Lenny used the Associative property of addition to show that rearranging the grouping of numbers being added does not change the outcome of the equation.
While solving an equation, Lenny used the Associative property of addition which guarantees that the second equation (2x + (1+5) = 9) is equivalent to the first ((2x + 1) + 5 = 9). This property states that the grouping of numbers being added does not change the sum, as shown:
(A + B) + C = A + (B + C).
In the context of the provided equations, Lenny grouped the 1 and 5 together without changing the sum, illustrating that it doesn't matter how the numbers are grouped in addition.
Here is the other question, the last one for this weeks homework, help will be very much appreciated!
Answer:
B
Step-by-step explanation:
3x+5x= 8x
5x^3 - 2x^3= 3x^3
-2x^2= -2x^2
13+11=24
What is the period of the function y=-4sin (2/3x-pi?3)?
The grades received on a test by twenty students were 100, 55, 75, 80, 65, 65, 95, 90, 80, 45, 40, 50, 85, 85, 85, 80, 80, 70, 65, and 60. What is the average of these grades?
A.) 70.5
B.) 72.5
C.) 77
D.) 80.3
E.) 100
You have $200 in your savings account. You take $35 from your account each week for four weeks. How much is left in your account at the end of the four weeks?
write the ratio six to seven in other ways
There are 3 drama movies 8 comedy movies and 4 action movies what's the ratio of dramas to movies ?
Please help me Factor -4d3 + 28d2 - 4d
Answer:
The factored form of the expression [tex]\( -4d^3 + 28d^2 - 4d \)[/tex] is [tex]\( -4d(d - 1)(d - 1)(6d - 1) \).[/tex]
Explanation:
To factor the expression [tex]\( -4d^3 + 28d^2 - 4d \)[/tex], we can first look for the greatest common factor (GCF) among the terms. In this case, the GCF is [tex]\( -4d \).[/tex]
So, we can factor out [tex]\( -4d \)[/tex] from each term:
[tex]\[ -4d(d^2 - 7d + 1) \][/tex]
Now, let's focus on factoring the quadratic expression inside the parentheses, [tex]\( d^2 - 7d + 1 \)[/tex]. To factor this quadratic expression, we need to find two numbers that multiply to give the constant term (1) and add to give the coefficient of the linear term (-7d). Since the constant term is 1, the only possible combination is 1 and 1.
So, we can rewrite the expression as:
[tex]\[ -4d(d^2 - 7d + 1) = -4d(d^2 - d - 6d + 1) \][/tex]
Now, we can group the terms and factor by grouping:
[tex]\[ -4d((d^2 - d) + (-6d + 1)) \][/tex]
[tex]\[ -4d(d(d - 1) - 1(6d - 1)) \][/tex]
Now, we can factor further:
[tex]\[ -4d(d - 1)(d - 1)(6d - 1) \][/tex]
Find the x-intercept of parabola with the vertex (-7,45) and y-intercept (0,-200). Write your answer in this form (x, y) , (x, y)
Answer:
(-10,0),(-4,0) for Plato/Edmentum Users
Step-by-step explanation:
Have a great day
Find the area of the shaded region. Show all work in order to receive credit.
area of square = 14^2 = 196 square cm
area of circle = 3.14 *7^2 = 153.86 square cm
196 - 153.86 = 42.14 square cm is shaded
Suppose you buy two sweaters. each sweater costs the same amount. the amount of money you spend varies directly with the number of sweaters you buy. if you spent $37.50 for two sweaters, what is the constant of variation?
Answer with Step-by-step explanation:
We spent $37.50 for two sweaters.
Each sweater costs the same amount.
Cost of each sweater=$37.50/2
=$18.75
The amount of money you spend varies directly with the number of sweaters you buy.
We have to find the constant of variation.
Here, cost of each sweater is the constant of variation.
Hence, constant of variation is:
$18.75
If it takes six men six days to dig six holes, how long will it take one man to dig half a hole?
It will take 3 days for 1 man to dig half of that complete hole.
What are direct and inverse proportion ?Direct proportion if increase in one quantity also results in increase in another quantity for example price and weight of something.
