The requried inverse function is [tex]f^{-1}(y) = (y + 3)/2[/tex].
To find the inverse of y = 2x - 3, we need to solve for x in terms of y.
Starting with y = 2x - 3:
Add 3 to both sides: y + 3 = 2x
Divide both sides by 2: (y + 3)/2 = x
Therefore, the inverse of y = 2x - 3 is:
x = (y + 3)/2
We can also express this as:
[tex]f^{-1}(y) = (y + 3)/2[/tex]
Thus, the inverse function is [tex]f^{-1}(y) = (y + 3)/2[/tex]
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solve 5 to the power of x+2 is less than or equal to 3 to the power of x
Step-by-step explanation:
5^(x+2) <= 3^x
5^x * 5^2 <= 3^x
25 <= 3^x / 5^x
25<= (3/5)^x LOG both sides
log 25 <= x log (3/5)
log 25 / log (3/5) <= x
- 6.3 <= x
What happens to the mode of the data set shown below if the number 6 is added? A The mode will change to two numbers. B The mode will increase by 4. C The mode will change to one number. D The mode will increase by 2.
Adding the number 6 to the given dataset did not affect the mode, as the number 19 still appeared the most frequently in the new dataset. (option c).
Now, if we add the number 6 to this dataset, we need to determine how this will affect the mode. We can start by looking at the number 19, which was the original mode. If the number 19 still appears the most frequently in the dataset after the addition of the number 6, then the mode will remain 19. However, if another number appears more frequently than 19 after the addition of 6, then the mode will change.
In this case, the number 6 does not appear anywhere in the original dataset, so it cannot be the mode. Therefore, the mode can either remain as 19 or change to a new number, depending on whether any other number appears more frequently than 19 after the addition of 6.
To determine if the mode changes, we need to calculate the frequency of each number in the new dataset. After adding 6, the dataset becomes:
18 24 19
19 18 20
26 25 19
6
From this dataset, we can see that the number 19 still appears twice, while all other numbers appear only once. Therefore, the mode of the new dataset is still 19, and the answer to your question is (C) "The mode will change to one number."
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Complete Question:
What happens to the mode of the data set shown below if the number 6 is added?
18 24 19
19 18 20
26 25 19
A The mode will change to two numbers.
B The mode will increase by 4.
C The mode will change to one number.
D The mode will increase by 2.
Faster please!! thanks!! 30 points + brainliest!!
Which is an example of simple random sampling created from each given population?
An example of simple random sampling is given as follows:
C. In a bag of more than 500 marbles, reaching the hand into a bag and drawing 25 of them.
How are samples classified?Samples may be classified as:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.Hence the samples for this problem are classified as follows:
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What is the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6)?
The vector in component form whose tail is the point (−1,5), and whose head is the point (8,−6) is (-9, 11)
What is a vector?A vector is a physical quabntity thet has both magnitude and direction.
To find the component form of the vector whose tail is the point (−1,5), and whose head is the point (8,−6), we proceed as folows
Since we have the points (-1, 5) and (8, -6) and we want the head to be at (8, -6),
Let A = (8, -6) and B = (-1, 5)
So, AB = B - A
= (-1, 5) - (8, -6)
= (-1 - 8), (5 - (-6))
= (-9, 5 + 6)
= (-9, 11)
So, the vector in component form is (-9, 11)
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I need help please !!
Answer:A,D
Step-by-step explanation:
y = [5.3, 27]
x= [-1,3]
Callie uses leather cord to make necklaces. She has a pieces of leather cord that has a length of 4 yards. Each necklace will have a length of 28 inches. How many necklaces can Callie make? Show your work.
Callie can make 5 necklaces.
What is the formula for yards to inches?So to convert from a value in inches to one in yards, we need to divide by 36. To convert a value in yards to inches, we need to multiply by 36.
Now, She has a pieces of leather cord that has a length of 4 yards.
Each necklace will have a length of 28 inches.
We have to determine the how many necklaces can Callie make?
