The correct answer is option (b): Square root of 4x^2.
The standard deviation of a random variable Y is the square root of its variance. In this case, the variance of Y is given as 4x^2. Taking the square root of 4x^2, we get the standard deviation of Y as 2x.
Therefore, the correct answer is the square root of 4x^2, which is the standard deviation of Y.
eight hundred twenty nine and six tenths as a decimal
Christine has 1 blue sock, 3 purple socks and 1 green sock in a box.
Christine takes one sock at random from the box, puts it back, and takes another sock from the box. Find the probability that Christine takes at least one blue sock.
Let {X₁} be independent standard normal random variables. Let Y = (X₁ + X3 + X5 + X7)² + (X₂ + X₁ + X6 + X8)². Determine a value c such that the random variable cY will have an x² distribution
The value of "c" such that the random variable cY has an x² distribution is 4.
To find the value of "c" such that the random variable cY has a chi-squared (x²) distribution, we need to consider the properties of the chi-squared distribution and the given expression for Y.
The chi-squared distribution with "k" degrees of freedom is obtained by summing the squares of "k" independent standard normal random variables. Each standard normal variable contributes one degree of freedom to the chi-squared distribution.
In the given expression for Y, we have two squared terms: (X₁ + X₃ + X₅ + X₇)² and (X₂ + X₁ + X₆ + X₈)². To obtain an x² distribution, we need to rewrite the expression in terms of squared standard normal random variables.
To achieve this, we can divide each squared term by its corresponding degrees of freedom and take the square root:
Y = (X₁ + X₃ + X₅ + X₇)² + (X₂ + X₁ + X₆ + X₈)²
= (1/4)(X₁ + X₃ + X₅ + X₇)² + (1/4)(X₂ + X₁ + X₆ + X₈)²
Now, we can rewrite Y as:
Y = (1/4)χ²₁ + (1/4)χ²₁
Here, χ²₁ and χ²₂ represent chi-squared random variables with 1 degree of freedom each.
To obtain an x² distribution, we need to make the coefficients of the chi-squared random variables equal to their degrees of freedom. In this case, we want the coefficient to be 1.
So, setting the coefficient of χ²₁ to 1, we get:
(1/4) = 1/c
Solving for "c", we find:
c = 4
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Which equation represents a line which is perpendicular to the line y = - 6/5 * x - 7
An equation representing a line perpendicular to y = -6/5 [tex]\times[/tex] x - 7 would be y = 5/6 [tex]\times[/tex] x + c, where c is any constant.
To determine a line that is perpendicular to the given line y = -6/5 [tex]\times[/tex] x - 7, we need to consider the slope of the given line.
The given line has a slope of -6/5.
For two lines to be perpendicular, their slopes must be negative reciprocals of each other.
The negative reciprocal of -6/5 can be found by flipping the fraction and changing the sign, which gives us 5/6.
Therefore, the equation of a line perpendicular to y = -6/5 [tex]\times[/tex] x - 7 will have a slope of 5/6.
To find the equation of this perpendicular line, we can use the point-slope form of a line, using a known point on the line.
Let's assume the line passes through the point (x1, y1).
The equation of the perpendicular line can be written as: y - y1 = (5/6) [tex]\times[/tex] (x - x1).
Since we do not have a specific point given, we cannot determine the exact equation of the perpendicular line without additional information.
In summary, the equation of a line perpendicular to y = -6/5 [tex]\times[/tex] x - 7 will have a slope of 5/6, but the specific equation depends on the point it passes through.
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Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
The coordinate of the fourth vertex is (9,11)
What is coordinate?Any of a set of numbers used in specifying the location of a point on a line, on a surface, or in space is called coordinate
For example (6,3) is a coordinate on a plane where 6 represent the value on x axis and 3 represent the value on y axis.
Since the shape is parallelogram;
√ -3-1)² + 8-0)² = √ x-5)² + y-3)²
= √4² +8² = √ x-5)² + y -3)²
therefore, relating the two values;
4 = x-5 and 8 = y -3
x = 4+5 = 9
y = 8+3 = 11
Therefore the coordinate of the fourth vertex = ( 9,11)
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PLEASEEEE HELP I GIVE YOU 100 POINTS
The missing dimensions from the given expression should be completed with the following:
(81.) A) 2
(82.) AD) x
(83.) E) 12
The expression as a product should be written as: DE) 2(x + 12).
