How many triangles are formed by dawing all the diagonals from a single vertex of a convex polygon

Answers

Answer 1

(n-2) triangles can be formed by drawing all the diagonals from a single vertex. n represents the number of sides the polygon has.

Answer 2

(n-2) triangles can be formed by drawing all the diagonals from a single vertex.

What is Polygon?

a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

Given a convex polygon with n vertices, the number of triangles that can be formed by drawing all the diagonals from a single vertex can be calculated.

a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge

Let's consider a convex polygon with 4 vertices.

(n-2) triangles can be formed by drawing all the diagonals from a single vertex.

Hence, (n-2) triangles can be formed by drawing all the diagonals from a single vertex.

To learn more on Polygon click:

https://brainly.com/question/24464711

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Related Questions

A reader of a book wants to estimate the mean word length in the book they are currently reading. they randomly select 19 pages from the book and count the length of 5 words they randomly selected on each of those pages. the table shows the results from the survey. using the sample results estimate the mean word length of any word in the book.
a.5.22 letters
b.5.49 letters
c.5.77 letters
d.5.92 letters

Answers

Answer:

B-5.49

Step-by-step explanation:

Use this function below to help find F(2)?

Answers

[tex]F(t) = 2 * \frac{1}{ 2^{3t} } [/tex] - Subsitiute 2 for t
[tex]F(2) = 2 * \frac{1}{ 2^{3*2} } [/tex]
[tex]F(2) = 2 * \frac{1}{ 2^{6} } [/tex]
[tex]F(2) = 2 * \frac{1}{64} [/tex]
[tex]F(2) = \frac{1}{32} [/tex]

Someone help me plz .....

Answers

I believe it's 3. Are those the only options?

The smaller circle inside the larger circle has a radius labeled as 4.
In a circle, all radii are congruent.
OP is also a radius of the smaller circle, so OP = 4.

Abcd is a parallelogram find the measure of a if b is (7x+13)degrees and d d is (8x-8)degrees brainly

Answers

7x+13=8x-8
13=1x-8
21=1x
21=x

WILL GIVE MEDAL AND FAN! your anniversary is usually when you are given _____ by a company
A. an award
B. a job review and possible increase in pay
C. an evaluation
D. a promotion

Answers

Your anniversary is usually when you are given a job review and possible increase in pay by a company. Most companies will review your performance for the past year and offer an increase in pay due to yearly inflation, or cost of living.

Answer: Option 'B' is correct.

Step-by-step explanation:

Your anniversary is usually when you are given a job review and possible increase in pay.

As in a job, job review is given at the time of anniversary, then on the basis of their performance there may be increase in pay.

So, Meaning of anniversary in a official way is when work performance of an individual is discussed and if there is good record , there is an increment.

Hence, Option 'B' is correct.

A machine is set up to cut metal strips of varying lengths and widths based on the time (t) in minutes. The change in length is given by the function I(t)=t^2-squrt(t),, and the change in width is given by w(t)=t^2-2t^1/2. Which function gives the change in area of the metal strips?

Answers

If your choices are the following:
a. a(t) = t^4 + 2t
b. a(t) = t^4 + 2t + 3t^(5/2)
c. a(t) = t^4 - 3t^(5/2) + 2t`
d. a(t) = t^4 + 2t - 2t^(1/2) + sqrt(t)

The answer is letter c.a(t) = t^4 - 3t^(5/2) + 2t`
Solution:
Area= length times width
Then to get the time, a=a(t), l=l(t), and w=w(t)
So, if Area= l times width
a(t)= l(t) • w(t)
a(t)=[t^2-squrt(t)] • [t^2-2t^1/2]
a(t) = [t^2 - t^(1/2)] • [t^2 - 2t^(1/2)]
=t^4 - 3t^(5/2) + 2t

Answer:

