The work done in pulling the rope up 10 ft is 864 ft-lbs, calculated by multiplying the rope's weight (72 lbs) by the distance (10 ft) it was lifted.
Work done = Weight x Distance
Work done = 72 lbs x 10 ft
Work done = 720 ft-lbs
Additional work done for weight of rope = Weight of rope x Distance
Additional work done for weight of rope = 90 x 10
Additional work done for weight of rope = 900 ft-lbs
Total work done in pulling the rope up 10 ft = 720 ft-lbs + 900 ft-lbs
Total work done in pulling the rope up 10 ft = 864 ft-lbs
The work done in pulling the rope up 10 ft is calculated by multiplying the weight of the rope (72 lbs) by the distance (10 ft) it was lifted. This gives us a result of 720 ft-lbs. However, since the rope is 90 ft long, we must also take into account the additional weight of the rope beyond the 10 ft that was lifted. So, we multiply the weight of the rope (90 lbs) by the distance (10 ft) to get an additional work done of 900 ft-lbs. Adding the two results together gives us 864 ft-lbs of work done in pulling the rope up 10 ft. This shows that the heavier a rope is, the more work must be done to lift it.
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what is the sum of the first fifteen terms of the sequence $2, 8, 14, \dots$, in which each term is six more than the preceding term?
The sum of the first fifteen terms of the given sequence is 220.
The given sequence can be expressed as: [tex]$2, 8, 14, \dots$[/tex], in which each term is six more than the preceding term. This is an arithmetic sequence, where the common difference between terms is 6. The formula to calculate the sum of the first n terms of an arithmetic sequence is given by [tex]$S_n = \frac{n}{2}(a_1 + a_n)$[/tex], where [tex]$a_1$[/tex] is the first term and [tex]$a_n$[/tex] is the nth term.
In the given sequence, the first term [tex]$a_1$[/tex] is 2 and the 15th term [tex]$a_n$[/tex] is 42. So, plugging these values to the formula gives us, [tex]$S_{15} = \frac{15}{2}(2+42) = \frac{15\times 44}{2} = 220$[/tex].
Therefore, the sum of the first fifteen terms of the given sequence is 220.
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Which kind of triangle is shown?
acute triangle
obtuse triangle
equilateral triangle
right triangle
The kind of triangle which is shown in the image is Obtuse triangle. The Option B is correct.
What is the features of Obtuse triangle?An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.
Characteristics of Obtuse Angled Triangle:
The sum of the two angles other than the obtuse angle is less than 90°.The side opposite the obtuse angle is the longest side of the triangle.An obtuse triangle will have one and only one obtuse angle. The other two angles are acute angles.Read more about Triangle
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Solve. -9+4 - 6 + (-11)
Answer:
-9+4-6+(-11)=-9+4-6-11=-22
first -9+4 is -5-6=-11then-11 = -22
Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
The area of the shaded region is
The area of the shaded region is given as follows:
0.0475.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for the IQ scores are given as follows:
[tex]\mu = 100, \sigma = 15[/tex]
The shaded region is the area to the right of 125, hence it's area is one subtracted by the p-value of Z when X = 125, hence:
Z = (125 - 100)/15
Z = 1.67
Z = 1.67 has a p-value of 0.9525.
Hence:
1 - 0.9525 = 0.0475.
Missing InformationThe shaded region is the area to the right of 125.
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You buy 3 packs of toilet paper for $8.53 each. How much do you spend?
Answer: $25.59
Step-by-step explanation: you can multiply 3 times 8.53 which comes too $25.59 but we can add as well.
8.53 + 8.53= 17.06 Now we have to add it 1 more time soo
17.06 + 8.53= $25.59..
Hope this helps :)
Money McGuire invests $50.00 in an account that she expects to double each year. How long will it take her investment to reach $3,200.00?
Answer:
6 years
Step-by-step explanation:
You want the length of time it takes for a $50 investment to total $3200 if it doubles in value each year.
