The length of a side of the square is 8 unit.
Area of Square:
The area of a square is defined as the number of square units required to fill the square. Area is generally defined as the area occupied within the bounds of a planar object. Measurements are in square units and the default unit is square meters (m²).
Area of a Square = Side × Side
Therefore, the area of square = Side² square units
and, the perimeter of a square = 4 × side units
Given:-
Area of square is equal to twice its perimeter
To find:-
Side of square = ?
Now,
Let the side of square be a
Perimeter of square=4a
Area of Square = a²
Now,
According to the Question:
Area of Square = 2 × Perimeter of Square
⇒ a² = 2 ×4a
⇒ a² = 8a
⇒ a = 8.
Therefore, the side of square is 8 unit.
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Determine which set of side measurements could be used to form a right triangle. 4, 11, 20 16, 21, 25 5, 13, 25 3, 4, 5
The triangle with sides measuring 3, 4, 5 will form a Right Nagle Triangle
What is Pyhtagorean Theorem?
The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.
Solution:
(i) 4, 11, 20
20² = 4² + 11²
400 = 16 + 121
400 ≠ 137 #Not a right angle triangle
(ii) 16, 21, 25
25² = 16² + 21²
625 = 256 + 441
625 ≠ 697 #Not a right angle triangle
(iii) 5, 13, 25
25² = 5² + 13²
625 = 25 + 169
625 ≠ 194 #Not a right angle triangle
(iv) 3, 4, 5
5² = 3² + 4²
25 = 9 + 16
25 = 25 #Right angle triangle
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ticket prices at an outdoor theatre performance are $2.50 for children and $5.00 for adults. one evening, $6350 is collected from a total of 1900 people attending. how many adults and how many children attend?:
As the ticket prices at an outdoor theatre performance are $2.50 for children and $5.00 for adults. one evening, $6350 is collected from a total of 1900 people attending. There are 640 adult and 1260 childrens.
Given in the questions:
Ticket price in outdoor Theater = $2.50
For Children = $5.00
Total tickets collected in evening = $6350(collected from 1900 people)
Let p be the adult and
1900 - p be the children's who attained the show.
Now,
2.5 × (1900- p) +5p = 6350
⇒ 4750 - 2.5p +5p =6350
⇒ 2.5p = 1600
⇒ p = 1600/2.5
⇒ p = 640
Since,
p = 640
Therefore,
1900 - p = children
⇒ Children = 1900 - 640
⇒ Children = 1260
Therefore, there are total 640 adults and 1260 children's in the theater.
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Solve the equation.
5x + -3 = 5x + 20
Answer:
Step-by-step explanation:
x=23
I think
5x+-3=5x+20
add 3 on both sides canceling the -3 so then you get
5x=5x+23
subtract the 5x from both sides so then you get
x=23
State the domain and range for the following relations.
12. If g(x) = -4²-3r + 2, determine g(−2).
C
Answer:
Step-by-step explanation:
a mail-order business prides itself in its ability to fill customers' orders in less than six calendar days, on average. periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. on one occasion when a sample of 39 orders was selected, the average number of days was 6.65 with a population standard deviation of 1.5 days. calculate the appropriate test statistic to test the hypothesis.
Therefore ,Since 2.7406 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal.
What is test statistics ?A test statistic is a statistic used for testing statistical hypotheses. A test statistic, which is a tally of a data set that can be used to conduct the test and boils the data down to a single figure, is a common way to characterize a hypothesis test.
Here,
a) H0 : u > 6 days
Ha : u < 6 days
Thus,
n=39
x'=6.65
α=1.5
b) test statistics = Z
Z=[tex]\frac{x'-u}{\alpha /\sqrt{n } }[/tex]
Z=[tex]\frac{6.65-6}{1.5 /\sqrt{39 } }[/tex]
Z=2.71
c) p value =P(Z<2.71)
p value = 1 - P(Z<2.71)
p value = 0.9966
Since 2.71 > 2.023, reject H0 and conclude that the mail-order business is not achieving its goal.
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Find the coordinates
(Simplify your answer.)
A (-6x, 4y)
D
B (-2x, -4y)
of midpoint D.
W
Midpoint Formula
X1+X2
Y1+y2
yı+y2)
2
M = (x¹+x²,
D = ([?],
C (8x, -2y)
Enter
The coordinates of midpoint D from the given triangle ABC is (-4x, 0).
What is the midpoint of a line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments.
The formula to find the midpoint of line segment is (x, y) = [(x1+x2)/2, (y1+y2)/2]
From the given figure, the coordinates are A(-6x, 4y) and B(-2x, -4y) and C(8x, -2y)
D(x, y)=[(-6x-2x)/2, (4y-4y)/2]
= (-4x, 0)
Therefore, the coordinates of midpoint D is (-4x, 0).