'a(t)=t^4-3t^(5/2)+2t'

what are the solutions to the equion

plz answer right no it is 14

Answers

For this case we have the following equation:
[tex]x^2 = 169[/tex]
What we must do for this case is to clear the value of x.
To do this, remember that when clearing you have two solutions.
A solution is positive.
A solution is negative.
We have then:
[tex]x = +/- \sqrt{169} x = +/- 13 [/tex]
Therefore, the solutions are:
[tex]x1 = 13 x2 = -13[/tex]
Answer:
the solutions to the equation are:
[tex]x1 = 13 x2 = -13[/tex]

Find the image of z(1,1) after two reflections first across L1 and then across L2

L1: y=2 L2: x-axis

L1: x=3 L2: y=2

Answers

I’m lab cooking up like rick s

Find the surface area of this square pyramid. The base has area 1764 cm^2 and perimeter 168 cm.

4116 cm^2

4704 cm^2

31,038 cm^2

2940 cm^2

Answers

In your question, there is a missing data: the slant height of the pyramid.

Indeed, the total surface area can be found adding the base surface plus the lateral surface. In order to find the lateral surface, you can use the formula:
LS = (slant height × perimeter) / 2

Therefore:
if your slant height is 28, your answer will be 4116cm²
if your slant height is 35, your answer will be 4704cm²
if your slant height is 348.5, your answer will be 31038cm²
if your slant height is 14, your answer will be 2940cm²

what is the vertex of the parabola

Answers

Let's consider the equation of parabola, y = a·(x - α)·(x - β)

where α, β are the x-intercepts.

From the given graph, the y-intercept is (0, -3).

From the given graph, the x-intercept are (-1, 0) and (3, 0) i.e. α = -1, β = 3.

So the equation of parabola would be now, y = a·(x + 1)·(x - 3)

We can plug the y-intercept (0, -3) in the equation to find value of 'a'.

-3 = a·(0+1)·(0-3)

-3 = -3a

a = 1

So the equation of parabola would be now, y = (x + 1)·(x - 3) = x² - 2x - 3

Comparing it with y = ax² + bx + c

The x-coordinate of vertex would be, [tex] x = \frac{-b}{2a} = \frac{-(-2)}{2(1)} =\frac{2}{2} = 1 [/tex]

the y-coordinate of vertex would be, y = (1)² - 2(1) - 3 = -4.

Hence, vertex would be (1, -4).

If you flip three fair coins, what is the probability that you'll get all three tails?

Answers

probability of getting a tail = 1/2
pr(3 Tail) = 1/2 × 1/2 × 1/2
= 1/8

Let H be the event that head occurs and let T be the event that tail.

Then the complete Sample Space,S for the experiment given in the question is:

S={ HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}

As we can see the total number of elements in the sample space is 8. Let us represent this by the letter N.

Therefore, N=8

Now, the event of interest to us is TTT and it's occurrence is once. Let represent this by the letter E.

Therefore, E=1

Thus, the probability of the event E occurring is given as:

[tex] P(E)=\frac{E}{N}=\frac{1}{8} [/tex]

[tex] \frac{1}{8} [/tex] is the required answer. This can be represented in percentage too as:

[tex] \frac{1}{8}\times 100=12.5 [/tex]%

osha requires a ladder to meet the ground at 75 degree angle in order to function as safely as possible. of you need the ladder to reach a ledge 20 feet up a vertical wall, how long does the ladder need to be?

Answers

Draw a right triangle with a right angle and a 75 deg angle at the bottom.
The hypotenuse is the length of the ladder.

sin A = opp/hyp

sin 75 = 20/hyp

hyp = 20/sin 75 = 20.7

Answer: 20.7 ft

A contractor purchases 7 dozen pairs of padded work gloves for $94.92. He incorrectly calculates the unit price as $13.56 per pair for the expense report. What is the correct unit price? What is the error?

Answers

94.92/(7*12)=1.13 each pair
13.56-1.13=12.43 absolute error

The correct unit price for the work gloves is $1.13 per pair, and the error in the reported unit price is $12.43 per pair, as the contractor incorrectly reported it as $13.56 per pair.

The question is asking to calculate the correct unit price for the padded work gloves purchased by the contractor and to identify the error in the calculation provided in the expense report.