We know that :
1 yard= 36 inches
So, Multiply by 36 into 4 yards
4 yards= 36x4= 144
Length of leather cord is 4 yards
144/4 = 5.14
Callie can make 5 necklaces.
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The average temperature for a dog is 101.8° F, but it can vary by as much as 0.7° F. Write an inequality to represent the normal temperature range of a dog, where t represents body temperature.
|t − 101.8| ≥ 0.7
|t − 101.8| ≤ 0.7
|t − 0.7| ≥ 101.8
|t − 0.7| ≤ 101.8
The correct inequality to represent the normal temperature range of a dog is |t − 101.8| ≤ 0.7. So, correct option is B.
Here, |t - 101.8| represents the absolute value of the difference between the body temperature of the dog (t) and the average temperature of dogs (101.8° F). The inequality states that this absolute value must be less than or equal to 0.7° F, which is the maximum amount that the temperature of a dog can vary from the average.
If the temperature of a dog is within this range, it is considered to have a normal body temperature. If the temperature is outside this range, it may indicate an underlying health issue or illness.
The other answer choices are incorrect because they do not accurately represent the relationship between the body temperature of a dog and the normal temperature range. For example, |t - 0.7| ≥ 101.8 makes no sense in the context of the problem, as there is no logical reason to subtract 0.7 from the body temperature.
So, correct option is B.
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An office building worth $1 million when completed in 2010 is being depreciated linearly over 25 years. What was the book value of the building in 2013? What will it be in 2019? (Assume the scrap value is $0
Answer:
2013 - $880,000
2019 - $640,000
Step-by-step explanation:
The office building is being depreciated linearly over 25 years, which means the annual depreciation rate is:
Depreciation rate = (Cost - Scrap value) / Useful life = ($1,000,000 - $0) / 25 = $40,000 per year
To find the book value of the building in 2013, we need to determine how many years have elapsed since 2010. Since 2013 is three years after 2010, the building has been depreciated for three years. Therefore, the book value in 2013 is:
Book value in 2013 = Cost - Depreciation = $1,000,000 - ($40,000/year x 3 years) = $880,000
To find the book value of the building in 2019, we need to determine how many years have elapsed since 2010. Since 2019 is nine years after 2010, the building has been depreciated for nine years. Therefore, the book value in 2019 is:
Book value in 2019 = Cost - Depreciation = $1,000,000 - ($40,000/year x 9 years) = $640,000
Therefore, the book value of the building was $880,000 in 2013 and will be $640,000 in 2019.
find the polar coordinates of a point with Cartesian coordinates (x,y)=(5√3/2,−5/2).Select the correct answer below:
(5,5π/6)
(10,4π/3)
(5,11π/6)
(10,5π/6)
(5,4π/3)
(10,11π/6)
Answer: The correct answer is (5, 11π/6). or C
Step-by-step explanation:
The polar coordinates of the point (x, y) = (5√3/2, -5/2) are (r, θ) = (5, 11π/6).
Explanation:
Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
Plugging in the given values:
r = √((5√3/2)^2 + (-5/2)^2)
= √(75/4 + 25/4)
= √(100/4)
= 5
θ = atan2(-5/2, 5√3/2)
≈ 11π/6 radians
So, the correct polar coordinates of the point (5√3/2, -5/2) are (r, θ) = (5, 11π/6).
Which of the points below correctly plots the point (4,π/3)?
Answer: The correct answer is B
Step-by-step explanation:
Remember that the coordinates (4,π3) tell us the radius r=4 and the angle θ=π3. So the point should be on the circle labeled 4 and form an angle of π3 with the positive x-axis. Point B is the correct point
Solve for BC: 3√2 A B C
Sides AB = 3√2 and BC = 6.
The given triangle ABC is a right-angled triangle, as ∠BAC = 90°.
In the given right triangle ABC,
Hypotenuse of the triangle = BC
Base and height = AC and AB.
Also, we see from the diagram that ∠ACB and ∠ABC are equal.