Inverse proportion is when increase in one quantity results in decrease in another quantity for example time is inversely proportional to (speed when distance is constant.
According to the given question
6 men are working together then it takes them 6 days to dig 6 holes.
∴ Number of men days = 6 days × 6 men = 36 men days
So, in 36 men days 6 holes are dug. Now the men days and the number of holes being dug are in direct proportion with one another.
Hence number of men-days required to dig one hole
= 36/6 men days
= 6 men days
∴ No. of men days required to dig half a hole
= 6/2
= 3 men days
So, It takes 1 man 3 days to dig half a hole.
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What is the factored form of 6n4 – 24n3 + 18n?
Answer:
Step-by-step explanation:
Notice to facts:
The numbers 6, -4 and 18 have a common factor: 6.In all the terms (n⁴, n³, n) are a factor n.The expression has a common factor 6n. Then,
6n⁴-24n³+18n = 6n(n³-4n²+3).
In order to factor the term n³-4n²+3 we use Ruffini-Horner rule, which gives us that
n³-4n²+3 = (n-1)(n²-3n-3).
Then,
6n⁴-24n³+18n = 6n(n³-4n²+3) = 6n(n-1)(n²-3n-3).
If you don't know the formula for the general solution of second degree equation, you are done. Otherwise, it is only to use it in the quadratic factor.
A taxi charges $2.50 for the first mile and $0.40 for each mile after that. The expression below shows how to find the total cost, in dollars, of a 20-mile taxi ride. 2.50 + 0.40 (20 - 1) What is the cost of the ride?
Answer:
Step-by-step explanation:
Alright , lets get started.
The first mile charge = [tex]$2.5[/tex]
Total miles taxi covered = [tex]20[/tex]
Subtracting first mile frm the total ride = [tex](20-1)[/tex]
Means the fare will apply on this mile.
So, cost of total ride = [tex]2.5 + 0.4 (20-1)[/tex]
cost of total ride = [tex]2.5+0.4*19[/tex]
cost of total ride = [tex]2.5+7.6[/tex]
cost of total ride = [tex]10.1[/tex]
The answer is $ 10.1 . : Answer
Hope it will help :)
Answer:
10.10 (B)
Step-by-step explanation:
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1/3(9-6m)+1/4(12m-8)
Answer:
[tex]m+1[/tex]
Step-by-step explanation:
The question is
Simplify the expression
we have
[tex]\frac{1}{3}(9-6m)+\frac{1}{4}(12m-8)[/tex]
using the distributive property
[tex]\frac{1}{3}(9)-\frac{1}{3}(6m)+\frac{1}{4}(12m)-\frac{1}{4}(8)[/tex]
[tex]3-2m+3m-2[/tex]
Combine like terms
[tex]m+1[/tex]
Use the graph below to fill in the blank with the correct number
Take -4 + 3a 2 from 7a - a 2
Subtracting [tex]\( -4 + 3a^2 \)[/tex] from [tex]\( 7a - a^2 \)[/tex] yields [tex]\( 7a - 3a^2 + 4 - a^2 \)[/tex], after distributing the subtraction and combining like terms.
To subtract [tex]\( -4 + 3a^2 \)[/tex] from [tex]\( 7a - a^2 \)[/tex], we need to distribute the subtraction across both terms in [tex]\( 7a - a^2 \)[/tex] and then combine like terms:
[tex]\[ (7a - a^2) - (-4 + 3a^2) \][/tex]
Distributing the subtraction:
[tex]\[ 7a - a^2 + 4 - 3a^2 \][/tex]
Now, combine like terms:
[tex]\[ (7a - 3a^2) + (4 - a^2) \][/tex]
So, the result of subtracting [tex]\( -4 + 3a^2 \)[/tex] from [tex]\( 7a - a^2 \)[/tex] is [tex]\( 7a - 3a^2 + 4 - a^2 \)[/tex].
Comlpete Question:
Take [tex]\( -4 + 3a^2 \)[/tex] from [tex]\( 7a - a^2 \)[/tex]
The sum of three consecutive even integers is fifty four. what is the second integer?
How you will go about preparing yourself to confidently teach numeracy?