Firstly, let's determine the total number of pairs of gloves. Since 1 dozen represents 12 items, 7 dozen pairs of gloves will be [tex]7 \times 12 = 84[/tex] pairs of gloves.

Now, to find the correct unit price, we divide the total cost by the total number of pairs:

Unit Price = Total Cost / Total Number of Pairs

Unit Price = $94.92 / 84 pairs

Unit Price = $1.13 per pair

The incorrect unit price was calculated as $13.56 per pair. Therefore, the error in the calculation is:

Error = Incorrect Unit Price - Correct Unit Price

Error = $13.56 - $1.13

Error = $12.43 per pair

The contractor overestimated the unit price by $12.43 per pair.

Algebra 2 help please? And explanation too. Thanks!

5. Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary.

2 log 4 – log 3 + 2 log x – 4 = 0
(1 point)
12.3308
43.3013
86.6025
1,875,

Answers

Use the log properties: LogA+logB=log(A*B) and log(A/B)=logA-logB. ALso NlogA=log(A^N). So 2log4=log4^2=log 16. 2logx=logx^2. Then we have log16-log3+logx^2-4=0. Bring the 4 to the other side: log16-log3+logx^2=4 Combine using the properties into one log: log(16/3)*x^2=4. With log, the understood base is 10. log _(10) [ (16/3)*(x^2]=4 where_10 means base 10. We know log_b M=N means b^N=M by the definition of log. We use that here and change log into an exponential equation: 10^4=(16/3)x^2 10000 *(3/16)=x^2 Taking the square root we have + or- 43.30127. We only want the positive solution since we can only take the log of positive numbers. Our answer rounded is 43.3013.

choose the most appropriate strategy and then use it to solve the quadratic equation.
7. (x-8)^2=121
8. 2a^2=8a-6
9. x^2+12x+36=4
10. x^2-x+30=0

Answers

(x-8) ^ 2 = 121
(x-8) = + / - root (121)
x = 8 +/- root (121)
The solutions are:
x1 = 8 + root (121)
x2 = 8 - root (121)
2a ^ 2 = 8a-6
2a ^ 2-8a + 6 = 0
a ^ 2-4a + 3 = 0
(a-1) (a-3) = 0
The solutions are:
a1 = 1
a2 = 3
x ^ 2 + 12x + 36 = 4
x ^ 2 + 12x + 36-4 = 0
x ^ 2 + 12x + 32 = 0
(x + 4) (x + 8) = 0
The solutions are:
x1 = -8
x2 = -4
x ^ 2-x + 30 = 0
x = (- b +/- root (b ^ 2 - 4 * a * c)) / 2 * a
x = (- (- 1) +/- root ((- 1) ^ 2 - 4 * (1) * (30))) / 2 * (1)
x = (1 +/- root (1 - 120))) / 2
x = (1 +/- root (-119))) / 2
x = (1 +/- root (119) * i)) / 2
The solutions are:
x1 = (1 + root (119) * i)) / 2
x2 = (1 - root (119) * i)) / 2

Jose wants to rewrite 24+9 using the greatest common factor and the distributive property. Which expression should he write?

Answers

First get the factors of 24: 2*2*2*3Then the factors of 9: 3*3 Comparing the factors, the GCF is 3 Then you can rewrite the expression: 3*8 + 3*3 At this point, I'm not sure whether what you mean is really distributive property or not since this case is more of a factoring. 3*(8+3)

Answer:

3(8+3)

Step-by-step explanation:

Solve the following system of equations. Express your answer as an ordered pair in the format (a,b), with no spaces between the numbers or symbols.

2x+7y=4
-4x-3y=14

how would i go about this? please help!!,

Answers

So we have 2x + 7y = 4 ---------(1) -4x - 3y = 14 -------(2) Multiplying (1) by 2. 4x + 14y = 8 -----(3) (2) + (3) we have 11y = 22 y = 2 If y = 2 then we substitute y into (2), and so we have: -4x - 3(2) = 14; -4x - 6 = 14; So -4x = 14 + 6 = 20 -4x = 20 and so x = -5 then our answer takes the form (-5,2)

Rudy collects baseball cards, and he currently has 300 cards. Starting tomorrow, he will purchase 1 pack of 15 baseball cards every day, and every pack he purchases will contain 1 card of a member of his brother???s favorite team. Every time Rudy purchases a pack of cards, he will immediately trade the card of the member of his brother???s favorite team to his brother for 3 cards of members of a different team. Which of these recursive formulas produces the sequence that represents the number of baseball cards that Rudy will have at the end of each day, starting today?