What is a factored form?In Mathematics and Geometry, a factored form simply refers to a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.
In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;
x 12
2 2x 24
Note: 2x/2 = x.
24/2 = 12.
Next, we would write the expression 2x + 24 as a product as follows;
(2x + 24) = 2(x + 12).
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Please help me solve this
Answer:
Step-by-step explanation:
anwser it pls aaaaaaaassaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
Step-by-step explanation:
Volume = Bh
Turn the shape so the trapezoid is on the bottom/base
h=18 for overall shape
B = area of base, trapezoid
B = 1/2 (b₁ + b₂) h
b₁ = 11
b₂ = 25
h = 24 for trapezoid
B = 1/2 (11 + 25)(24)
B = 432
V = Bh
V = (432)(18)
V= 7776 in³
NO LINKS!! URGENT HELP PLEASE!!
Find the value of x
Answer:
x = 4
Step-by-step explanation:
You want the value of x in the figure of a circle with intersecting secants.
Secant relationThe product of lengths from the near and far circle intercepts to the point where the secants intersect is the same for both secants:
6(6+10) = 8(8+x)
6·16 = 8·(8+x)
12 = 8 +x . . . . . . . divide by 8
4 = x . . . . . . . . . . subtract 8
The length x is 4 units.
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Find the area of the shape shown below.
Answer:
The answer is 32
Step-by-step explanation:
The formula for finding the area of a trapezoid is:
((base 1 + base 2)/ 2 )* h
Now all you have to do is substitute the numbers in.
Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.
Answer:
32 square units
Step-by-step explanation:
[tex]\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32[/tex]
Note that [tex]b_1[/tex] and [tex]b_2[/tex] are the lengths of each base of the trapezoid, so it doesn't matter which is which.
Tell whether the information in the diagram allows you to conclude that c is on the perpendicular bisector of an
11. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB.
12. Yes, the information provided can be used to conclude that C is on the perpendicular bisector of AB because C is equidistant from AB.
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector can be used for bisecting or dividing a line segment exactly into two (2) equal halves, in order to form a right angle with a magnitude of 90° at the point of intersection.
Question 11.
By critically observing the geometric shape, we can logically deduce that the information provided can be used to conclude that C is on the perpendicular bisector of AB because CE bisects AB:
AC ≅ BC
CD ≅ CD
AE ⊥ EC
Question 12.
By critically observing the geometric shape, we can logically deduce that the information provided can be used to conclude that C is on the perpendicular bisector because C is equidistant from line segment AB.
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the image is the question
a) c = 22 feet
b) c = 23
c) c = 24
d) c = 30
The length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."
The Pythagorean theorem, which asserts that given a right triangle, the sum of the squares of the two shorter sides (a and b), is equal to the square of the hypotenuse (c), can be used to determine the length of the triangle's hypotenuse (c).
a = 10 feet
b = 20 feet
Using the Pythagorean theorem, we can calculate c as follows:
c^2 = a^2 + b^2
c^2 = 10^2 + 20^2
c^2 = 100 + 400
c^2 = 500
To find c, we take the square root of both sides:
c = √500
c ≈ 22.36
Rounding the answer to the nearest whole number, we get c ≈ 22.
Therefore, the length of the triangle's hypotenuse (c) is approximately 22 feet. The closest option provided is "a) c = 22 feet."
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Describe in words where √30^(3) would be plotted on a number line.
The cube root of 30 would be between 3 and 4, but closer to 3.
How to find cube root of a number?Cube root is the number that needs to be multiplied three times to get the original number.
The cube root of a number can be determined by using the prime factorization method. In order to find the cube root of a number:
Step 1: Start with the prime factorization of the given number.
Step 2: Then, divide the factors obtained into groups containing three same factors.
Step 3: After that, remove the cube root symbol and multiply the factors to get the answer. If there is any factor left that cannot be divided equally into groups of three, that means the given number is not a perfect cube and we cannot find the cube root of that number.
We have to find the cube root of 30.
Prime factorization of 30 = [tex]2\times3\times5[/tex].
Therefore the cube root of 30 = [tex]\sqrt[3]{ (2\times3\times5)}= \sqrt[3]{30}[/tex].
