If x varies directly as y. Find x when y = 1 if x= 12 when y= 4
Answers
Step-by-step explanation:
x/y=constant
12/4=3
x/1=3
x=3
Here, if x varies directly as y. When y=1, then x=3.
Given that, x varies directly as y.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
If x= 12 when y= 4
Here, x varies directly as y is x∝y
⇒ x=ky
⇒ 12=k(4)
⇒ k=3
So, x=3y
When y=1, we have
x=3(1)
⇒ x=3
Here, if x varies directly as y. When y=1, then x=3.
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Related Questions
Find the balance in an account at the end of 12 years if $4000 is invested at an interest rate of 9% that is compounded continuously
Answers
Answer:
7250.66
Step-by-step explanation:
With media clutter and fragmentation: Select one: a. there are very few media choices available to advertisers. b. the probability of any one advertisement making a real difference has increased manifold. c. promotion options are no longer attractive to advertisers. d. integrated brand is all the more important.
Answers
With media clutter and fragmentation, integrated brand is all the more important. Therefore, the correct option is D.
Media clutter refers to the enormous amount of advertising that the average individual encounters daily. This encompasses everything from billboards and product placement to digital advertising on websites and social media.
Fragmentation, on the other hand, refers to the proliferation of new media channels and technologies that are changing the way consumers communicate with one another, as well as how they access and consume media content.
Media fragmentation makes it more difficult for advertisers to reach their intended audiences. It also makes it more difficult to create advertisements that are relevant and memorable. Therefore, in order to stand out in the cluttered media landscape, companies must rely on integrated marketing tactics that are well-planned and coordinated.
Integrated brand communications is an approach that integrates all of a brand's communications to ensure that they are coherent and consistent with one another. This is important because it allows the brand to establish a strong identity and stand out from the crowd. As a result, in a media environment that is increasingly cluttered and fragmented, an integrated brand is more important than ever before. So, the correct option is D.
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2. Which of the following represents the relationship between the circumference, C, and diameter, d, of any circle?
Answers
Answer:
The ratio of the circumference of a circle to the diameter of that circle is the value pi (22/7)
Step-by-step explanation:
Mathematically,
the circumference of a circle is by the formula;
C = 2 * pi * r
Now, as we know, 2r is d where r is the radius of the circle and d is the diameter of the circle
that means;
C = pi * d
hence;
C/d = pi
So the ratio of the circumference of any circle to the diameter is the value called pi
Review Questions
1. Cindy is a baker and runs a large cupcake shop. She has already
a. How many workers will the firm hire if the market wage rate is
hired 11 employees and is thinking of hiring a 12th. Cindy esti- $27.95 ? \$19.95? Explain why the firm will not hire a larger or mates that a 12 th worker would cost her $100 per day in wages $ smaller number of units of labor at each of these wage rates. and benefits while increasing her total revenue from $2,600per. day to $2,750 per day. Should Cindy hire a 12 th worker? b. Show this firm Explain. L016.2 c. Now again determine the firm's demand curve for labor. Complete the following labor demand table for a firm that is assuming that it is selling in an imperfectly competitive marhiring labor competitively and selling its product in a competiket and that, although it can sell 17 units at $2.20 per unit, it tive market. L016.2 ginal product of each successive labor unit. Compare this demand curve with that derived in part b. Which curve is more elastic? Explain. 3. Alice runs a shoemaking factory that uses both labor and capital to make shoes. Which of the following would shift the factory's demand for capital? You can select one or more correct answers from the choices shown. LO16.3 a. Many consumers decide to walk barefoot all the time. b. New shoemaking machines are twice as efficient as older machines. c. The wages that the factory has to pay its workers rise due to an economywide labor shortage.