Answers

Answer: The equation to find the number of cards could be: c = 300 + 17d, where c equals the total number of cards and d represents the number of days.

The 300 value is the starting amount of cards that Rudy has.

The 17 represents the number of cards that he is getting per day. It started at 15 because that is the amount in a pack of cards. However, he trades one to his brother and gets 3 in return.

15 - 1 + 3 = 17 extra cards per day

Emma likes to knit hats and mittens for friends and family. Last fall, she knitted 4 hats and 3 pairs of mittens, which took a total of 46 hours. This fall, she knitted 2 hats and 1 pair of mittens, which took a total of 18 hours. If each hat and each pair of mittens takes the same amount of time to knit, how long does it take Emma to knit a hat and a pair of mittens?

Answers

Final answer:

Emma takes 4 hours to knit a hat and 10 hours to knit a pair of mittens, which was determined by solving two linear equations based on the time she spent knitting during two different falls.

Explanation:

Emma likes to knit hats and mittens, and we need to find out how long it takes her to knit a hat and a pair of mittens individually. Given that last fall she knitted 4 hats and 3 pairs of mittens in 46 hours, and this fall she knitted 2 hats and 1 pair of mittens in 18 hours, we can set up two equations to solve for the time it takes to knit each item.

Let's define H as the number of hours it takes to knit one hat and M as the number of hours it takes to knit one pair of mittens. The equations based on the given information are:

4H + 3M = 46 (Last fall's knitting)

2H + 1M = 18 (This fall's knitting)

To solve these equations, multiply the second equation by 2 to align the hats:

2(2H + 1M) = 2(18)

4H + 2M = 36

Now subtract this equation from the first equation to find M:

4H + 3M - (4H + 2M) = 46 - 36

M = 10

Substituting M back into the second original equation:

2H + 1(10) = 18

2H = 8

H = 4

Emma takes 4 hours to knit a hat and 10 hours to knit a pair of mittens.

Angela spent $30.00 at a resturaunt. if she leaves a 15% tip, how much wll her total bill be

Answers

Answer: Her total bill will be: " $34.50 " .
_____________________________________________________
Explanation:
_____________________________________________________
15% = 15/100 = 15 ÷ 100 = 0.15 .

$30 + {0.15 * $30} = $30 + ($4.50) = " $34.50 " .
_____________________________________________________

Note: "15% of $30 = (0.15 * $30) = $4.50 .

We add the "$4.50" tip to the $30.00 that is spent; to get: " $34.50 " .
_____________________________________________________

Final answer:

Angela's total restaurant bill, after adding a 15% tip to her $30.00 original charge, will be $34.50.

Explanation:

To find out how much Angela's total bill will be after leaving a 15% tip at a restaurant, you first need to calculate the tip amount and then add it to the original bill. You calculate the tip by converting the percentage to a decimal and then multiplying by the cost of the meal. In this case, 15% of $30.00 is found by multiplying $30.00 by 0.15 which gives you $4.50. After calculating the tip amount, add it to the original bill to get the total amount Angela will pay.

Tip: $30.00 * 0.15 = $4.50.

Total bill: $30.00 + $4.50 = $34.50.

Therefore, Angela's total bill, including the 15% tip, will be $34.50.

The diameter of a sphere is 8 centimeters. What is the volume of the sphere? Use 3.14 for pi. Enter your answer, as a decimal, in the box. Round only your final answer to the nearest tenth. cm³

Answers

The volume of a sphere is given by the equation [tex]V= \frac{4}{3} \pi r^3[/tex], where r is the radius.