As [tex]\sqrt[3]{30}[/tex] cannot be reduced further, then the result for the cube root of 30 is an irrational number as well.
So here we will use approximation method to find the cube root of 30 using Halley's approach:
Halley’s Cube Root Formula:
[tex]{\sqrt[3]{\text{a}} = \dfrac{\text{x}[(\text{x}^3 + 2\text{a})}{(2\text{x}^3 + \text{a})]}}[/tex]
The letter “a” stands in for the required cube root computation.
Take the cube root of the nearest perfect cube, “x” to obtain the estimated value.
Here we have a = 30
and we will substitute x = 3 because 3³ = 27 < 30 is the nearest perfect cube.
Substituting a and x in Halley's formula,
[tex]\sqrt[3]{30} = \dfrac{3[(3^3 + 2\times30)}{(2\times3^3 + 30)]}[/tex]
[tex]= \dfrac{3[(27+60)}{(54+30)]}[/tex]
[tex]= 3\huge \text(\dfrac{87}{84} \huge \text)[/tex]
[tex]= 3\times1.0357[/tex]
[tex]\bold{\sqrt[3]{30} = 3.107}[/tex].
Hence, the cube root of 30 is 3.107.
Therefore, we can conclude that the cube root of 30 would be between 3 and 4, but closer to 3.
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Complete question:
Describe in words where cube root of 30 would be plotted on a number line.
A. Between 3 and 4, but closer to 3
B. Between 3 and 4, but closer to 4
C. Between 2 and 3, but closer to 2
D. Between 2 and 3, but closer to 3
Margie has a $50.00 budget to purchase a $45.00 pair of boots. If
there is an 8% sales tax rate, then how much under budget will
Margie be?
Answer:
She willl be $1.40 under budget
Step-by-step explanation:
8% = 8/100 = 0.08
Adding this to 100% of the price of the shoes, we get 108% = 108/100 = 1.08.
We multiply the price of the shoes by this:
45*1.08 = 48.60
Subtract this from 50:
50 - 48.60 = 1.40
PLSS HELP HURRYYY
ILL GIVE BRAINLIST
Answer:
hope you understand it and please follow me
Find a delta that works for ε = 0.01 for the following
lim √x + 7 = 3
x-2
A suitable delta (δ) for ε = 0.01 is any positive value smaller than √6.
To find a suitable delta (δ) for the given limit, we need to consider the epsilon-delta definition of a limit.
The definition states that for a given epsilon (ε) greater than zero, there exists a delta (δ) greater than zero such that if the distance between x and the limit point (2, in this case) is less than delta (|x - 2| < δ), then the distance between the function (√x + 7) and the limit (3) is less than epsilon (|√x + 7 - 3| < ε).
Let's solve the inequality |√x + 7 - 3| < ε:
|√x + 7 - 3| < ε
|√x + 4| < ε
-ε < √x + 4 < ε
To remove the square root, we square both sides:
(-ε)^2 < (√x + 4)^2 < ε^2
ε^2 > x + 4 > -ε^2
Since we're interested in the interval around x = 2, we substitute x = 2 into the inequality:
ε^2 > 2 + 4 > -ε^2
ε^2 > 6 > -ε^2
Since ε > 0, we can drop the negative term and solve for ε:
ε^2 > 6
ε > √6
Please note that this solution assumes the function √x + 7 approaches the limit 3 as x approaches 2. To verify the solution, you can substitute different values of δ and check if the conditions of the epsilon-delta definition are satisfied.
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PLEASE I NEED HELP I DONT UNDERSTAND THIS
(3x-1)(x-2)=5x+2 ecuación cuadrática incompleta
Hence, the arrangements to the quadratic equation (3x-1)(x-2) = 5x + 2 are x = and x = 4.
Quadratic equation calculation.
To unravel the quadratic equation (3x-1)(x-2) = 5x + 2, let's to begin with grow the cleared out side of the equation:
(3x - 1)(x - 2) = 5x + 2
Growing the condition:
3x^2 - 6x - x + 2 = 5x + 2
Streamlining the condition:
3x^2 - 7x + 2 = 5x + 2
Another, let's move all terms to one side of the condition:
3x^2 - 7x - 5x + 2 - 2 =
Combining like terms:
3x^2 - 12x =
Presently, we have a quadratic condition in standard shape: ax^2 + bx + c = 0, where a = 3, b = -12, and c = 0.