Exponential equationThe value of the investment can be described by ...
v = 50·2^t
where t is the number of years.
You want t when v=3200:
3200 = 50·2^t
64 = 2^t
log(64) = t·log(2) . . . . . take logarithms
t = log(64)/log(2) = 6
It will take 6 years for her investment to reach $3200.
__
Additional comment
If you're familiar with powers of 2, you recognize that 64 = 2⁶. Comparing exponents in ...
64 = 2^t
2^6 = 2^t . . . . . use 2^6 for 64
we can see that t=6. The logarithms are used to formalize this comparison.
solve for y -36=8y+4(y-6)
Answer: y= -1
Step-by-step explanation:
1) Distribute the 4 to the y and the -6 to get 4y-24, so our new equation is -36= 8y+4y-24.
2) Add like terms 8y and 4y to get 12y. Our new equation is -36=12y-24.
3) Remove the constant -24 by adding 24 to both sides to get -12=12y.
4) Remove the coefficient 12 by dividing 12 on both sides to get y= -1
Sue bought a dress that normally cost $50 .00 it was on sale for 25% off How much did she save?
Answer: 25% of 50 is 25/2 or 12½ as a fraction and 12.5 as a decimal.
Let's find 25% of 50.
Explanation:
25% of 50 can be written as 25% × 50
= 25/100 × 50
= 25/2 = 12½ = 12.5
Thus, 25% of 50 is 25/2 or 12½ as a fraction and 12.5 as a decimal.
John has 2 books. Peter has twice books more then John. How many books they have together?
John has average 2 books and Peter has 4 books. Together, they have 6 books.
John has 2 books
Peter has twice books more than John = 2 * 2 = 4 books
Total books they have together = 2 + 4 = 6 books
John has 2 books, so Peter has twice books more than John. This means that Peter has 2 * 2 = 4 books. Together, John and Peter have 2 + 4 = 6 books. John’s books are the starting point of the problem, so it is important to keep track of John’s books. Since Peter has twice books more than John, we can calculate the number of books that Peter has by multiplying the number of books that John has by two. Once we have calculated the number of books that Peter has, we can add the number of books that John has to the number of books that Peter has and get the total number of books that they have together. In this example, the total number of books that John and Peter have together is 6. This can be arrived at by adding the number of books that John has (2) to the number of books that Peter has (4).
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The double-reciprocal transformation of the Michaelis-Menten equation, also called the Lineweaver- Burk plot, is given by
1/V_0 = K_m /(V_max[S]) + 1/V_max
To determine Km from a double-reciprocal plot, you would:
A) multiply the reciprocal of the x-axis intercept by -1.
B) multiply the reciprocal of the y-axis intercept by -1.
C) take the reciprocal of the x-axis intercept.
D) take the reciprocal of the y-axis intercept.
E) take the x-axis intercept, where V_0 = 1/2 V_max.
To determine Km from a double-reciprocal plot, you would choose option (A) which is to multiply the reciprocal of the x-axis intercept by -1.
In the double-reciprocal plot equation, the x-axis intercept is -1/Km, and the y-axis intercept is 1/Vmax. Therefore, if you take the reciprocal of the x-axis intercept, you get -Km, and multiplying it by -1 gives you Km.
This method is preferred because it is more accurate than estimating Km based on the position of the curve on the plot or by taking the x-axis intercept where V0 = 1/2 Vmax, which can be influenced by experimental error.
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What is 2 thirds of 42
Answer:
Step-by-step explanation:
42*2/3=84/3=28
suppose that your boss must choose five employees in your office to attend a conference in jamaica. because all 15 of you want to go, he decides that the only fair way is to draw names out of a hat. what is the probability that you, diana, kyle, nancy, and arthur are chosen? enter a fraction or round your answer to 4 decimal places, if necessary.