∴ Triangle ABC is isosceles, with sides AC = AB = 3√2.
Now, by Pythagoras' theorem,
Hypotenuse² = Base² + Height²
Or, BC² = AC² + AB²
Or, BC² = (3√2)² + (3√2)²
⇒ BC² = 36
Or, BC = 6
Hence, sides AB = 3√2 and BC = 6.
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14. During 2006, a swimming lesson at a particular school lasted 45 minutes.
(a) In 2007, the lesson time will be 50 minutes.
Find the increase in the lesson time from 2006 to 2007 as a percentage of the lesson time in 2006.
(b) The lesson time in 2007 will be 25% more than it was in 2005. Find how long the lesson lasted in 2005.
(c) At present, James takes 240 seconds to swim 100 metres. In a year's time, he would have improved his swimming time by 25%. Calculate the time he will take to swim 100 metres in a year's time.
m (d) Robert, at present, also takes 240 seconds to swim 100 metres. In a year's time, he would have increased his swimming speed by 25%. Calculate the time he will take to swim 100 metres in a year's time.
(e) Who will be the faster swimmer, James or Robert, in a year's time?
(a) The lesson time in 2007 is 11.1% more than the lesson time in 2006.
(b) The lesson lasted 40 minutes in 2005.
(c) James will take 180 seconds to swim 100 meters in a year's time.
(d) Robert will also take 180 seconds to swim 100 meters in a year's time.
(e) James and Robert will swim equally which means that their speed will be same and they will be complete at same time.
(a) The increase in lesson time from 2006 to 2007 is:
Increase = 50 - 45 = 5 minutes
The percentage increase is:
Percentage increase = (5 / 45) x 100% = 11.1%
Therefore, the lesson time in 2007 is 11.1% more than the lesson time in 2006.
(b) Let x be the lesson time in 2005. The lesson time in 2007 is 25% more than it was in 2005, so:
1.25x = 50
Solving for x, we get:
x = 40
Therefore, the lesson lasted 40 minutes in 2005.
(c) James currently takes 240 seconds to swim 100 meters. If he improves his time by 25%, his new time will be:
New time = 240 - (0.25 x 240) = 180 seconds
Therefore, he will take 180 seconds to swim 100 meters in a year's time.
(d) Robert currently takes 240 seconds to swim 100 meters. If he increases his speed by 25%, his new time will be:
New time = 240 - (0.25 x 240) = 180 seconds
Therefore, he will also take 180 seconds to swim 100 meters in a year's time.
(e) Both James and Robert will take the same time to swim 100 meters in a year's time, so they will be equally fast.
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Contrary to common belief, the price of a single item as listed in the CPI (Consumer Price Index) does not always rise and fall in tandem with the price of the same item in the PPI (Producer Price Index). Which of the following is not a reason that makes this so?
a.
Imports are excluded from PPI, but included in CPI.
b.
Taxes paid as part of the purchase are not included as part of the PPI but are included in the CPI.
c.
The PPI includes the prices of goods purchased by other producers while the CPI includes only the prices of goods purchased by consumers.
d.
Since the PPI measures the change of the price the producer receives for their product and the CPI measure the change of the price the consumer pays for the product, one should rise while the other will fall.
What does not make the context given as such is since PPI measures the change of the price the producer receives for their product and the CPI measure the change of the price the consumer pays for the product, one should rise while the other will fall. The Option D is correct.
Why does the price not always rise and fall in tandem?This is because two indexes measure different things. The PPI measures change in prices of goods and services at the producer level while CPI measures the change in prices of goods and services at the consumer level.
That tells us PPI assess prices producers receive for their goods while CPI assess prices consumers pay for those same goods. So, while we have overlap between them, they are measuring different aspects of the economy and their trends may not always move in lockstep with each other.