To fathom the quadratic equation, able to calculate out the common calculate of x:
x(3x - 12) =
From this equation, we are able see that the esteem of x can be or unravel for 3x - 12 = 0:
3x - 12 =
Including 12 to both sides:
3x = 12
Isolating both sides by 3:
x = 4
Hence, the arrangements to the condition (3x-1)(x-2) = 5x + 2 are x = and x = 4.
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NO LINKS!! URGENT HELP PLEASE!!
Answer:
[tex]\text{a.} \quad m\angle NLM=93^{\circ}[/tex]
[tex]\text{c.} \quad m\angle FHG=31^{\circ}[/tex]
Step-by-step explanation:
The inscribed angle in the given circle is ∠NLM.
The intercepted arc in the given circle is arc NM = 186°.
According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc.
Therefore:
[tex]m\angle NLM=\dfrac{1}{2}\overset{\frown}{NM}[/tex]
[tex]m\angle NLM=\dfrac{1}{2} \cdot 186^{\circ}[/tex]
[tex]\boxed{m\angle NLM=93^{\circ}}[/tex]
[tex]\hrulefill[/tex]
According to the Inscribed Angle Theorem, the measure of an inscribed angle is half the measure of the intercepted arc. Therefore:
[tex]m\angle HFG=\dfrac{1}{2}\overset{\frown}{HG}[/tex]
[tex]m\angle HFG=\dfrac{1}{2}\cdot 118^{\circ}[/tex]
[tex]m\angle HFG=59^{\circ}[/tex]
As line segment FH passes through the center of the circle, FH is the diameter of the circle. Since the angle at the circumference in a semicircle is a right angle, then:
[tex]m\angle FGH = 90^{\circ}[/tex]
The interior angles of a triangle sum to 180°. Therefore:
[tex]m\angle FHG + m\angle HFG + m\angle FGH =180^{\circ}[/tex]
[tex]m\angle FHG + 59^{\circ} + 90^{\circ} =180^{\circ}[/tex]
[tex]m\angle FHG +149^{\circ} =180^{\circ}[/tex]
[tex]\boxed{m\angle FHG =31^{\circ}}[/tex]
19
Select the correct answer.
This table represents function f.
0
2
I
f(x)
0
-2
If function g is a quadratic function that contains the points (-3, 5) and (0, 14), which statement is true over the inter
-3
-4.5
-2
-2
-1
-0.5
1
-0.5
3
-4.5
OA. The average rate of change of fis less than the average rate of change of g.
O B.
The average rate of change of fis more than the average rate of change of g.
'O C.
The average rate of change of fis the same as the average rate of change of g.
OD. The average rates of change of f and g cannot be determined from the given information.
The correct statement is OB. The average rate of change of f is more than the average rate of change of g.
To determine the average rate of change (slope) of the functions f and g, we can use the formula:
Average Rate of Change = (f(x2) - f(x1)) / (x2 - x1)
For function f, using the given table, we can calculate the average rate of change between the points (0, 0) and (2, -2):
Average Rate of Change (f) = (-2 - 0) / (2 - 0) = -2 / 2 = -1
For function g, using the given points (-3, 5) and (0, 14), we can calculate the average rate of change:
Average Rate of Change (g) = (14 - 5) / (0 - (-3)) = 9 / 3 = 3
Comparing the average rates of change, we find that the average rate of change of f is -1, while the average rate of change of g is 3.
Therefore, the correct statement is:
OB. The average rate of change of f is more than the average rate of change of g.
The average rate of change of f is greater than the average rate of change of g, indicating that the function f is increasing at a faster rate than function g over the given interval.
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A research study claims that 68% of adults drink regularly. Edward conducts a random sample of 200 people and finds that 140 people drink regularly.
z equals fraction numerator p with hat on top minus p over denominator square root of begin display style fraction numerator p q over denominator n end fraction end style end root end fraction
Using the formula and data provided, what is the value of the z-test statistic? Answer choices are rounded to the hundredths place.
a.)
0.41
b.)
0.61
c.)
0.39
d.)