Answers
Cindy should hire the 12th worker as it would result in a net increase in profit, with additional revenue exceeding the cost of hiring. Insufficient information is provided to determine the demand curve for labor or compare its elasticity. Events that would shift the factory's demand for capital include new, more efficient machines and rising wages due to a labor shortage.
a. To determine whether Cindy should hire a 12th worker, we need to compare the additional revenue generated with the additional cost incurred. Hiring the 12th worker would increase total revenue by $150 ($2,750 - $2,600) per day, but it would also increase costs by $100. Therefore, the net increase in total profit would be $50 ($150 - $100). Since the net increase in profit is positive, Cindy should hire the 12th worker.
b. By hiring the 12th worker, Cindy can increase her total revenue from $2,600 per day to $2,750 per day. The additional revenue generated by the 12th worker exceeds the cost of hiring that worker, resulting in a net increase in profit.
c. To determine the firm's demand curve for labor, we need information about the marginal product of labor (MPL) and the wage rates. Unfortunately, this information is not provided, so we cannot complete the labor demand table or derive the demand curve for labor.
Without specific data or information about changes in the quantity of labor demanded and wage rates, we cannot determine which demand curve (from part b or c) is more elastic. The elasticity of the demand curve depends on the responsiveness of the quantity of labor demanded to changes in the wage rate.
The events that would shift the factory's demand for capital are:
a. New shoemaking machines being twice as efficient as older machines would increase the productivity of capital. This would lead to an increase in the demand for capital as the factory would require more capital to produce the same quantity of shoes.
b. The wages that the factory has to pay its workers rising due to an economy-wide labor shortage would increase the cost of labor relative to capital. This would make capital relatively more attractive and lead to an increase in the demand for capital as the factory may substitute capital for labor to maintain production efficiency.
The event "Many consumers decide to walk barefoot all the time" would not directly impact the demand for capital as it is related to changes in consumer behavior rather than the production process of the shoemaking factory.
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The net of a rectangular prism is shown below. Each square represents 1 square unit.
What is the total surface area of the net shown?
Answers
Answer:
56 units²Step-by-step explanation:
There are two bases of 3x4 and 4 sides of 2x4
Total surface area is:
2(3*4) +4(2*4) = 56 units²A box contains 23 yellow, 33 green and 37 red jelly beans. if 9 jelly beans are selected at random, what is the probability that:_________
Answers
The probability that exactly 10 are yellow out of 9 random selections is 0.
ProbabilityTo calculate the probability of exactly 10 jelly beans being yellow out of 9 selected at random, we need to consider the total number of favorable outcomes (selecting exactly 10 yellow jelly beans) divided by the total number of possible outcomes (selecting any 9 jelly beans).
The total number of jelly beans in the box is 23 (yellow) + 33 (green) + 37 (red) = 93.
The number of ways to select exactly 10 yellow jelly beans out of 9 is 0, as we have fewer yellow jelly beans than the required number.
Therefore, the probability of exactly 10 yellow jelly beans is 0.
In this case, it is not possible to have exactly 10 yellow jelly beans out of the 9 selected because there are not enough yellow jelly beans available in the box.
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A box contains 23 yellow, 33 green and 37 red jelly beans. if 9 jelly beans are selected at random, what is the probability that: exactly 10 are yellow?
A scale drawing of a house is 2:9. If the length of the actual kitchen is 18 feet, how long was it in the drawing?
Answers
Answer: 4:18
Work:
2:9
2 inch:9 feet
2 · 9 = 18
2 · 2 = 4
4 inch:18 feet
5. (08.01) Line M is represented by the following equation: x + y = -1 What is most likely the equation for line P so the set of equations has infinitely many solutions?
O 2x + 2y = 2
O 2x + 2y = 4
O 2x + 2y = -2
O x - y = 1
Answers
Answer:
2x + 2y = -2
Step-by-step explanation:
you can divide a 2 from all three terms in 2x + 2y = -2 to get x + y = -1 which overlaps the original equation to provide an infinite number of solutions
Write a linear function f with the values f(10)=5 and f (2) =-3
Answers
The linear function f with the values f(10) = 5 and f(2) = -3 is f(x) = x - 5.
Write a linear function f with the values f(10) = 5 and f(2) = -3The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
hence, to write a linear function f with the values f(10) = 5 and f(2) = -3, we need to find the slope and y-intercept of the function.
The slope of a linear function can be found by using the formula:
Slope m = (y2 - y1) / (x2 - x1)
Using the values of f(10) = 5 and f(2) = -3,
we can find the slope:
Slope m = (5 - (-3)) / (10 - 2)
= 8 / 8
= 1
Now that we have the slope, we can use the point-slope form to find the equation of a line:
y - y1 = m(x - x1)
Where m is the slope and (x1, y1) is one of the points on the line.