In preparation of yourself in having to teach numeracy, it is best to substantiate if learning the numeracy will have benefits or advantages, such as having to help other people or even empower them as an adult people learning and think of ways how will this could be important to them.
What is the converse of the linear pairs theorem
What is the distance between -3 and 6?
-9
-3
3
9
Compare and contrast equation notation and function notation
TRUE OR FALSE:if a function uses variables other than x and y for its input and output variables, you take the original and solve for the output variable to find the inverse.
Answer: False for apex
Step-by-step explanation: 1. because it is
2. for the junior monitor that deleted my answer, back off.
Answer:
false for apex
Step-by-step explanation:
What is the solution to the compound inequality in interval notation? 2(x+3)>6 or 2x+3≤−7
Answer: The required solution in interval notation is [tex](0,\infty)U(-\infty,-5].[/tex]
Step-by-step explanation: We are given to find the solution to the following compound inequality in interval notation :
[tex]2(x+3)>6~or~2x+3\leq -7~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
To find the solution to (i), we must solve both the parts separately.
The inequality (i) can be solved as follows :
[tex]2(x+3)>6\\\\\Rightarrow x+3>\dfrac{6}{2}\\\\\Rightarrow x+3>3\\\\\Rightarrow x>3-3\\\\\Rightarrow x>0\\\\\Rightarrow x\epsilon (0,\infty)[/tex]
or
[tex]2x+3\leq-7\\\\\Rightarrow 2x\leq-7-3\\\\\Rightarrow 2x\leq -10\\\\\Rightarrow x\leq -\dfrac{10}{2}\\\\\Rightarrow x\leq-5\\\\\Rightarrow x\epsilon(-\infty,-5].[/tex]
Thus, the required solution in interval notation is [tex](0,\infty)U(-\infty,-5].[/tex]
solve for n
4n + 2 = 6 (1/3n - 2/3)
The solution of expression for the value of n is, n = - 3.
Used the concept of expression that states,
Mathematical expression is defined as the collection of numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that,
The expression is,
[tex]4n + 2 = 6 (\dfrac{1}{3} n - \dfrac{2}{3} )[/tex]
Now simplify the expression by combining like terms and apply the distributive property as,
[tex]4n + 2 = 6 (\dfrac{1}{3} n - \dfrac{2}{3} )[/tex]
Apply distributive property,
[tex]4n + 2 = (\dfrac{6}{3} n - \dfrac{12}{3} )[/tex]
[tex]4n + 2 = 2n - 4[/tex]
Combine like terms,
[tex]4n - 2n = - 4 - 2\\[/tex]
[tex]2n = - 6\\[/tex]
[tex]n = - 3[/tex]
Therefore, the value of n is - 3.
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Which shows one way to determine the factors of x3 – 9x2 + 5x – 45 by grouping?
If someone could help me!
Which mathematical property is demonstrated?
40 * (25 * 74) = (40 * 25) * 74
Question 3 options:
associative property of addition
commutative property of multiplication
commutative property of addition
associative property of multiplication
Answer:
Step-by-step explanation:
The associative property of multiplication states that the product is the same regardless of their grouping. In this case, after simplifying the expression given, we can see that indeed the products are the same hence that fact that they have different grouping
What is the measure of an exterior angle of a regular 7-sided polygon?
Enter your answer as a decimal in the box.
Round to the nearest tenth of a degree.
Answer: [tex]51.4^{\circ}[/tex]
Step-by-step explanation:
We know that the sum of all the exterior angles of a regular polygon with n sides is [tex]360^{\circ}[/tex].
The measure of an exterior angle of a regular n-sided polygon is given by :-
[tex]\dfrac{360^{\circ}}{n}[/tex]
Now, the measure of an exterior angle of a regular 7-sided polygon is given by :-
[tex]\dfrac{360^{\circ}}{7}=51.4285714286^{\circ}\approx51.4^{\circ}[/tex]
Hence, the measure of an exterior angle of a regular 7-sided polygon =[tex]51.4^{\circ}[/tex]
Simplify
Y+ z -2y. If y=4 and z=2
What's the answer ????