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Where’s the center of dilation located?
Answer: Dilations centered at the origin
Step-by-step explanation:
You can dilate figures on the coordinate plane. The origin is often used as the center of dilation. If you are dilating a figure centered at the origin, you can multiply the coordinates of the points in the preimage by the scale factor to determine the points in the image.
Consider the vector field F(x,y,z)=⟨−7y,−7x,9z⟩. Show that F is a gradient vector field F=∇V by determining the function V which satisfies V(0,0,0)=0.V(x,y,z)=
The gradient of the vector field F(x , y , z) = ⟨−7y , −7x , 9z⟩ be
F'(x , y , z) = < 0 , 0 , 9 > i.e. F'(x , y , z) = 9k.
Given, a vector field F(x , y , z) = <-7y , -7x , 9z>.
we have to find the gradient of the vector field F = ∇V.
Also, the function V satisfies the condition V(0 , 0 , 0).
As, we know to find the gradient of the vector field F(x , y , z) we differentiate the vector field or differentiate the vector field partially.
F(x , y , z) = <-7y , -7x , 9z>
F(x , y , z) = -7yi - 7xj + 9zk
On differentiating, we get
F'(x , y , z) = <d(-7y)/dx , d(-7x)/dy , d(9z)/dz>
F'(x , y , z) = < 0 , 0 , 9 >
F'(x , y , z) = 9k
So, the gradient of the vector field F(x , y , z) be, 9k
Hence, the gradient of the vector field F(x , y , z) be
F'(x , y , z) = < 0 , 0 , 9 >
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Amelia i buliding 3 quare garden bed that are all the ame ize. He arrange them ide by ide to eparate certain plant. Amelia want to know the total area of the garden
The total area of 3 square garden beds = [tex]3s^{2}[/tex] square units
What exactly is a square shape?A square is a closed two-dimensional shape with four equal sides and four vertices. Its opposing sides are perpendicular to each other. A square can also be thought of as a rectangle with equal length and width. Many things resemble the square shape when you look around.
What is the formula for the area of a square?A square's area is equal to its side. As a result, the area of a square equals Side2 square units. and the perimeter of a square is equal to four side units.
Given:
She want to bulid = 3 square garden beds
All are for same size,
Therefore total area of three square garden beds = 3 × area of one square garden bed
[tex]area of 3 garden beds = 3 ( s^{2} )\\area of 3 garden beds = 3 s^{2}[/tex]
Therefore, total area of 3 square garden beds = [tex]3s^{2}[/tex] square units
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Javier wants to prove that the base angles of an isosceles triangle are congruent. To do this, he draws triangle ABC,
with AB = BC. He will then prove that ZA and C are congruent by dividing triangle ABC into two triangles and
using triangle congruence.
Which of the following must be part of Javier's proof?
drawing a line parallel to AC through the midpoints of AB and BC
drawing a line parallel to BC through the midpoints of AB and AC
drawing a line perpendicular to AC through point B
drawing a line perpendicular to BC through point A
Answer:
C. Drawing a line perpendicular to [tex]\overline{AC}[/tex] through point [tex]B[/tex]
Step-by-step explanation:
The triangles formed by the perpendicular can be proved congruent by HL, and thus [tex]\angle A \cong \angle C[/tex] by CPCTC.
please answer question 10
Answer: A song costs 0.99$, and an album 9.99$
Step-by-step explanation:
14.94=5x+1y
22.95=3x+2y
29.88=10x+2y
22.95=3x+2y
subtract
6.93=7x
x=0.99$
y=9.99
Triangle bcd was dilated using the rule d subscript q, one-half. what are the values of the unknown measures? m∠c'b'd' = ° cq = b'd' =
The values of unknown measures are m∠C'B'D' = 95°, CQ = 6 and B'D' = 11
We are given that triangle BCD was dilated using the rule d subscript q, one-half.
Since the sum of the measure of all the angles in a triangle is 180°.
m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'
m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC (by dilation)
m∠C'B'D = 180° - 34° - 51° = 95°
[tex]\frac{B C}{B^{\prime} C^{\prime}}=\frac{B D}{B^{\prime} D^{\prime}}=\frac{36}{18}=2[/tex]
[tex]B^{\prime} D^{\prime}=\frac{1}{2} B D[/tex]
= 1/2(22)
=11
The dilated triangles are similar to each other.