Using the point (10, 5) and slope m = 1, we have:
y - y1 = m(x - x1)
y - 5 = 1(x - 10)
Simplifying, we get:
y - 5 = x - 10
y = x - 5
f(x) = x - 5
Therefore, the linear function is f(x) = x - 5.
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1a. A company produces wooden tables. The company has fixed costs of $2700 each month, and it costs an additional $49 per table. The company charges $64 per table. How many tables must the company sell in order to earn $7,104 in revenue?
1b. A company produces wooden tables. The company has fixed costs of $1500, and it costs an additional $32 per table. The company sells the tables at a price of $182 per table. How many tables must the company produce and sell to earn a profit of $6000?
1c. A company produces wooden tables. The company has fixed costs of $1500, and it costs an additional $34 per table. The company sells the tables at a price of $166 per table. Question content area bottom Part 1 What is the company's revenue at the break-even point?
Answers
The company's revenue at the break-even point is:
Total Revenue = Price per Table x Number of Tables Sold Total Revenue = 166 x 50 = $8,300
1a. In order to earn revenue of $7,104, the number of tables that the company must sell is 216.
We can find the solution through the following steps:
Let x be the number of tables that the company must sell to earn the revenue of $7,104.
Total Revenue = Total Cost + Total Profit64x = 49x + 2700 + 710464x - 49x = 9814x = 216
1b. In order to earn a profit of $6,000, the number of tables that the company must produce and sell is 60.
We can find the solution through the following steps:
Let x be the number of tables that the company must produce and sell to earn a profit of $6,000.
Total Profit = Total Revenue - Total Cost6,000 = (182x - 32x) - 1500(182 - 32)x = 7,500x = 60
The company must produce and sell 60 tables to earn a profit of $6,000.
1c. To find the company's revenue at the break-even point, we need to first find the number of tables at the break-even point using the formula:
Total Revenue = Total Cost64x = 34x + 150064x - 34x = 150030x = 1500x = 50 tables
The company's revenue at the break-even point is:
Total Revenue = Price per Table x Number of Tables Sold Total Revenue = 166 x 50 = $8,300
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How many F ratios (i.e. F statistic values) are figured in a two-way analysis of variance known as a 2x2 Factorial Design?
a) as many as there are cells in the design
b) 2
c) 3
d) 1
Answers
Therefore, the correct answer is c) 3, as there are three F ratios calculated in a 2x2 factorial design.
How many F ratios in a 2x2 Factorial Design?In a two-way analysis of variance (ANOVA) known as a 2x2
factorial design, there are three F ratios or F statistic values calculated. This design involves two independent variables, each with two levels or categories.
The three F ratios represent the main effects of each independent variable and the interaction between the two variables.The main effects F ratios determine whether there are significant differences between the levels of each independent variable individually, ignoring the other independent variable.
There will be two main effects F ratios, one for each independent variable.The interaction F ratio examines whether there is a significant interaction between the two independent variables. It determines whether the effect of one independent variable differs across the levels of the other independent variable.
This F ratio assesses the joint influence of both independent variables.
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Planes x and y are perpendicular. Points a, e, f, and g are points only in plane x. Points r and s are points in both planes x and y. Lines ea and fg are parallel. Based on this information, which pair of lines, together, could be perpendicular to rs? select two options.
Answers
The pair of lines perpendicular to RS are EA and FG.
A flat surface on which a straight line joining any two points on it would wholly lie is known as a plane.
What is plane?
A plane is a point, a line, and three-dimensional space's equivalent in two dimensions.
Main Body:
Given
E,F and G are on plane X. R and S are in both planes X and Y. EA and FG are parallel. AE and FG are vertical lines and are present on plane X. RS is present at the intersection of the 2 planes.
Explanation:
The lines which together could be perpendicular to RS are EA and FG.
We have to first draw both the planes according to the given information in question.
X is a vertical plane so draw a plane vertical on the horizontal plane that is Y plane. Now plot A and F And G in X plane and R,S in such a way that they are in both plane so they will be at the intersection of both the planes. Now draw lines from A and F to form lines EA and FG.
