for this significance test (rounded to the nearest tenth)?
The value of the standardized test statistic for this significance test is -1.3
For the standardized test statistic for this significance test, we need to compare the sample proportion to the hypothesized population proportion.
The null hypothesis (H₀)
H₀: The proportion of patients missing a medical justification for opioid prescriptions at the hospital is equal to 30%.
The alternative hypothesis (H₁)
H₁: The proportion of patients missing a medical justification for opioid prescriptions at the hospital is different from 30%.
The sample size is 25 and 5 of those files are missing a medical,
The sample proportion (p) can be calculated as
(p) hat = (Number of files missing justification) / (Total number of files)
(p) hat = 5 / 25
(p) hat = 0.2
The standard error is given by
SE = √[((p) hat × (1 - (p) hat)) / n]
SE = √[(0.2 × (1 - 0.2)) / 25] = √(0.16 / 25) = 0.08
For the standardized test statistic, we use the formula:
z = ((p) hat - p₀) / SE
where p₀ is the hypothesized population proportion.
p₀ = 30% = 0.3
z = (0.2 - 0.3) / 0.08 = -0.1 / 0.08 = -1.25 = -1.3
The value of the standardized test statistic for this significance test is approximately -1.3
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a bird leaves its nest, and flies back and forth from its nest to a nearby ditch to gather worms. the distance between the nest and the ditch is 200 meters. in one and a half hours, the bird manages to bring worms to its nest 15 times. what is the speed of the bird in kilometers per hour?
Therefore, the speed of the bird is approximately 1.001 kilometers per hour.
We can start by calculating the total distance the bird flew, which is the distance between the nest and the ditch multiplied by the number of round trips:
total distance = 2 × distance between nest and ditch × number of round trips
total distance = 2 × 200 meters × 15
total distance = 6000 meters
Next, we can calculate the bird's average speed by dividing the total distance by the time it took to make the trips:
average speed = total distance ÷ time
average speed = 6000 meters ÷ (1.5 hours × 3600 seconds/hour)
average speed = 0.278 meters/second
To convert this to kilometers per hour, we can multiply by the conversion factor of 3.6:
average speed = 0.278 meters/second × 3.6 kilometers/meter
average speed = 1.001 kilometers/hour
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Help me please??????
The mean absolute deviation of the given data set, 94, 86, 95, 99, 88, 90, is 4
The values differ from the mean by an average of 4.
Calculating the mean absolute deviationFrom the question, we are to calculate the mean absolute deviation of the given data
The given data
94, 86, 95, 99, 88, 90
To calculate the mean absolute deviation of the given data,
First, we will calculate the mean
Mean = (94 + 86 + 95 + 99 + 88 + 90) / 6
Mean = 552 / 6
Mean = 92
Now,
We will determine the absolute value of the difference between each data and the mean
|94 - 92| = 2
|86 - 92| = 6
|95 - 92| = 3
|99 - 92| = 7
|88 - 92| = 4
|90 - 92| = 2
Now,
We will determine the mean of these absolute differences
Mean absolute deviation = (2 + 6 + 3 + 7 + 4 + 2) / 6
Mean absolute deviation = 4
Hence,
The mean absolute deviation is 4
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Find tan 0, where 0 is the angle shown.
Give an exact value, not a decimal approximation.
Answer:
4/3
Step-by-step explanation:
Tan(x)=Opposite/adjacent
We need to find the opposite side.
We can use the Pythagorean theorem to help us:
5^2=3^2+x^2
25=9+x^2
16=x^2
x=4
4 is the measure of the opposite side
The adjacent side has measure of 3
Tan(theta)= 4/3
*theta is the weird 0 with a bar thingy at the angle, its some letter in the greek alphabet that denotes an unknown angle in geometry
John plans to hike a distance of 21 miles. If he
only travels 1 3/4 miles per hour, how long will it
take him to finish his journey?
Answer:
12 hours
Step-by-step explanation:
1 3/4=1.75
21÷1.75=12
Which set of numerical values represents the minimum, lower quartile, median, upper quartile, and maximum, in that order, of the box plot of this data set?
51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60
51, 54, 56, 58, 60
51, 53, 56, 59, 60
53, 54, 55, 59, 60
51, 53, 55, 58, 60
The set of numerical values that represents the minimum, lower quartile, median, upper quartile, and maximum, in that order, is:
51, 53, 55, 58, 60
To determine the minimum, lower quartile, median, upper quartile, and maximum of the given data set, we can arrange the values in ascending order:
51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60
Arranging the values in ascending order gives us:
51, 51, 53, 53, 54, 55, 55, 56, 58, 58, 58, 59, 60
The minimum value is 51.
The lower quartile (Q1) is the median of the lower half of the data, which is 53.
The median (Q2) is the middle value of the data set, which is 55.
The upper quartile (Q3) is the median of the upper half of the data, which is 58.
The maximum value is 60.
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Which property does the following equation illustrate?
3 + (5+6) = (5+6) + 3
A) Distributive Property
B) Associative property of addition
C) inverse property of addition
D) commutative property of addition
Answer:
The Correct answer is C
communicative property