There are 15 employees in the office and 5 need to be chosen, so there are a total of (15 choose 5) possible ways to select the employees. This can be calculated using the formula for combinations:
(15 choose 5) = 15! / (5! * 10!) = 3003
Now, we need to find the number of ways that the specific group of you, Diana, Kyle, Nancy, and Arthur can be chosen. This is simply (5 choose 5), since we want to choose all 5 members of the group.
(5 choose 5) = 5! / (5! * 0!) = 1
Therefore, the probability of this specific group being chosen is:
(5 choose 5) / (15 choose 5) = 1 / 3003 ≈ 0.0003
So the probability of you, Diana, Kyle, Nancy, and Arthur being chosen is very low, at approximately 0.0003 or 3 in 10,000. This is because there are many other possible groups of 5 employees that could be chosen from the pool of 15, and all of these groups have an equal chance of being selected.
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Paula fue al super mercado y para pagar su cuenta dio 360 si dio 120porciento de lo que tenia pagar. Pregunta cuanto le tuvieron que devolver de cambio
She had to pay they have to pay her back $ 132.
Multiply: -
Payback = 360 x 120/100
= 132
Payback is a financial metric that measures the time it takes to recover the initial investment cost of a project. It is commonly used in investment analysis to evaluate the viability of potential projects by estimating the time it takes for the project to start generating profits.
The payback period is calculated by dividing the initial investment by the expected cash flow of the project on an annual or monthly basis until the investment is fully recovered. The shorter the payback period, the more attractive the project is to investors. Payback is a simple and straightforward metric, but it has some limitations. It does not consider the time value of money or the long-term profitability of the project.
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Complete Question: -
Paula went to the supermarket and to pay her bill she gave $ 360 if she gave 120% of what she had to pay, how much did they have to pay her back?
community college faculty is negotiating a new contract with the school board. The distribution of faculty salaries is skewed right by several faculty members who make over $100,000 per year. If the faculty impression that they deserve higher sales should they a r e the meanor median of their current salaries? A. The faculty should use the mean to make their argument. The mean will be higher than the median since the mean is influenced by the few extremely high res.B. The faculty should use the mean to make o rgument. The man will be lower than the median since it will be henced by the few high salariesC. The faculty should use the median to make their argument. The median will be higher than the mean since the media is unced by the high e s D. The faculty should use the median to make their argument. The median will be lower than me since the means i nced by the extremely histories
Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.
Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.
So for example, if the salaries of any 5 faculty members are as follows:
$10,000 , $50,000 , $80,000 , $150,000 , $160,000
Mean= (10,000+50,000+80,000+150,000+160,000) / 5
Mean= $90,000
Median= (5+1) / 2
Median= 6/2
Median= 3rd value
As the data is already arranged in ascending order, Median is $80,000
Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.
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two cities are 1020 miles apart. Two trains simultaneously left these cities heading toward one another. The speed of one train was 10 mph greater than the speed of the other one. In 5 hours, the trains had not met yet and were 170 miles apart. Find the speed of the trains.
The speed of both the trains would be 400 mph and 450 mph respectively.
What is the formula to calculate the distance travelled?The formula to calculate the distance travelled is -
Distance = Speed x Time
Given is that two cities are 1020 miles apart. Two trains simultaneously left these cities heading toward one another. The speed of one train was 10 mph greater than the speed of the other one. In 5 hours, the trains had not met yet and were 170 miles apart.
Let the speed of one train be {x} mph. Then, the speed of the other train would be {x + 10} mph.
Distance covered by both the trains would be -
train { 1 } = 5x ... { 1 }
train { 2 } = 5(x + 10) ... { 2 }
Now, we can write -
1020 - {5x + 5(x + 10)} = 170
1020 - 170 = 10x + 50
10x = 800
x = 80
Speed of train { 1 } = 400 mph
Speed of train { 2 } = 450 mph
Therefore, the speed of both the trains would be 400 mph and 450 mph respectively.
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Determine the given lengths in the rectangle
Step-by-step explanation:
AC =18 (ac = bd opposite sides of a rectangle)
AB= 40(AB = CD)
AD = 22 ( ad = cb diagonals of a rectangle)
determine if its a depicts a function or not
The relations that are functions are 2, 3, 4, 5, 6, and 7.