0.59
Using the z-statistic relation given, the value of the z-statistic in the scenario would be 0.61
Z - statistic relationshipThe Z-statistic relation is written thus:
z = (phat - p) / √(p * q / n)phat = 140 / 200 = 0.7
p = 0.68
q = 1 - p = 0.32
n = 200
Inputting the values into our formula
z = (phat - p) / sqrt(p * q / n)
= (0.7 - 0.68) / sqrt(0.68 * 0.32 / 200)
= 0.02 / 0.0583
= 0.61
Therefore, Z-statistic is 0.61
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Quincy used this linear system to represent a situation involving a collection of $5 bills and $10 bills:
f+t=70
5f + 10t = 575
a) What problem might Quincy have written?
b) What does each variable represent?
So, 'f+t=70' represents the constraint that the total number of $5 bills and $10 bills is equal to 70. And '5f + 10t = 575' represents the condition that the total value of the $5 bills and $10 bills is equal to $575.
a) Quincy might have written a problem involving the number of $5 bills (represented by variable 'f') and the number of $10 bills (represented by variable 't'), with certain constraints and conditions.
Quincy might have written a problem related to a scenario where he needed to determine the number of $5 bills and $10 bills. The problem could involve a specific situation.
b) In this linear system:
'f' represents the number of $5 bills.
't' represents the number of $10 bills.
So, 'f+t=70' represents the constraint that the total number of $5 bills and $10 bills is equal to 70.
In the linear system, 'f' represents the number of $5 bills Quincy has, while 't' represents the number of $10 bills. The equation 'f+t=70' implies that the total number of bills. The second equation, '5f + 10t = 575', represents the condition that the total value of the $5 bills (5f) and the $10 bills (10t) together amounts to $575.
And '5f + 10t = 575' represents the condition that the total value of the $5 bills and $10 bills is equal to $575.
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A total of 90 groom's guests and 85 bride's guests attended a wedding. The bride's guests used 100 tissues. The groom's guests used 180 tissues. Calculate approximately how many tissues each groom's guest used.
Approximately 2 tissues were used by each groom's guest at the wedding.
The calculation is as follows:
180 tissues ÷ 90 guests = 2 tissues per guest.
To determine how many tissues each groom's guest used, we need to find the average number of tissues per guest. We start by adding up the number of tissues used by the groom's guests, which is 180.
Then, we divide this total by the number of groom's guests, which is 90. This division gives us an average of 2 tissues per guest.
By dividing the total number of tissues used by the total number of guests, we can find the average number of tissues per guest. In this case, each groom's guest used approximately 2 tissues.
It's important to note that this calculation assumes an equal distribution of tissues among all the groom's guests.
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Linda is opening a bakery and needs to figure out how much to charge for donuts. She checks with a number of other bakeries and compares their prices to their reported profits.
Donut Price Profits
$1.55 $5244
$0.95 $5244
$0.75 $3900
$1.25. $6000
$1.05 $5664
$1.35. $5916
Bakery
Dan's Delicious Donuts
The Corner Bakery
Bake 'n Wake
Donuts 'R' Us
Dan's Delicious Donuts
Dan's Delicious Donuts $1.35
A: Find the quadratic function that fits this data. Express this function in vertex form.
B: Use your model to predict Linda's profits if she undercuts the competition by selling her donuts for 55 cents each.
Linda's profits will be $
4x-5 2x+7 Find the value of x
answers should be from
27
37
47
57
Find the measure of the indicated arc.
90°
80°
100
70°
H
40°
F
The measure of an arc in a circle is determined by the central angle that subtends it. Let's analyze each given measure of the indicated arcs:
90°: A 90° arc spans one-fourth of the entire circle since a full circle has 360°.
80°: An 80° arc is smaller than a quarter of the circle but larger than a sixth since 360° divided by 4 is 90°, and by 6 is 60°. Therefore, it lies between these two values.
100°: A 100° arc is slightly larger than a quarter of the circle but smaller than a third, as 360° divided by 4 is 90°, and by 3 is 120°.
70°: A 70° arc is smaller than both a quarter and a sixth of the circle, falling between 60° and 90°.
H: The measure of an arc denoted by "H" is not provided, so it cannot be determined without further information.
40°: A 40° arc is smaller than a sixth of the circle but larger than a twelfth, as 360° divided by 6 is 60°, and by 12 is 30°.
F: Similarly, the measure of the arc denoted by "F" is not provided, so it remains unknown without additional data.