Hence we can observe that lines EA and FD are perpendicular on line RS.
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Which expression is equivalent to left-bracket log 9 one-half log x log (x cubed 4) right-bracket minus log 6?
Answers
The equivalent expression of \(\log(9) + \frac 12 \log(x) + \log(x^3) - \log(6)\) is \(3\frac 12\log(\frac 32 x)\)
How to determine the equivalent expression?The logarithmic expression is given as:
\(\log(9) + \frac 12 \log(x) + \log(x^3) - \log(6)\)
Apply the power rule of logarithm
\(\log(9) + \log(x^\frac 12) + \log(x^3) - \log(6)\)
Apply the product rule of logarithm
\(\log(9 * x^\frac 12 * x^3) - \log(6)\)
Evaluate the product
\(\log(9 * x^{3\frac 12}) - \log(6)\)
Apply the quotient rule of logarithm
\(\log(9 * x^{3\frac 12} \div 6)\)
Evaluate the quotient
\(\log(\frac 32 x^{3\frac 12})\)
Rewrite as:
\(3\frac 12\log(\frac 32 x)\)
Hence, the equivalent expression of \(\log(9) + \frac 12 \log(x) + \log(x^3) - \log(6)\) is \(3\frac 12\log(\frac 32 x)\)
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Please please please help asapp
question: in the movie lincoln lincoln says "euclid's first common notion is this: things which are equal to the same things are equal to each other. that's a rule of mathematical reasoning and it's true because it works - has done
and always will do. in his book euclid says this is self-evident. you see there it is even in that 2000 year old book of mechanical law it is the self-evident truth that things which are equal to the same things are equal to each other."
explain how this common notion is an example of a postulate or a theorem
Answers
The statement made by Lincoln in the movie "Lincoln" refers to a mathematical principle known as Euclid's first common notion. This notion can be seen as an example of both a postulate and a theorem.
In the statement, Lincoln says, "Things which are equal to the same things are equal to each other." This is a fundamental idea in mathematics that is often referred to as the transitive property of equality. The transitive property states that if a = b and b = c, then a = c. In other words, if two things are both equal to a third thing, then they must be equal to each other.
In terms of Euclid's first common notion being a postulate, a postulate is a statement that is accepted without proof. It is a basic assumption or starting point from which other mathematical truths can be derived. Euclid's first common notion is considered a postulate because it is not proven or derived from any other statements or principles. It is simply accepted as true. So, in summary, Euclid's first common notion, as stated by Lincoln in the movie, can be seen as both a postulate and a theorem. It serves as a fundamental assumption in mathematics, and it can also be proven using other accepted principles.
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there are two ducks in front of a duck, two ducks behind a duck and a duck in the middle. how many ducks are there?
Answers
Answer:
3 Ducks
Step-by-step explanation:
Two ducks are in front of the last duck; the first duck has two
ducks behind; one duck is between the other two
Hence , there are 3 ducks
Hope it is correct
Answer: I think 7
Step-by-step explanation: Sorry if its wrong.
Graph the image of ΔLMN under a reflection across the x-axis
Answers
ANSWER
EXPLANATION
To reflect the triangle over the x-axis, the x-coordinates of the vertices remain the same, and the y-coordinates change to their opposites. Thus, to draw the image, we have to draw auxiliary vertical lines across each vertex of triangle LMN and graph the image of each vertex at the same distance from the x-axis on the opposite side,
How many Pennies did she collect in total
Answers
Answer: 4
Step-by-step explanation:
And I also don’t know how to do this.
Answers
C is the answer because i did this and it not that hard if you let the teacher explain to u
What is the result of 1.58/3.793 written with the correct number of significant figures?
A.) 0.41656
B.) 0.4166
C.) 0.417
D.) 0.42
E.) 0.4
Answers
Answer:C
Step-by-step explanation:
!solve this!
.
2x − 50 > 75
Answers
what can someone do to show their progress
Answers
Answer:
lol what is it....