The ones that aren't functions are 1 and 8.
Which relations are functions?A relationship maps elements from one set (the domain) into elements from another set (the range), and a relation is a function only if each element of the domain is mapped into only one value of tha range.
For example, if you look at the relation 8, you can see that the input x = 1 is mapped into two different outputs, then this is not a function.
With that in mind, the options that are functions are:
2, 3, 4, 5, 6, and 7.
The ones that aren't functions are 1 and 2.
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Find the value of x to the nearest tenth.
The side x = 9.4 approximately to nearest tenth using the cosine rule.
What is the cosine rule?In trigonometry, the cosines rule relates the lengths of the sides of a triangle to the cosine of one of its angles.
Considering the given triangle, side x is calculated with cosine rule as follows;
a² = b² + c² - 2(b)(c)cosA
x² = 8² + 15² - 2(8)(15)cos33°
x² = 64 + 225 - 240(0.8387)
x² = 289 - 201.2809
x² = 87.7191
x = 9.3658 {take square root of both sides}
With proper application of the cosine rule, we can conclude the value of the side x of the triangle is approximately 9.37 to the nearest tenth.
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4. Which of these is the most helpful first step for solving Fran's equation, 2x + 28 = 40? (1 point)
Circle the best answer.
⦁ Multiply both sides by 2
⦁ Subtract 28 from both sides
⦁ Divide both sides by 2
⦁ Add 28 to both sides
subtract 28 from both sides ....
2x+28-28=40-28
2x= 12
x=12 Ans........
thank you!
Question 5(Multiple Choice Worth 2 points) (Linear Functions MC) Which of the following tables represents a linear function? x −2 −1 0 1 2 y 4 1 −2 −5 −8 x −2 −1 0 1 2 y 4 1 0 1 4 x 2 2 0 2 2 y −2 −1 0 1 2 x 0 1 2 3 4 y −2 1 0 1 −2
50 POINTS HURRY UP!!!!
Answer:
The table that represents a linear function is:
x 0 1 2 3 4
y −2 1 0 1 −2
Step-by-step explanation:
Answer:
Step-by-step explanation:
Step-by-step explanation: The linear function is a function that has a straight line when plotted on a
graph.
The correct option;
The table of ordered pairs that represent a linear function is the option; x/y -8/-7 0/0 8/7 16/14
Reasons why the above selection is correct:
Given;
The given data can be presented as follows;
x/y -8/22 0/1 8/22 16/102
x/y -8/-7 0/1 8/9 8/2
x/y -8/-7 0/0 8/7 16/14
x/y -8/-7 0/1 8/5 16/4
Representation of the options in tabular form;
In a tabular format, we have;
Characteristic of linear function;
In a linear function, when the x-values have a constant rate of increase the
the first difference in the y-values is constant.
Selection of the table representing a linear function;
The option that has a constant first difference along with a continuous rate of
increase in the x-value is the option with the following table;
, which is the option x/y -8/-7 0/0 8/7 16/14
Which transformation maps △UVW to △EFG?
The transformation that maps △UVW to △EFG is (d) (x, y) = (-2x, -2y)
How to determine the transformationFrom the question, we have the following parameters that can be used in our computation:
The figure
From the figure, we can see that
Triangle EFG is twice the triangle UVW in side lengths
This means that
(x, y) = (2x, 2y)
The orientations are 180 degrees apart
So, we have
(x, y) = (-2x, -2y)
Hence, the transformation is (d) (x, y) = (-2x, -2y)
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I poured a bowl of cereal in a Tupperware container with the following dimensions (L=9 in, w=6 in, h=3). I want no more than a density of 0.3 cheerios per sq in in my "bowl." How many cheerios can I pour into the bowl. Round your answer to the nearest whole number.
we can pour no more than 541 cheerios into the bowl while maintaining a density of no more than 0.3 cheerios per square inch.