We are given the diameter of the sphere, but recall that the diameter is twice the radius: [tex]d=2r[/tex]. So the radius is half of the diameter: [tex]r= \frac{1}{2}d[/tex].

Half of 8 cm is 4 cm.

We substitute this for r in the equation and we use 3.14 for π.

[tex]V= \frac{4}{3}(3.14)(4)^3= \frac{(4^4)(3.14)}{3}=267.9 \ cm^3 [/tex]

the steps for this are below

recall volume of sphere formula is
[tex] \frac{4}{3} \pi \times r {}^{3} [/tex]
we know the diameter so to get the radius we just divide the diameter by 2 to get the radius
[tex]r = 8 \div 2[/tex]
[tex]r = 4[/tex]
know we can plug it into the volume of a sphere formula and solve using 3.14 for pi
[tex]v = (4 \times 3.14 \times 4 {}^{3} ) \div 3[/tex]
simplify the parentheses and get
[tex]v = \frac{803.84}{3} [/tex]
FINAL ANSWER (rounding to nearest tenth)
[tex]v = 267.9 \: cm {}^{3} [/tex]

f(x) = (x − 3)(x + 3)[x − (2 − i)][x − (2 + i)] The function has real roots and imaginary roots.

Answers

The real roots are 3 and -3.
Imaginary roots:-
x - (2 - i) = 0
x = 2 -i is one imaginary root and the other is 2 + i

Answer:

The function has

2 real roots and

2 imaginary roots.

The vertex of this parabola is at (3, -2). When the x-value is 4, the y-value is 3. What is the coefficient of the squared expression in the parabola's equation?

Answers

the equation of a parabola in its vertex form is y=a(x-h)²+k, where (h, k) is the vertex of the parabola.
in this case, h=3, k=-2, so y=a(x-3)-2
plug (4,3) in the equation: 3=a(4-3)²-2, a=5
so the coefficient of the squared expression is 5.

Answer:[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]

Step-by-step explanation:

Given

Vertex of Parabola is [tex]\left ( 3,-2\right )[/tex]

and parabola passes through [tex]\left ( 4,3\right )[/tex]

Let us take a parabola of the form

[tex]\left ( y-y_0\right )^2=4a\left ( x-x_0\right )[/tex]

And here [tex]\left ( x_0,y_0\right ) is \left ( 3,-2\right )[/tex]

therefore

[tex]\left ( y+2\right )^2=4a\left ( x-3\right )[/tex]

Now put [tex]\left ( 4,3\right)[/tex] as it lies on parabola

[tex]\left ( 3+2\right )^2=4a\left ( 4-3\right )[/tex]

[tex]a=\frac{25}{4}[/tex]

Thus Equation of parabola is

[tex]\left ( y+2\right )^2=25\left ( x-3\right )[/tex]

You are shopping for T-shirts. Clothing Warehouse sells 3 T-shirts for $52. The Scene sells 2 T-shirts for $83. New Threads sells 4 T-shirts for $127. Which store has the best deal?

Answers

The 3 for $52 each shirt is 17.33

A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times. What is the experimental probability of the arrow stopping over Section 3? Section 1: 18 Section 2: 30 Section 3 :32

Answers

the answer is 32/80 because the arrow stopped on section three 32 times out of the 80 spins

Answer: [tex]\dfrac{2}{5}[/tex]

Step-by-step explanation:

From the given table, The number of times arrow stops over Section 3 = 32

The total number of times spinner spins = 80

Now, the experimental probability of the arrow stopping over Section 3 is given by :-

[tex]P(S-3)=\frac{32}{80}\\\\\Rightarrow P(S-3)=\dfrac{2}{5}[/tex]

Hence, the experimental probability of the arrow stopping over Section 3 is [tex]\dfrac{2}{5}[/tex]

PLEASE MATH HELP WILL GIVE BRAINLIEST!!
The center of a circle is located at (-5, 2), and the radius of the circle is 5 units.