Hence, we can say that ΔC'P'Q ∼ ΔCPQ,
[tex]\frac{C^{\prime} Q}{C Q}=\frac{C^{\prime} D^{\prime}}{C D}=\frac{D^{\prime} Q}{P Q}[/tex]
C Q= C'Q x [tex]\frac{C D}{C^{\prime} D^{\prime}}[/tex]
=C'Q x [tex]\frac{B C}{B^{\prime} C^{\prime}}[/tex]
=2 C'Q
=2(3)
=6
Thus, m∠C'B'D' = 95°, CQ = 6 and B'D' = 11.
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Answer: 95, 6, 11
Step-by-step explanation:
which expression represents w^-7 · w³ written in simplest form
Answer:
1/w^4
Step-by-step explanation:
What does the bar in a fraction mean?
Answer:
A fraction bar separates the numerator and denominator of a fraction. It indicates that a division of the numerator by the denominator will be performed.
Step-by-step explanation:
In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions. Fraction bars or fraction strips are a part-to-whole representational model. Each part of a fraction bar represents one unit out of a whole.
Answer:To separate the top and bottom numbers.
Step-by-step explanation:In math, a fraction bar can be defined as a visual representation of fractions that helps in comparing fractions and carrying out operations with fractions.
18 plums cost $12. how many pluma can u buy for $2
Answer: 18 plums cost 12 dollar means
1 plum costs 18 divide by 12
That means 1 dollar and 50 cents for 1 plum
that is 1 plum for 2 dollar
Answer:
Step-by-step explanation:
the answer its 3
There are 750 registered voters in one precinct in a primary selection 64 out of 100 voters actually vote how many persons in the precinct voted
Out of the 750 registered voters in the precinct, 480 people actually voted in the primary selection.
What is an expression? What is a expression? What is a mathematical equation? A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, of the given problem.We have 750 registered voters in one precinct and in a primary selection 64 out of 100 voters actually voted.
Out of 100 people, only 64 voted. So, the percentage of people voted can be calculated as follows -
64 = x% of 100
64 = x/100 x 100
x = 64%
So -
64% 0f 750
(64/100) x 750
480
Therefore, 480 people out of 750 registered voters in one precinct actually voted.
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Can Someone Please Solve This By Using The Formula a^2+b^2=c^2
Answer: a= 16
Step-by-step explanation:
a^2 + 30^2 = 34^2
a^2 + 900 = 1,156
a^2 = 256
a = 16
simplify the expression √24 + 3.85
Answer: Simplify each radical, then combine.
Exact Form:
2√6+ 3.85
Decimal Form:
8.74897948
What is 2’s absolute value
Answer:
2
Step-by-step explanation:
The way to find the absolute value of a number is to remove the negative symbol (-) if it has one.
The number 2 does not have one, so just leave it as it is.
Another way to think about it is, how far is 2 from 0 on a number line? Well, 2 is obviously 2 units away from 0.
If you can buy 2 bags of chips for $125. How many bags of chips can you get with $9,455 dollars? $7,600?
$1,000,000? Use a Ratio, ratio table, or equation to solve.
By using $9,455 dollars we can get 151 bags of chips and $7,600 dollars we can get 122 bags of chips and 16000 bags for $1,000,000 dollars.
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that you can buy 2 bags of chips for $125.
We need to find how many bags of chips we can get by $9,455 dollars,
$7,600 dollars and $1,000,000 dollars.
2/125=x/9455
Apply cross multiplication
2×9455=125x
18900=125x
Divide both sides by 125
x=151
So 151 bags we can get by using $9,455 dollars.
Now for $7,600 dollars.
2/125=x/7,600
2(7600)=125x
15200=125x
x=121.6 =122
So 122 bags we can get by using $7,600 dollars.
Now for $1,000,000
2/125=x/1,000,000
2000000=125x
Divide both sides by 125
16000=x
16000 bags for $1,000,000
Hence, 151 bags we can get by using $9,455 dollars, 122 bags we can get by using $7,600 dollars and 16000 bags for $1,000,000
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Which point is a solution to the system of inequalities graphed here?
y ≤ 2x + 2
y2-5x + 4
Both equations are satisfying by substituting (5, 0) in the system of inequalities.
What is a system of inequalities?
"A system of linear inequalities in two variables consists of at least two linear inequalities in the same variables. The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system and the graph of the linear inequality is the graph of all solutions of the system."