What is rectangle ?
Rectangle can be defined in which the opposite sides are equal and area of rectangle is product of length and breadth.
Given ,
I poured a bowl of cereal in a Tupperware container with the following dimensions (L=9 in, w=6 in, h=3). I want no more than a density of 0.3 cheerios per sq in in my "bowl."
We can start by calculating the surface area of the Tupperware container, which is equal to 2 times the sum of the area of the base and the area of the two rectangular sides:
Area of base = Length * Width = 9 in * 6 in = 54 in²
Area of two rectangular sides = Height * Length = 3 in * 9 in = 27 in²
Surface area = 2 * (54 in² + 27 in²) = 2 * 81 in² = 162 in²
Next, we can find the maximum number of cheerios that can be poured into the bowl by dividing the surface area by the maximum allowed density of 0.3 cheerios per square inch:
Maximum number of cheerios = Surface area / Maximum allowed density = 162 in² / 0.3 cheerios/in² = 541 cheerios
Hence, we can pour no more than 541 cheerios into the bowl while maintaining a density of no more than 0.3 cheerios per square inch.
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need solution to this
Let's first understand what's relative here, it refers to Point of reference , the point, in respect to which other's position are to be considered, which here is O, the Origin with coordinates (0,0) as we are talking about two-dimensional reference frame. What position vector means? Say, we have the point of Reference X, and we've the position vector of Y with respect to X, then it can be written as [tex]{\overrightarrow{XY}}[/tex]. Now, using this simple rule we can have,
[tex]{\overrightarrow{OA}=-2\hat{i}+7\hat{j}}[/tex][tex]{\overrightarrow{OB}=2\hat{i}-\hat{j}}[/tex][tex]{\overrightarrow{OC}=6\hat{i}+\lambda \hat{j}}[/tex]Now, let's calculate [tex]{\overrightarrow{AC}}[/tex] firstly;
[tex]{:\implies \overrightarrow{AC}=\overrightarrow{OC}-\overrightarrow{OA}}[/tex]
[tex]{:\implies \overrightarrow{AC}=8\hat{i}+(\lambda -7)\hat{j}}[/tex]
Now, here [tex]{AC}[/tex] just means the the magnitude of the vector [tex{\overrightarow{AC}}[/tex], and we're aware that magnitude of a vector [tex]{\overrightarrow{X}=x\hat{i}+y\hat{j}}[/tex] is given by, [tex]{X=\sqrt{x^{2}+y^{2}}}[/tex], so according to question;
[tex]{:\implies \sqrt{64+(\lambda -7)^{2}}=17}[/tex]
Squaring both sides;
[tex]{:\implies (\lambda -7)^{2}=289-64=225}[/tex]
[tex]{:\implies \lambda -7=\pm 15}[/tex]
[tex]{:\implies \boxed{\underline{\bf{\lambda =22,\:or\:-8}}}}[/tex]
PLEASE HELP!!! WILL MARK BRAINLIST
Savannah buys a bag of cookies that contains 8 chocolate chip cookies, 9 peanut butter cookies, 7 sugar cookies and 6 oatmeal cookies. What is the probability that Savannah randomly selects a sugar cookie from the bag, eats it, then randomly selects a chocolate chip cookie? Express you answer as a reduced fraction.
total cookies first to find ratio values
8 + 9 + 7 + 6 = 30 total
first ratio is sugar cookie to total
7 / 30 chances
after eating the sugar cookie, the total reduces to 29
second ratio is the new total
8 / 29 chances.
potential bonus??
the odds of this happening in this exact order is both odds multiplied.
so (7/30) × (6/29) = 7 / 145 chances she completes this in the exact order stated.
A TV at £800 plus VAT at 20%
What is the total cost of the TV
Answer:
it will be £960
Step-by-step explanation:
first £800×20/100
simplify £8×20
£160= VAT
Total cost=VAT+ normal cost
£160+£800
=£960
Mr. Jones' tally showed that 0.6 of
the students brought in scissors.