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Correct answer gets brainliest
Answer:
C. Points have no size and no dimensions.
Answer:
I think it is choice A and choice C
someone pls help me asapppp
Answer:
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : a₁ = 7
Step-by-step explanation:
a recursive formula allows a term in the sequence to be found from the preceding term.
the sequence here has a common ratio between consecutive terms
[tex]\frac{21}{7}[/tex] = [tex]\frac{63}{21}[/tex] = 3
thus to find a term in the sequence multiply the previous term by 3, that is
[tex]a_{n}[/tex] = 3[tex]a_{n-1}[/tex] : first term a₁ = 7
Express sin
�
L as a fraction in simplest terms.
Answer:
3/5
Step-by-step explanation:
opposite/hypotenuse
21/35
Simplify by dividing by 7 on the numerator and denominator
3/5
hey guys, im b-o-r-e-d in class... what should i do?
Answer:
Do whatever you want, but paying attention would really help you.
Step-by-step explanation:
If you find yourself bored in class, consider the following options to make the most of your time and stay engaged:
1. Actively participate: Ask questions, contribute to discussions, and try to engage with the material. Active participation can make the class more interesting and help you retain the information better.
2. Take notes: Focus on taking detailed notes, even if you think you understand the material. This will help you stay engaged and make it easier to review the content later.
3. Find connections: Try to relate the class material to your interests or real-world applications. This can make the content more engaging and relevant.
4. Set learning goals: Set specific learning objectives for each class, and try to achieve them during the session. This can help you stay focused and motivated.
5. Practice active listening: Pay attention to the teacher and try to understand the main points they are making. This can help you stay focused and better comprehend the material.
6. Break down the material: Divide the content into smaller chunks and focus on understanding each part. This can make the material more manageable and engaging.
7. Speak with your teacher: If you're consistently bored in class, consider discussing your concerns with your teacher. They may be able to offer suggestions or modify their teaching approach to better suit your learning style.
Remember, it's essential to stay engaged in class to maximize your learning experience and make the most of your education.
Answer:
watch RUN BTS EPISODE simple
Cole and his sister took part in a canned food drive. Cole brought in 21 cans of food. His sister brought in 7 fewer cans than he did. Together, how many cans did they bring in?
If Cole brought 21 cans and his sister brought 7 cans less, then the total number of cans brought by them is 35 cans.
The number of cans which Cole brought = 21 cans of food.
His sister brought in 7 fewer cans than he did, which means she brought in:
⇒ 21 - 7 = 14 cans of food,
Let the total number of food-cans be = "f",
So, the equation to find the number of cans is written as :
⇒ x = 21 + 14,
On adding the number of cans,
We get,
⇒x = 21 + 14 = 35,
Therefore, together they brought in 35 cans of food.
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Point K is located at ( 1 , 2 ) on the following coordinate plane. A square that has a perimeter of 20 units will be drawn so that K is one vertex of the square. Which three ordered pairs could represent the location of another vertex of the square? Select the three correct answers.
Three ordered pairs that could represent the location of another vertex of the square are (7, 2), (-5, 2), (1, 8).
To find the possible locations of the other vertices of the square, we need to determine the distance from point K to any other vertex of the square. Since the perimeter of the square is 20 units, each side of the square has a length of 20/4 = 5 units.
One way to find the other vertices is to draw a circle with center at K and radius 5 units, and then look for points on the circle that have integer coordinates. Alternatively, we can use the distance formula to calculate the distance from K to another point (x, y), which must be 5 units, and then solve for y in terms of x.
Using the distance formula, we get:
[tex]\sqrt{(x-1)^{2} +(y-1)^{2} }[/tex] = 5
Simplifying and squaring both sides, we get:
(x-1)^2 + (y-2)^2 = 25
Expanding the left side and simplifying, we get:
[tex]x^{2}[/tex] - 2x + [tex]y^{2}[/tex] - 4y + 20 = 0
Completing the square for x and y, we get:
[tex](x-1)^{2}[/tex] + [tex](y-1)^{2}[/tex] = [tex]6^{2}[/tex]
This is the equation of a circle with center at (1, 2) and radius 6 units. Any point on this circle that has integer coordinates could be a vertex of the square, since it will be exactly 5 units away from K.
