The properties needed to prove n + n + n + 2n = 5n are: Distributive Property of Multiplication, Associative Property of Addition, and Commutative Property of Addition.
What is Commutative Property of Addition?The commutative property of addition states that when two or more numbers are added, the order in which they are added does not affect the sum. In other words, for any two numbers a and b, a + b = b + a.
The properties required to prove n + n + n + 2n = 5n are as follows:
Distributive Property of Multiplication: This property states that a(b + c) = ab + ac. In this case, we can apply the distributive property to 2n, which gives us 2n = n + n.Associative Property of Addition: This property states that (a + b) + c = a + (b + c). We can use the associative property of addition to group the n's together and the 2n's together, which gives us (n + n + n) + (2n) = 5n.Commutative Property of Addition: This property states that a + b = b + a. We can use the commutative property of addition to rearrange the terms in the equation, which gives us (n + n + n + 2n) = (n + n + 2n + n) = 5n.Thus, these properties can be used.
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Final answer:
To prove n + n + n + 2n = 5n, we use the commutative and associative properties of addition to group and combine like terms, then apply the distributive property to show that the sum equals 5n.
Explanation:
To prove the equation n + n + n + 2n = 5n, we need to use properties of equality and algebraic manipulation. First, we apply the commutative property of addition, which allows us to rearrange the terms in any order without changing the sum.
This property isn't strictly necessary here, as all terms involve 'n', but it's a useful property in general for manipulating equations.
Next, we utilize the associative property of addition, which allows us to group numbers in any combination when adding. In this specific case, we group all the 'n' terms together:
(n + n + n) + 2n
Using the associative property, we can simplify the equation further by combining like terms:
3n + 2n = 5n
Lastly, we apply the distributive property, which in this case shows that multiplying the coefficient (being 1 for n in this example) by the number of times 'n' appears (3 for the first set and 2 for the second set), gives the same result as adding 'n' that many times.
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What is the equation of the following graph in vertex form?
y = (x − 3)2 − 1
y = (x + 3)2 − 1
y = (x − 4)2 − 2
y = (x − 4)2 + 8
Answer:
y = (x + 3)2 − 1
:)
Which proportion could be used to solve the question?
What percent of 80 is 23?
A. p/23 = 80/100
B. p/80 = 23/100
C. p/100 = 23/80
D. none could be used
A conjecture and the paragraph proof used to prove the conjecture are shown.
Drag an expression or statement to each box to complete the proof.
It is given that ∠1≅ ∠4 . By the vertical angle theorem, [blank] ≅∠1 . Therefore, ∠2≅∠4 by the substitution property. By the [blank] , ∠4≅∠3 . So, ∠2≅[blank] by the [blank]
choices:
verticle angle theorim, transitive property of congruence, ∠4, ∠3, ∠2, ∠1
Answer:
∠2; vertical angle theorem; ∠3; transitive property of congruence
Step-by-step explanation:
∠2 and ∠1 are opposite angles that share only a vertex. This is the definition of vertical angles, and by the vertical angle theorem they are congruent.
Substituting ∠2 for ∠1 in our "given" statement, we now know that ∠2≅∠4.
∠4 and ∠3 are opposite angles that share a vertex. This makes them vertical angles, and the vertical angle theorem states that they are congruent.
The transitive property, algebraically, states "if a=b and b=c, then a=c." Applied to this proof, it states "if ∠2≅∠4, and ∠4≅∠3, then ∠2≅∠3."
The required solution for the blacks,
Blank 1 = ∠2;
Blank 2 = vertical angle theorem;
Blank 3 = ∠3; the transitive property of congruence.
It is given that
∠1≅ ∠4 . By the vertical angle theorem, [blank] ≅∠1 . Therefore, ∠2≅∠4 by the substitution property. By the [blank] , ∠4≅∠3 . So, ∠2≅[blank] by the [blank].
To determine the missing statement at the place of blanks in the statement.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Since
Black 1
∠2≅∠4
and ∠1≅ ∠4
So ∠2 ≅ ∠1
Blank 2
∠2≅∠4 are equal by the vertical angle theorem.
Blank 3
∠4≅∠3
∠3 ≅∠1
So,
∠2 ≅ ∠1 ; ∠2≅∠3 and ∠4≅∠3 it is transitive property of congruence.