Thus, the measures of the indicated arcs are as follows: 90°, between 60° and 90°, between 90° and 120°, between 60° and 90°, unknown (H), between 30° and 60°, and unknown (F).
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me movement o
Which choice shows (3+9) + 13 correctly rewritten using the associative property and then
correctly simplified?
O 13+(3+9) = 13 + 12 = 25
13+(9+ 3) = 13 + 12 = 25
O 3+ (91+3) = 3 +94 = 97
O 3+ (9+13) = 3 +22= 25
(3+9) + 13 correctly rewritten using the associative property and then correctly simplified is 13+(9+3) = 13 + 12 = 25.
1. Start with the expression (3+9) + 13.
2. According to the associative property of addition, we can group the numbers in any order without changing the result.
3. Rearrange the expression by grouping the numbers differently: (9+3) + 13.
4. Now simplify the grouped numbers: 9+3 = 12.
5. The expression becomes 12 + 13.
6. Finally, simplify the addition: 12 + 13 = 25.
Therefore, the correct rewritten expression using the associative property and the simplified result is 13+(9+3) = 13 + 12 = 25.
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Antiderivative with the equation
The antiderivative of the function is f(x) = 2x + 5x³ + 2x⁶ - 9.
Find an antiderivative of f(x)To find an antiderivative of f(x), we can integrate each term of f'(x) individually.
Given:
f'(x) = 2 + 15x² + 12x⁵
To integrate 2, we get:
∫2 dx = 2x + C₁, where C₁ is the constant of integration.
To integrate 15x², we get:
∫15x² dx = 5x³ + C₂, where C₂ is another constant of integration.
To integrate 12x⁵, we get:
∫12x⁵ dx = 2x⁶ + C₃, where C₃ is another constant of integration.
Putting it all together, the antiderivative of f(x) is:
f(x) = 2x + 5x³ + 2x⁶ + C,
where C = C₁ + C₂ + C₃ represents the constant of integration.
To find the specific value of C, we are given that f(1) = 0. Substituting x = 1 into the antiderivative equation:
0 = 2(1) + 5(1)³ + 2(1)⁶ + C,
0 = 2 + 5 + 2 + C,
0 = 9 + C.
Therefore, C = -9.
The final expression for f(x) is:
f(x) = 2x + 5x³ + 2x⁶ - 9.
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Evaluate the algebraic expression for the given values of the variables
Answer: substitute the given number for the variable in the expression and then simplify the expression using the order of operations
Step-by-step explanation:3a2 - 4b2 for a = -3/4 and b = 1/2
Choose the justification for each step of the given equation. -6=-2/3(x+12)+1/3x
The steps used in the solution of the equation -6 = -2/3(x + 12) + 1/3x are based on the principles of the Distributive Property, combining like terms, addition property of equality, symmetric property, subtraction property of equality, and multiplication property of equality.
Let's analyze the steps of the solution for the given equation -6 = -2/3(x + 12) + 1/3x:
Step 1: Distributive Property
The equation begins with the Distributive Property, which states that you can distribute a factor to each term inside parentheses. In this case, we distribute -2/3 to (x + 12), resulting in -2/3 * x and -2/3 * 12.
Step 2: Simplification
We simplify the expression -2/3 * 12 to -8, as multiplying -2/3 by 12 gives us -24, and simplifying the fraction -24/3 yields -8.
Step 3: Combine Like Terms
We combine the like terms -2/3x and -8. The equation becomes -2/3x - 8 + 1/3x.
Step 4: Combine Like Terms
We combine the like terms -2/3x and 1/3x by adding their coefficients. The sum of -2/3x and 1/3x is -1/3x.
Step 5: Addition Property of Equality
We add -1/3x to both sides of the equation to isolate the constant term. The equation becomes -6 - 1/3x = -1/3x.
Step 6: Symmetric Property
Since the equation has a form of -1/3x = -6 - 1/3x, we can rearrange the terms using the Symmetric Property.
Step 7: Addition Property of Equality
We add 1/3x to both sides of the equation to isolate the constant term. The equation becomes -6 = 0.
Step 8: Subtraction Property of Equality
We subtract 0 from both sides of the equation to simplify it further. The equation remains -6 = 0.
Step 9: Multiplication Property of Equality
We multiply both sides of the equation by any non-zero number to check for consistency. In this case, there is no need for multiplication as the equation is already in its simplified form.
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