Using this method, we can find several possible locations of the other vertices of the square. Three of them are:
(7, 2), (-5, 2), (1, 8)
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Hello, I hope you are having a great day so far, I was wondering if someone ca (seriously) help me and not play around. I really need an Answer asap as soon as possible
PLEASE HELP (I NEED AN ANSWER QUICK!)
Answer:
the corresponding sides are proportional
The Bayview Community Pool has a snack stand where Juan works part-time. He tracked his total sales during each shift last month. This box plot shows the results. Total sales per shift ($) 100 150 Submit 200 250 300 What fraction of Juan's shifts had total sales of $225 or more? 350
It looks like there are five data points in the box plot, representing Juan's total sales during each shift. The third data point is $200, which is the median value. Since there are an odd number of data points, we know that the median is exactly in the middle of the data set. This means that two of the data points are less than $200, and two of the data points are greater than $200.
The last data point is $300, which is the maximum value. So we know that only one of the data points is between $200 and $300. Therefore, the fraction of Juan's shifts that had total sales of $225 or more is 1/5, or 20%.
Answer:
Step-by-step explanation:
6. Find the components of the vector V with initial point P(-4,5) and terminal point
Q(-2,7).
(i) < -2,-2>
(iv) <-6, 12>
(ii) < 8,35 >
(iii) <2, 5/7>
(v) <2,2>
(vi) not listed
Answer:
Okay, let's break this down step-by-step:
The initial point is P(-4, 5)
The terminal point is Q(-2, 7)
To find the components of the vector V, we need to determine:
The change in x-coordinate = -4 - (-2) = -2
The change in y-coordinate = 5 - 7 = -2
So the vector components are:
<change in x-coordinate, change in y-coordinate>
= <-2, -2>
Therefore, the answer is choice (i): < -2,-2>
The other choices do not represent the correct changes between the given points P and Q.
Step-by-step explanation:
TONS OF POINTS - please help
The Cannon: Ernest's friend Nik is about to be shot out of a cannon. The path he will
travel follows a parabolic arch that can be described by this polynomial.
f(x) = -0.05(x2-26x-120)
He is supposed to land on a safety net 30 feet away. Does the function give you
enough information to tell you where he will land? If so, how far from the cannon will he land?
Make Sense of the Problem
3 points: 1 point for each answer.
-What do you know?
-What do you want to find out?
-What kind of answer do you expect?
1. The function f(x)=-0.05(x2-26x-120)
Represents the path coming out of the cannon. If x is the horizontal distance from the cannon, what does f(x) represent
2.what do the zeros of this function represent? Remember the zeros are where f(x)=0
3. Will the zeros tell you where the net should be placed? Why or why not?
4.to find zeros, set the function equal to 0, and then factor the polynomial start by setting the function equal to 0
5. Next factor the polynomial x2-26x-120. To identify the factors, complete the table: note this does not contain all the factors of -120, but it has enough to let you factor the polynomial
(I tried to type out the table )
pqp+q
P. q. p. |
————————— |
10. | 12 | blank. |
—————————.|
-10 | 12 |. Blank. |
—————————.|
30. |. -4. |. Blank. |
—————————-|
4. |. 30. | blank. |
—————————.|
6. Which values of p and w give the correct factors
7. Factor the polynomial completely
0=-0.05(x2 - 26x -120)
8. Find the roots of equation by setting each factor equal to 0 and solving for x.
Hint: there are three factors, but the constant factor, -0.05, does not equal zero
Solve for x with the other two factors
9. Identify the roots
Answer:
Step-by-step explanation:
2344
Gretta travels 77 miles per hour for 5 hours, find the distance traveled in miles
Answer: 358 miles
Step-by-step explanation:
Answer: 385
Step-by-step explanation: 77x5
Suppose you invest $5,000 in an account earning 4.71% APR compounded
monthly. How much money will be in the account after 15 years?