Thus, the required solution for the blacks,
Blank 1 = ∠2;
Blank 2 = vertical angle theorem;
Blank 3 = ∠3; the transitive property of congruence.
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Mike and Julie surveyed students to determine how many had a grade of A in math. They recorded their findings for each survey in the table below.
Students with an A in Math
Number of A grades Number of students surveyed
20
4
40
8
60
12
80
16
What is the constant of proportionality of the ratio of students surveyed to the number of A grades?
0.2
0.5
2
5
20/4 = 5
40/8 = 5
60/12 = 5
80/16 = 5
Answer is 5
Answer:
Option D 5
Step-by-step explanation:
Mike and Julie surveyed students to determine how many had a grade of A in math as given in the table.
We have to find the proportionality constant of the ratio of students surveyed to the number of A grades.
Since proportionality constant = [tex]\frac{\text{Students Surveyed}}{\text{number of A grades}}[/tex]
=[tex]\frac{20}{4}=5[/tex]
Similarly we can get the constant form other data which is equal to 5.
Therefore, Option D. 5 is the correct option.
what is 5 divided by 9374
Determine the exponential function that satisfies the given conditions:
The initial mass is 1.4g and it is halving every 4 days.
To determine the exponential function, use the general form of an exponential function and substitute the given values. The equation is y = 1.4 * (1/2)^(x/4).
Explanation:An exponential function represents exponential growth or decay. In this case, the given information states that the initial mass is 1.4g, and it is halving every 4 days. We can use the general form of an exponential function, y = ab^x, where a is the initial value, b is the growth/decay factor, and x is the time in days.
Since the mass is halving every 4 days, the decay factor is 1/2, since the mass is halving. The equation becomes y = 1.4 * (1/2)^(x/4).
This equation represents the exponential function that satisfies the given conditions.
A 3-cup bottle of dish soap costs $5.28. What is the price per fluid ounce?
Answer:A 3-cup bottle of dish soap costs $3.36. What is the price per fluid ounce.
Step-by-step explanation:
Colby worked three more hours on tuesday than he did on monday. on wednesday, he worked one hour more than twice the number of hours that he worked on monday. if the total number of hours is two more than five times the number of hours worked on monday, how many hours did he work on monday>
Answer:
a,b,c
Step-by-step explanation:
i guessed and then they told me the right answer .
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What is the value of x ?
what is the common ration between successive term in the sequance? 2,-4,8,-16,32,-64
What are the odd numbers between 3497 and 3511?
Maths question below please help
At a discount grocery store, Jessica paid 0.72 for an 8-ounce bottle of spring water. What is the cost of the spring water per ounce?
PLEASE HELP!!!!!!!!!
solve for x
-2(x+1/3)+9x=4
x=
Annette drives her car 120120 miles and has a mean of a certain speed. if the mean speed had been 3mph3mph more, she could have traveled 128128 miles in the same length of time. what was her mean speed?
Allison practices her violin for at least 12 hours per week. She practices for three fourths of an hour each session.if Allison already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her weekly practice goal ?
Evaluate 32 + (7 − 2) ⋅ 4 − 6 / 3.
a. 24
b.54
c.27
d.28
For some reason I keep getting the result 50.
Madison wants to make cookies for her little sisters birthday party. She is cutting a roll of cookie dough into pieces that are 1/2 inch thick. If the roll is 13 inche long, how many cookies can she make
Answer:
26 cookies
Step-by-step explanation:
13 times 2
A baker sells bread for $5 a loaf and rolls for $1 each. The baker needs to sell $35 worth of baked goods by the end of the day. Enter a linear equation that describes the problem.
Explanation:
Cost of 1 loaf of bread = $5
Cost of 1 roll = $1
The baker needs to sell both items and it should be worth $35.
To find the linear equation, Suppose, the baker sells “b” loaves of bread and “r” rolls.
Then the total cost of the sales has to be $35.