Step-by-step explanation:
Charlie lives halfway between Chicago and Hoopertown. Amanda lives halfway between Charlie and Chicago. Raymond lives between Charlie and Hoopertown. All three houses lie on a straight line from Chicago to Hoopertown. If Raymond lives 15 miles from Amanda and 23 miles from Chicago, how far does he live from Hoopertown?
Answers
Answer:
Let's assume that the distance between Chicago and Hoopertown is represented by 'x' miles.
According to the given information:
Raymond lives 23 miles from Chicago, so the distance between Amanda and Chicago is 23 - 15 = 8 miles.
Since Amanda lives halfway between Charlie and Chicago, the distance between Charlie and Chicago is also 8 miles.
Therefore, the distance between Charlie and Hoopertown is x - 8 miles.
Since Charlie lives halfway between Chicago and Hoopertown, the distance between Raymond and Charlie is (x - 8) / 2 miles.
Given that Raymond lives 15 miles from Amanda, we can set up the following equation:
(x - 8) / 2 = 15
To solve for x, we can multiply both sides of the equation by 2:
x - 8 = 30
Next, we can isolate x by adding 8 to both sides of the equation:
x = 38
Therefore, the distance between Chicago and Hoopertown (x) is 38 miles.Therefore, the distance between Chicago and Hoopertown (x) is 38 miles.Since Raymond lives 23 miles from Chicago, he lives (38 - 23) = 15 miles from Hoopertown.Therefore, the distance between Chicago and Hoopertown (x) is 38 miles.Since Raymond lives 23 miles from Chicago, he lives (38 - 23) = 15 miles from Hoopertown.Thus, Raymond lives 15 miles from Hoopertown.froen 1oday 2 t nccording to the uriblaspd expectintions theory? (Do not round intermediate calculations. Rtound yout percentage answer to 2 decimal places: (ee−32.16) ) from today, a fa eccording to the unblased expectations theory? (Do rot round intermediate calculations. Rourd your percentage answer to 2 decimal ploces. (e.9. 32.16))
Answers
According to the unbiased expectations theory, the forward rate from today to a future date can be estimated by taking the exponential of the difference between the interest rates. The percentage answer, rounded to two decimal places is 3.08 x \(10^{-13}\) percent.
The unbiased expectations theory is a financial theory that suggests the forward rate for a future date can be determined by considering the difference in interest rates. In this case, we need to calculate the forward rate from today to a future date. The formula for this calculation is \(e^{(-r*t)}\), where "r" represents the interest rate and "t" represents the time period.
In the given question, the interest rate is -32.16. To calculate the forward rate, we need to take the exponential of the negative interest rate. The exponential function is denoted by "e" in mathematical notation. Therefore, the calculation would be \(e^{-32.16}\).
To arrive at the final answer, we can use a calculator or computer software to evaluate the exponential function. The result is approximately 3.0797 x \(10^{-15}\).
To convert this to a percentage, we multiply the result by 100. So, the forward rate from today to the future date, according to the unbiased expectations theory, is approximately 3.08 x \(10^{-13}\) percent.
Please note that the specific date for the future period is not mentioned in the question, so the calculation assumes a generic forward rate calculation from today to any future date.
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Resuelva los siguientes problemas que incluyen fracciones y números decimales. Ejercicios 1 al 10. De una bolsa de caramelos, los 5/12 del total son de fresa y los 7/18 del total son de menta. Si los 35 caramelos sobrantes son de piña, ¿cuántos caramelos hay en total en la bolsa?
Answers
Answer:
180 dulces
Step-by-step explanation:
Deje que el número total de dulces sea x.
De la bolsa de dulces, 5/12 del total son de fresa y 7/18 del total son de menta.
Primero encontremos la fracción total que es:
5/12 + 18/7 = 29/36
Por lo tanto, la fracción de los dulces restantes será:
1 - 29/36 = 7/36
Hay 35 dulces sobrantes, lo que significa que:
7/36 * x = 35
x = (35 * 36) / 7
x = 180 dulces
Hay un total de 180 dulces en la bolsa.