$9,664.47
After 15 years the account will have $9,664.47
[tex](x+7)x^{2} -(x-3)x^{2} =(x+35)x^{2} -(x+34)x^{2}[/tex]
The equation (x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2 has no solution for x
Evaluating the equationFrom the question, we have the following parameters that can be used in our computation:
(x+7)x^2 -(x-3)x^2 =(x+35)x^2 -(x+34)x^2
Divide through the equation by x^2
so, we have the following representation
(x+7) -(x-3) = (x+35) -(x+34)
When the brackets are removed and the like terms are evaluated, we have
2x + 10 = 2x - 1
Evaluate the like terms again
So, we have
10 = -1
The above equation is false
Hence, the equation has no solution for x
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Spinning a coin, unlike tossing it, may not give heads and tails equal probabilities. I spun a penny 300 times and got 134 heads. We wish to find how significant is this evidence against equal probabilities.
What is the sample proportion of heads?
0.444
Incorrect Round to 3 places.
Heads do not make up half of the sample. Is this sample evidence that the probabilities of heads and tails are different?
Take p to be the probability of getting heads in a spin of a penny. Which hypotheses do we want to test?
H0: p = 0.5
H0: p > 0.5
H0: p = 0.5
H0: p ≠ 0.5
H0: p ≠ 0.5
H0: p = 0.5
H0: p = 0.5
H0: p < 0.5
Incorrect
Compute the z test statistic.
z =
0.444
Incorrect Round to 2 places.
The resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.
The problem we are trying to solve is to determine if the sample proportion of heads obtained from spinning a penny 300 times (134 heads) is significant evidence against equal probabilities of heads and tails. To do this, we will be testing the null hypothesis H0: p = 0.5, which states that the probability of getting heads is equal to 0.5.
We can calculate the z-test statistic using the formula z = (sample proportion - hypothesized proportion) / (standard error). In this case, the z-test statistic is z = (0.444 - 0.5) / (√(0.5 * 0.5 / 300)) = -0.86. This means that the sample proportion of heads is 0.86 standard errors away from the hypothesized proportion of 0.5.
Therefore, the resulting z-test statistic is 0.44, indicating that the evidence is not significant enough to reject the null hypothesis that the probability of heads is equal to 0.5.
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SOS need help on this math project with all the work
To perform this and any other construction in math, you need to use the right tools which include a compass, your drawing board or paper, and a clear understanding of the instruction.
How to construct the shapes and anglesA key to getting the shape and angles of any construction includes knowing what is required of you and implementing these in your construction. In the second slide, you are told to use the segment tool to create segment AB. This tool will be a scale and the measurement will be that of a line AB.
Next, identify the radius of the circle. This is the point from the center of the circle to any line on the circle. Understanding the instructions is key to bisecting the segment and completing the other activities.
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A scientist has 68 lbs of a material. In 40 years , there is 63.3 lbs left. How much will be there be left in 200 years?
Evaluating the exponential decay we can see that 200 years, there will be 47.43 pounds left of the material.
How much will be there be left in 200 years?A general exponential decay is:
f(x) = A*(b)^x
Where A is the initial value, b is the rate of decay, x is the variable.
We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:
63.3 = 68*(b)^40
Where b defines how it decays, we can solve that equation for b to get:
(63.3/68)^(1/40) = b
0.9982 = b
Then the decay is:
f(x) = 68*(0.9982)^x
The amount left after 200 years will be:
f(200) = 68*(0.9982)^200 = 47.43
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Write a two-column proof for the following information. Upload your proof below.
Given: M is the midpoint of CD; CM = 5x – 2; MD = 3x + 2
Prove: x = 2
The required two column proof is explained below.
What is a midpoint?A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.
The two column proof for the information is given as:
M is the midpoint of CD (Given)
CD = CM + MD (addition property of a line segment)
CM = MD (definition of a midpoint)
So that;
5x – 2 = 3x + 2 (Definition of midpoint)#
Then,
5x - 3x = 2 + 2 (collecting like terms)
2x = 4
x = 2
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