So, the linear equation will be:
5b + 1r = 35
Solve for y 3x-4y=10
Diameters AB and CD of circle K intersect such that m∠BKD = 100°. The measure of arc AC is:
Answer:
Measure of arc AC = 100°
Step-by-step explanation:
For better understanding of the solution, see the attached figure :
Given : AB and CD are the diameters of the circle K and m∠BKD = 100°
To find : measure of arc AC
Solution :
The angle which is formed by the arc AC is m∠AKC so we need to find the measure of the angle ∠AKC
Now, m∠BKD = 100°
and m∠BKD = m∠AKC ( Vertically opposite angles are always equal)
⇒ m∠AKC = 100°
Hence, Measure of the arc AC = 100°
Megan's DVD club membership, which is $8, is deducted automatically from her bank account every month. Which expression shows the total deductions for the year?
1. (−$8) ÷ 12
2. (−$8) ⋅ 12
3. (−$8) − 12
4. (−$8) + 12
Hello,
100% CorrectThe correct answer is B) (-$8) × 12
Hope this helps!!!! :)
(Took the Math test)
**(Vanessa)**
4/3 of a number is 20. What is the number?
What is the playing surface called where the college basketball semi- finals are played
The playing surface where the college basketball semi-finals are played is called the court. It is rectangular in shape and has various markings such as the three-point line and free-throw line.
Explanation:The playing surface where the college basketball semi-finals are played is called the court or the basketball court. The court is rectangular in shape with a length of 94 feet and a width of 50 feet. It is divided into two halves with a midcourt line and has markings such as the three-point line, free-throw line, and key.
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What is the solution of the system? Use the elimination method. 2x+y=206x−5y=12 Enter your answer in the boxes.
Answer:
The answer to your question is: x = 7; y = 6
Step-by-step explanation:
2x+y=20 ( 1 ) Multiply by 5
6x−5y=12 ( 2 )
5 (2x+y=20) = 10x + 5y = 100
10x + 5y = 100
6x − 5y = 12 Eliminate y
16 x = 112
x = 112 / 16
x = 7
2(7) + y = 20 Substitution
14 + y = 20
y = 20 - 14
y = 6
Identify the values of a b and c in the quadratic function y = 3x -5x +2
How can I tell if they are none transversal?
A non-transversal line in geometry is a line that does not intersect two or more lines at distinct points. Similarly, in geology, folds with a horizontal axial line, called non-plunging folds, can be analogous to non-transversal lines as they don't intersect with another structure at a distinct point.
Explanation:In mathematics, specifcally in geometry, transversal is a line that passes through two lines in the same plane at two distinct points. If a line does not intersect two or more lines at distinct points, it can be considered as a non-transversal line.
According to the information provided, in the context of folds in geology, the axial line becomes a key concept. The axial line refers to an imaginary line drawn along the crest of a fold. If the axial line is horizontal, the fold is referred to as a non-plunging fold and it could be analogous to a non-transversal line in geometry, as it doesn't intersect with another structure at a distinct point.
However, if the axial line is tilted (plunging), it might be considered as a transversal in the sense that it 'intersects' the horizontal plane at a distinct angle. Similarly, if a line in geometry is tilted and intersects two or more lines at distinct points, it is a transversal line.
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What has a greater area, a square or an equilateral triangle?
This year, the parade had 127 floats. That was 34 fewer floats than last year. How many floats were in te parade last year ?
Answer:
Last year were 161 floats, that is, 34 more than this year.Step-by-step explanation:
Givens
There are 127 floats this year.That represents 34 fewer floats than last year.The second given statement expresses that this year there are 34 LESS floats. So, to know how many floats were there last year, we just need to sum
[tex]127+34=161[/tex]
Therefore, last year were 161 floats, that is, 34 more than this year.
Find the greatest possible value of the product xy, given that x and y are both positive and x + 2y = 30
Answer: The maximum value of the product x*y is 112.5
Step-by-step explanation:
We have that x + 2y = 30
so we can isolate one of the variables and get:
x = 30 - 2y
now, the product of x*y can be written as:
x*y = (30 - 2y)*y = 30y - 2y^2
now, we want to find the maximum of 30y - 2y^2
because the leading coeficient is negative (-2), we know that the hands of the quadratic function will go downwards, so the zero of the derivate of this quadratic equation will give us the value where the equation has a maximum:
f(y) = -2*y^2 + 30*y
f'(y) = -4*y + 30 = 0
y = -30/4 = 7.5
So the maximum value is:
f(7.5) = -2*7.5^2 + 30*7.5 = 112.5