What is the equation of the circle in standard form?
Question 1 options:

(x−5)2 + ( y+2)2 = 10

(x+ 5)2 + (y−2)2 = 25

(x+5)2 + (y−2)2 = 10

(x−5)2 + (y+2)2 = 25

Answers

Hello,

Answer B

(x-(-5))²+(y-2)²=5²

(x+5)²+(y-2)²=25

Help me on this please

Answers

First you have to find the area of the rectangle.
A=Lw
A=91(68)
A=6,188 m
Next you have to find the area of the semi- circles.
A of circle= radius to the second power times pi
A=68x68
A= 4,624
Multiply the area of the semi- circles by 2 since there are two of them. That will give you 9,248 m. Add 9,248 with 6,188 and that will give you your final answer which is 15,436 m.

it is 6188 because 91 times 68 is 6188

Crop researchers plant 15 plots with a new variety of corn. The yields in bushels per acre are: 138.0 139.1 113.0 132.5 140.7 109.7 118.9 134.8 109.6 127.3 115.6 130.4 130.2 111.7 105.5 Assume that bushels per acre. a) Find the 90% confidence interval for the mean yield for this variety of corn. b) Find the 95% confidence interval. c) Find the 99% confidence interval. d) How do the margins of error in (a), (b), and (c) change as the confidence level increases?

Answers

There is a relationship between confidence interval and standard deviation:
[tex]\theta=\overline{x} \pm \frac{z\sigma}{\sqrt{n}}[/tex]
Where [tex]\overline{x}[/tex] is the mean, [tex]\sigma[/tex] is standard deviation, and n is number of data points.
Every confidence interval has associated z value. This can be found online.
We need to find the standard deviation first:
[tex]\sigma=\sqrt{\frac{\sum(x-\overline{x})^2}{n}[/tex]
When we do all the calculations we find that:
[tex]\overline{x}=123.8\\
\sigma=11.84[/tex]
Now we can find confidence intervals:
[tex]($90\%,z=1.645): \theta=123.8 \pm \frac{1.645\cdot 11.84}{\sqrt{15}}=123.8 \pm5.0\\($95\%,z=1.960): \theta=123.8 \pm \frac{1.960\cdot 11.84}{\sqrt{15}}=123.8 \pm 5.99\\ ($99\%,z=2.576): \theta=123.8 \pm \frac{2.576\cdot 11.84}{\sqrt{15}}=123.8 \pm 7.87\\[/tex]
We can see that as confidence interval increases so does the error margin. Z values accociated with each confidence intreval also get bigger as confidence interval increases.
Here is the link to the spreadsheet with standard deviation calculation:
https://docs.google.com/spreadsheets/d/1pnsJIrM_lmQKAGRJvduiHzjg9mYvLgpsCqCoGYvR5Us/edit?usp=sharing

a) For a 90% confidence interval: (117.838, 130.056)

b) For a 95% confidence interval: (117.543, 130.352)

c) For a 99% confidence interval: (113.816, 134.078)

d) As the confidence level increases, the margins of error also increase, resulting in wider confidence intervals, indicating greater certainty in the estimation of the true population mean yield.

To find the confidence intervals, we first calculate the sample mean and standard deviation of the yields. Then, we use the t-distribution with degrees of freedom (n-1) to determine the critical values for the given confidence levels. Finally, we use these critical values along with the sample mean and standard deviation to calculate the margins of error and construct the confidence intervals.

a) For a 90% confidence interval:

Sample mean = 123.947

Sample standard deviation = 11.669

Margin of error = t * [tex](s / sqrt(n)) = 1.761 * (11.669 / sqrt(15)) ≈ 6.109[/tex]

90% confidence interval: (123.947 - 6.109, 123.947 + 6.109) ≈ (117.838, 130.056)

b) For a 95% confidence interval:

Margin of error = [tex]2.145 * (11.669 / sqrt(15)) ≈ 7.404[/tex]

95% confidence interval: (117.543, 130.352)

c) For a 99% confidence interval:

Margin of error = [tex]2.947 * (11.669 / sqrt(15)) ≈ 10.131[/tex]

99% confidence interval: (113.816, 134.078)

d) As the confidence level increases, the margin of error also increases because the critical value from the t-distribution becomes larger, resulting in wider confidence intervals. This reflects the increased certainty associated with higher confidence levels.