Given
System of inequalities graphed equation
y ≤ 2x + 2.................(1)
y ≥ -5x + 4................(2)
Substituting the point (5, 0) in equations 1 and 2
y ≤ 2x + 2
⇒ 0 ≤ 2(5) + 2
⇒ 0 ≤ 27
It is true
y ≥ -5x + 4
⇒ 0 ≥ -5(5) + 4
⇒ 0 ≥ -25 + 4
⇒ 0 ≥ -21
It is also true
In this option, Both equations are satisfying by substituting (5, 0)
Both equations are not satisfying by substituting (0, 5)
Hence, Both equations are satisfying by substituting (5, 0) in the system of inequalities given.
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Consider the inequalities -2r<10 and -6<-2x
The value of the variable 'x' is less than 3 and the value of the variable 'r' is greater than negative 5.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequalities are given below.
-2r < 10 and -6 < -2x
The value of the variable 'r' is given as,
-2r < 10
2r > -10
r > - 10/2
r > - 5
The value of the variable 'x' is given as,
-6 < -2x
2x < 6
x < 6 / 2
x < 3
The value of the variable 'x' is less than 3 and the value of the variable 'r' is greater than negative 5.
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what is the equation of the horizontal asymptote associated with this function . describe waht this means in termsof the mouths ph overtimer
The horizontal asymptote of function f(x) is y=6.5, which is a straight line, which means that even if time is infinite, the pH of the mouth will not rise above 6.5, which is the normal pH of the mouth.
A function's horizontal asymptote is a horizontal line with which the function's graph appears to coincide but does not actually coincide. The horizontal asymptote is used to determine the behavior of the function.
When either lim x f(x) = k or lim x - f(x) = k, the horizontal asymptote of a function y = f(x) is a line y = k. . It is commonly abbreviated as HA. In this case, k is a real number that the function approaches when x is extremely large or extremely small.However, the maximum number of asymptotes that a function can have is 2.
Given,
[tex]f(x)=\frac{6.5x^2-89.4x+3734}{x^2+576}[/tex]
The horizontal asymptote of the function f(x) can be determined by
[tex]y=\lim_{x \to \infty} f(x)\\\\=\lim_{x \to \infty}\frac{6.5x^2-89.4x+3734}{x^2+576}\\\\=\lim_{x \to \infty}\frac{x^2(6.5-\frac{89.4}{x}+\frac{3734}{x^2})}{x^2(1+\frac{576}{x^2})}\\\\=\lim_{x \to \infty}\frac{(6.5-\frac{89.4}{x}+\frac{3734}{x^2})}{(1+\frac{576}{x^2})}\\\\=\frac{(6.5-\frac{89.4}{ \infty}+\frac{3734}{ \infty})}{(1+\frac{576}{ \infty})}\\\\=\frac{6.5-0+0}{1+0}\\\\=\frac{6.5}{1}=6.5[/tex]
Thus, the horizontal asymptote of function f(x) is y=6.5 which is straight line which means even the time reaches infinity the pH of mouth will not increase more than 6.5, which is the normal pH of mouth.
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Your question is incomplete, here is the complete question.
The function [tex]f(x)=\frac{6.5x^2-89.4x+3734}{x^2+576}[/tex] models the pH level f(x) of a mouth x minutes after eating food containing sugar. The graph of this function is shown.
What is the equation is the horizontal asymptote associated with is function? Describe what this means in terms of mouth's pH level over time.
Find the area of a polygon with vertices A(–3, 1), B(–3, 4), C(7, 1), D(7, 4)
The area of the given polygon is 30 square units.
How to calculate the area of a triangle with coordinates of its vertices?The area of a triangle can be calculated using the formula 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)] where (x₁, y₁), (x₂, y₂) and (x₃, y₃) are the coordinates of its vertices. This formula is also useful in finding the area of any polygon with given coordinates.
The area of the given polygon can be calculated by the expression of the area of triangle as 1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)].
The given polygon can be divided into two ΔABC and ΔACD,
Then, the area is given as follows,
Area of ΔABC + Area of ΔACD
= 1/2|[-3(4 - 1) + -3(1 - 1) + 7(1 - 4)]| + 1/2|[-3(1 - 4) + 7(4 - 1) + 7(1 - 1)]|
= 1/2 × 30 + 1/2 × 30
= 30
Hence, the area of the given polygon is 30 square units.
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A traveler is walking on a moving walkway airport. The traveler must walk back on the walkway to get a bag he forgot. The travelers ground speed is 2ft/s against the walkway and 8ft/s with the walkway. What is the travelers speed off the walkway? What is the speed of the moving walkway?
The travelers speed off the walkway is
The speed of the moving walkway is
If a traveler is walking on a moving walkway airport. The traveler's speed off the walkway is 5 ft/sec and the speed of the moving walkway is 3 ft/sec.
What is speed?Speed can simply be defined as how fast an object move.
Let t represent the traveler's speed in ft/sec
Let w represent the walkway's speed in ft/sec
So,
t-w =2
t+w=8
Add the equation
2t =10
Divide both side by 2t
t= 10/2
t=5fr/sec ( traveler's speed )
Speed of moving walkway
t+w =8
5+w=8
w=8-5
w=3ft/sec
Therefore the traveler's speed off the walkway is 5 ft/sec and the speed of the moving walkway is 3 ft/sec.
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A line passes through the points (4,19) and (8,23) Write a linear function rule in terms of x and y for this line.
the linear function rule = y __
The equation of line passing through points [tex](x_{1} ,y_{1} )[/tex] = (4,19) and [tex](x_{2},y_{2})[/tex] =
( 8,23 ) is represented in the slope intercepted form as y = x + 15
What is the Slope Intercept Form ?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula,
y = mx + b. (0, b) The symbol b in the formula stands for the y value of the y intercept point.
According to the given information
We are given with two points
[tex](x_{1} ,y_{1} )[/tex] = (4,19)
[tex](x_{2},y_{2})[/tex] = ( 8,23 )
So
Now we need to find the slope of the given line having the above coordinate points
m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
Putting the values
We get
m = [tex]\frac{23-19}{8-4}[/tex]
m = [tex]\frac{4}{4}[/tex]
m = 1
Equation of line passing through points [tex](x_{1} ,y_{1} )[/tex] = (4,19) and having
slope = 1
[tex]y-y_{1} = m(x-x_{1})[/tex]
y - 19 = x - 4
y = x + 15
So
The equation of line passing through points [tex](x_{1} ,y_{1} )[/tex] = (4,19) and [tex](x_{2},y_{2})[/tex] =
( 8,23 ) is represented in the slope intercepted form as y = x + 15
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Tickets to a basketball game can be ordered online for a set price per ticket plus a $5. 50 service fee. The total cost in dollars for ordering 5 tickets is $108. 0. Which linear function represents c, the total cost, when x tickets are ordered? (a service fee is a single fee applied to the total, no matter the number of tickets purchased). C(x) = 5. 50 + 20. 50x c(x) = 5. 50x + 20. 50 c(x) = 5. 50 + 21. 60x c(x) = 5. 50x + 21. 60.
The linear function that represents c, the total cost, when x tickets are ordered is
c=5.50+20.50x
What is the equation in math?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
What are the 3 types of equations?There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.
Let
The overall price is c.
the quantity of tickets, x
the price of one ticket, excluding service charges, is z.
Knowing this
108=5.50+5z
finding z
z=20.50
therefore
The linear equation equals
c=5.50+20.50x
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Which expression does not factor? m3 1 m3 – 1 m2 1 m2 – 1
The expression that does not factor on the mentioned is m² + 1.
Why it cannot be factor?Because other expression can be factored, while m² + 1 has no factor form. For make it clear we can calculate to find the form expression and find the calculate power or result.
m³ + 1 =
The formula to calculate it is, a³ + b³ = m³ + 1³ And then it could be, (m + 1) (m² - m + 1).m³ - 1 =
The formula to calculate it is, a³ + b³ = m³ - 1³ a³ + b³ = (a + b) (a² - ab + b²)And then the power could be, (m - 1)(m² + m + 1²) = (m-1)(m² + m + 1).m² - 1 =
The formula to calculate it is, a² - b² = (a + b)(a - b).and then it could be, m² - 1 = (m + 1)(m - 1).
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Write at least 6 equivalent expressions to the expression below.
12x - 6
Answer:
Here are six equivalent expressions to 12x - 6:
6(2x - 1)
3(4x - 2)
2(6x - 3)
1(12x - 6)
4(3x - 1)
(12x - 6) + 0
These expressions are all equivalent to 12x - 6 because they all have the same value, regardless of the value of x. This is because the terms on the right side of the equation cancel out, leaving only the constant value on the left side. For example, in the first expression, 6(2x - 1), the 2x and -1 terms cancel out, leaving only 6. This is the same for the other expressions listed above.
Step-by-step explanation:
Answer:
12x - 612x + (-6)12(x) + (-1)(6)12(x - 0.5)12x + (-1)(-6)12(x - 1/2)Step-by-step explanation:
Here are six equivalent expressions to the given expression:
12x - 612x + (-6)12(x) + (-1)(6)12(x - 0.5)12x + (-1)(-6)12(x - 1/2)Note that in each of the above expressions, the value of 12x - 6 is preserved, but the terms and the order of operations may be different. For example, in the second expression, the subtraction has been expressed as addition with a negative number, and in the fourth and sixth expressions, the subtraction has been expressed as multiplication with a fraction.