What fraction of the students did
not bring in scissors?
Answer:
Mr. Jones' tally showed that 0.6 of the students brought in scissors, so the remaining fraction of students would be 0.4 or 40%, who did not bring in scissors.
Step-by-step explanation:
simple
Answer:
40% of the students did not bring in scissors
Step-by-step explanation:
Since % means out of 1.
0.6 would equal 60%
1.0 - 0.6 = 0.4
Other forms of 0.4 would include:
0.40
40%
2/5s
4/10s
40/100s
who has a better chance of winning the super bowl 2023
The Kansas City Chiefs has a better chance of winning the super bowl 2023.
In 1967's Super Bowl I, Las Vegas sportsbooks gave the Green Bay Packers a 14-point advantage against the Kansas City Chiefs. Nevada was the only state up until 2018 to allow legal Super Bowl sports betting.
The reigning champion Kansas City Chiefs are the early favorited in the Super Bowl 58 odds, according to the top NFL betting companies. At BetMGM, the Super Bowl 58 odds for the Kansas City Chiefs are +600. You can evaluate the odds on a team you prefer to discover the best price because competing sportsbooks provide different odds for each team to win the Super Bowl.
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Watch help video
What is the greatest common factor of 21, 14, and 7
Answer:
Submit Answer
The greatest common factor ( GCF ) of 21 , 14 and 7 is given by A = 7
What is HCF and LCM?The Greatest Common Divisor GCF or the Highest Common Factor HCF is the highest number that divides exactly into two or more numbers. It is also expressed as GCF or HCF
Least Common Multiple (LCM) is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers
Product of HCF x LCM = product of two numbers
Given data ,
Let the GCF of the numbers be represented as A
Now , the equation will be
Let the first number be p = 21
Let the second number be q = 14
Let the third number be r = 7
Now , the factors of 21 = 1 , 2 , 3 , 7 and 21
The factors of 14 = 1 , 2 , 7 and 14
The factors of 7 = 1 and 7
So , the greatest common factors of 21 , 14 and 7 is 7
Hence , the GCF is 7
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3. Kate likes to run a route in town
that forms the triangle shown
below. How many times would she
need to run this route to complete
12 miles?
0.7 mi
1.4 mi
0.9 mi
The number of rounds that Kate has to run along the perimeter of town to complete 12 miles is 4 rounds.
What is the perimeter of a triangle?
Any two-dimensional figure's perimeter is determined by the space surrounding it. By summing the lengths of the sides, we can determine the perimeter of any closed shape. The perimeter of any polygon is equal to the sum of its side lengths. Considering a triangle, the sum of the three sides equals the perimeter.
Given the town is the shape of a triangle.
The distance covered after running one round around town is equal to the perimeter of the triangle.
The sides of the triangle are 0.7 miles, 1.4 miles and 0.9 miles.
Perimeter = 0.7+0.9+1.4 = 3 miles.
The distance covered in one round = 3 miles.
So the number of rounds required to complete 12 miles = 1/3 * 12 = 4 rounds.
Therefore the number of rounds that Kate has to run along the perimeter of town to complete 12 miles is 4 rounds.
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A
(12x-1)º
(10x)
C
Find m Z A.
(3x+6)°
B
The measure of angle A is 83 degrees.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
In the triangle ABC, ∠A=(12x-1)º, ∠B=10x and ∠C=3x+6
Now we need to find the value of angle A.
We know that from angle sum property that the sum of three angles is 180 degrees.
∠A+∠B+∠C=180
12x-1+10x+3x+6=180
25x+5=180
25x=175
Divide both sides by 25
x=175/25
x=7
Now angle A is 12(7)-1=84-1=83 degrees
Hence, the measure of angle A is 83 degrees.
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The complete question is In Triangle ABC, ∠A=(12x-1)º, ∠B=10x and ∠C=3x+6 then the measure of m∠A