The margins of error increase as the confidence level increases, indicating wider confidence intervals and greater certainty in the estimation of the true population mean yield.

I need help to answer this please thank you ?

Answers

it's 11 dollars because 82.50/7.5 = 11

What is the value of x in the proportion StartFraction 6 x plus 1 over 7 EndFraction equals StartFraction 18 x minus 2 over 14 EndFraction?
A. 0
B. 3
C. two-thirds
D. one-fourteenth

Answers

The correct answer is: [C]: " two-thirds " .
____________________________________________________
" x = " [tex] \frac{2}{3} [/tex] " ; which is: " two-thirds " .
____________________________________________________
Explanation:
____________________________________________________

Given: " [tex] \frac{6x + 1}{7} = \frac{18x-2}{14} [/tex] " ; Solve for "x" ;
____________________________________________________
First, multiply the first fraction by "[tex] \frac{2}{2} [/tex]" ;
{ since: "[tex] \frac{2}{2} [/tex] = 1" ; and since any value, multiplied by "1" results in that exact same value. By multiplying the first fraction by: "[tex] \frac{2}{2} [/tex]" , we can get the "denominator" in the first fraction equal to the "denominator" of the second fraction.

→ [tex] \frac{2}{2}*( \frac{6x + 1}{7})=\frac{2(6x+1)}{2(7)} =

"\frac{2(6x+1)}{14} [/tex]" .
___________________________________________________________
Note the "distributive property of multiplication" :
_______________________________________________________
a(b + c) = ab + ac ;

a(b – c) = ab – ac .
_______________________________________________________
As such, take the "numerator" ; which is:

" 2(6x + 1) " ; and expand:

→ = (2*6x) + (2*1) = " 12x + 2 " ;

Now, we can rewrite the entire expression:
________________________________________
"[tex] \frac{12x+2}{14} [/tex]" ; and we can rewrite the entire equation:
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→ " [tex] \frac{12x+2}{14} [/tex] = \frac{18x-2}{14} [/tex] " ;

Let us simplify this: " 12x + 2 = 18x – 2 " ; Solve for "x" ;
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→ 18x – 2 = 12x + 2 ;

→ Subtract "12x" from each side of the equation; and subtract "2" from each side of the equation:

→ 18x – 2 – 12x – 2 = 12x + 2 – 12x – 2 ;

to get:

→ 6x – 4 = 0 ;

Add "4" to each side of the equation:

→ 6x – 4 + 4 = 0 + 4 ;

to get:

→ 6x = 4 ;

Divide each side of the equation by "6" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ 6x / 6 = 4 / 6 ;

→ x = 4/6 ; → "4/6" = "(4÷2)/(6÷2)" = "2/3" .

→ x = 2/3 ; → x = " [tex] \frac{2}{3} [/tex] " ; which is "two-thirds" ;

→ which is: Answer choice: [C]: " two-thirds" .
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The correct value of x is [tex]\frac{2}{3}[/tex].

To find the value of x in the proportion [tex]\frac{6x+1}{7} = \frac{18x-2}{14}[/tex], follow these steps:

Cross-multiply to eliminate the fractions. Multiply 7 by (18x - 2) and 14 by (6x + 1):

7(18x - 2) = 14(6x + 1)

Expand both sides:

126x - 14 = 84x + 14

Move all terms involving x to one side and constant terms to the other side:

126x - 84x = 14 + 14

Simplify the equation:

42x = 28

Divide both sides by 42 to solve for x:

x = 28 ÷ 42 = [tex]\frac{2}{3}[/tex]

Therefore, the value of x is [tex]\frac{2}{3}[/tex] and the correct answer is option C.

Complete question: What is the value of x in the proportion [tex]\frac{6x+1}{7} = \frac{18x-2}{14}[/tex]?

A. 0

B. 3

C. [tex]\frac{2}{3}[/tex]

D. [tex]\frac{1}{14}[/tex]

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