Which number is ninetythree and six hundredths
Answers
Answer: 93/600 or 93.06
Step-by-step explanation:
x + 4/3 = 55 + x -44
what is x
Answers
Answer: no solution
Step-by-step explanation:
There is no value for x that makes the equation true
Answer:
the answer is -0.8
I need help pleasureeee
Answers
Answer:
no u
Step-by-step explanation:
Answer:
t + 3 years old
Step-by-step explanation:
t + 3 = Scott's age
Simplify: cot(theta)sin(theta)
A) cos(theta)
B) sin(theta)
C) cot(theta)
Answers
Step-by-step explanation:
Since cotθ = (cosθ/sinθ)
(cotθ)(sinθ) = (cosθ/sinθ)(sinθ) = cosθ. (A)
5. Centroid for right triangle ABC with Angle A=40 degrees and AB= 10 cm. Include centroid
on constructed triangle. Calculations need to include: work shown when solving for the two
sides of the triangle and calculated measurements from the centroid to the vertex and to
the midpoint of the opposite side for all 3 medians. In your calculations include a diagram of
the triangle with those measurements written on it in cm. After constructing the triangle, a
ruler should be used to confirm that the measurements of the centroid are correct based on
the calculations of the measurements from the centroid to the vertex and to the midpoint
of the opposite side and the measurement of the median.
Explain with drawings of the triangle and measurements
Hint: Use tan sin cos and draw it out (doesn’t have to be to scale)
Answers
\(sin(40) = BC/10\)\(sin(40) = BC/10\)Distance from Centroid to Midpoint of AB ≈ 2.5 cm. Therefore, the measurements of the centroid and the medians of the triangle have been calculated and confirmed using a ruler. The diagram of the triangle with the measurements.
To find the centroid of a right triangle ABC with angle A = 40 degrees and AB = 10 cm, we first need to find the lengths of the other sides of the triangle. Let's call the length of BC as x and the length of AC as y.
Using trigonometry, we can find that:
\(sin(40) = BC/10\)
\(BC = 10*sin(40)\)
BC ≈ 6.427 cm
\(cos(40) = AC/10\)
\(AC = 10*cos(40)\)
AC ≈ 7.664 cm
Now that we have the lengths of all three sides of the triangle, we can find the coordinates of the centroid. The centroid is the point where the three medians of the triangle intersect, and each median passes through a vertex of the triangle and the midpoint of the opposite side.
To find the centroid, we first find the midpoint of each side of the triangle:
\(Midpoint of AB = (0, 5)\)
\(Midpoint of AC = (3.832, -1.864)\)
\(Midpoint of BC = (-3.832, -1.864)\)
Next, we find the coordinates of the centroid by averaging the coordinates of the three vertices:
\(Centroid = ((0+3.832-3.832)/3, (5-1.864-1.864)/3)\)
\(Centroid = (0, 0.424)\)
To confirm that the measurements of the centroid are correct, we can measure the distances from the centroid to the vertex and to the midpoint of the opposite side for all three medians. These distances are known as the medians of the triangle.
The median from vertex A passes through the centroid and the midpoint of BC. The distance from the centroid to vertex A is one-third the length of this median. Using the distance formula, we can find that:
\(Distance from Centroid to A = \sqrt((0-0)^2 + (0.424-0)^2)\)
Distance from Centroid to A ≈ 0.424 cm
The distance from the centroid to the midpoint of BC is also one-third the length of the median from vertex A. The midpoint of BC is (-3.832/2, -1.864/2) = (-1.916, -0.932). Using the distance formula, we can find that:
\(Distance from Centroid to Midpoint of BC = \sqrt((0-(-1.916))^2 + (0.424-(-0.932))^2)\)
Distance from Centroid to Midpoint of BC ≈ 2.532 cm
We can use similar methods to find the distances from the centroid to the vertices and midpoints of the other sides of the triangle. The final measurements and diagram are shown below:
Distance from Centroid to A ≈ 0.424 cm
Distance from Centroid to Midpoint of BC ≈ 2.532 cm
Distance from Centroid to B ≈ 2.532 cm
Distance from Centroid to Midpoint of AC ≈ 3.508 cm
Distance from Centroid to C ≈ 3.608 cm
Distance from Centroid to Midpoint of AB ≈ 2.5 cm
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I need help with this question. PLZZ HELP!!!
Answers
Answer:
the 8 in the graph
Step-by-step explanation: