Parallelogram B is a scaled copy of parallelogramA

What is the value of c

Parallelogram B Is A Scaled Copy Of ParallelogramAWhat Is The Value Of C

Answers

Answer 1

The value of C in the parallelogram B would be = 1.5

How to determine the value of C in the parallelogram B?

To determine the value of C from the parallelogram B, the formula for scale factor should be used and it's given below as follows:

Scale factor = bigger dimension/smaller dimension

where:

bigger dimension = 5.6

smaller dimension = 4.2

scale factor = 5.6/4.2 = 1.33

The value of C = 2/1.33 = 1.5

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Related Questions

−2 + x ≤ −16 a closed or open circle?

Answers

Answer:

Closed circle

Step-by-step explanation:

If the sign is less than or equal too/greater than or equal too the circle will be closed

Answer:

closed

Step-by-step explanation:

use an open circle for "less than" or "greater than", and a closed circle for "less than or equal to" or "greater than or equal to".

Are the ratios 5:4 and 19:12 equivalent?

Answers

Answer: No

Step-by-step explanation: Let's look at one pair at a time. In order to go from 5 to 19 you would need to multiply 5 by 3.8, and to go from 4 to 12 you would need to multiply 4 by 3

I need help please..

I need help please..

Answers

The perimeter and the area of each composite figure is summarized below:

Case 1: p = 2 · (4√2 + 5), A = 20

Case 2: p = 28, A = 16

Case 3: p = 4 · (√13 + 2), A = 48

How to determine the perimeter and area of a composite figure

In this problem we find three cases of composite figures, whose perimeters and areas should be found. The perimeter is the sum of all side lengths and the area is the sum of areas of simple figures. The area formulas needed are introduced below:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Where:

A - Area of the figure, in square units.b - Base, in unitsh - Height, in units

The length of oblique lines are determined by Pythagorean theorem, whereas lengths of horizontal and vertical lines are found by direct inspection. Now we proceed to find the perimeter and area of each figure:

Case 1:

p = 4 · √(2² + 2²) + 2 · 5

p = 4√8 + 10

p = 8√2 + 10

p = 2 · (4√2 + 5)

A = 4 · 5

A = 20

Case 2:

p = 2 · 6 + 4 · 1 + 4 · 2 + 2 · 2

p = 12 + 4 + 8 + 4

p = 28

A = 2 · 6 · 1 + 2²

A = 12 + 4

A = 16

Case 3:

p = 4 · √(2² + 3²) + 2 · 4

p = 4√13 + 8

p = 4 · (√13 + 2)

A = 4 · 6 + 4 · 0.5 · 2 · 3

A = 24 + 24

A = 48

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What is a reasonable estimate for the addition equation 1.5 + 0.9 = ________ when you round each addend to the nearest whole number? (2 points)
A. 1.5
B. 2
C. 2.5
D. 3

Answers

The answer is C
hope this helps
1.5 is rounded to 2. 0.9 is rounded to 1. 2 + 1 = 3.

3 is the answer.

Points 1 to 6To present y=-x^3+3x^2, 9 points must be selected, point 1: Domain, 2: zeros of the function, 3: period and symmetry, 4: sign of the function, 5: going to the edge of the function, 6: asymptotes, 7: monotony and extreme values, 8: concavity and convexity, 9: to present the function graphically.

Answers

ANSWERS

1. Domain: all real values

2. Zeros: 0 (with multiplicity 2) and 3

3. Not periodic. Symmetric about the point (1, 2)

4. Positive for x < 3; negative for x > 3

5. f → ∞ as x → -∞; f → -∞ as x → ∞

6. none

EXPLANATION

1. The domain of a function is the set of all the x-values for which the function exists. In this case, we have a polynomial function and, therefore, the domain is all real values.

2. To find the zeros of the function, we have to solve,

\(-x^3+3x^2=0\)

First, factor x² and -1 out. To do so, we have to divide each term by x² and by -1 - or, in other words, divide by -x²,

\(\begin{gathered} -x^2\left(\frac{-x^3}{-x^2}+\frac{3x^2}{-x^2}\right)=0 \\ \\ -x^2(x^{3-2}-3x^{2-2})=0 \end{gathered}\)

So, we have,

\(-x^2(x-3)=0\)

In this equation, we can see that if x = 0, then the equation is true. Also, if x = 3 the equation is true. So, these are the two zeros, with the particularity that x = 0 has multiplicity 2. This is because the factor related to that zero is x squared.

Hence, the zeros are 0 and 3. 0 has multiplicity 2.

3. As mentioned before, this is a polynomial function, which means that it is not a periodic function. A cubic function is an odd function, and it is symmetric about the origin. However, this function is not the parent function, x³, but it is symmetric about the point (1, 2).

4. We know that the function is zero at x = 0 and at x = 3. For x < 0, the function is positive,

\(with\text{ }x=-1:\text{ }y=-(-1)^3+3(-1)^2=-(-1)+3\cdot1=1+3=4\)

For 0 < x < 3, the function is also positive. This is because x = 0 with multiplicity 2.

Then, since the function crosses the x-axis at x = 3 and that zero has multiplicity 1, we can conclude that the function is negative for x > 3.

Hence, is the function is positive for x < 3 and negative for x > 3.

5. As mentioned in part 4, the function is positive for all values of x less than 3, which means that the function goes to infinity as x goes to negative infinity.

Since for x > 3 the function is always negative, it goes to negative infinity as x goes to infinity.

6. A polynomial function has no restrictions in the domain and, therefore, has no asymptotes.

Simplify:
– 2.6(5-c)-c +8

Answers

Answer:

1.6c - 5

Step-by-step explanation:

Step 1: Distribute

-13 + 2.6c - c + 8

Step 2: Combine like terms

1.6c - 5

Would f(x) be the answer for both and how do you graph the g(x) table graph. What I have to solve for is on top in bold. I am asking for number 12
Algerba 1

Would f(x) be the answer for both and how do you graph the g(x) table graph. What I have to solve for

Answers

The graph of f(x)=√x+3+2 is shifted 3 units up and 2 units to the right from the parent graph of f(x)=√x.

We have,

Graph is a type of data structure that consists of a set of nodes (also called vertices) and edges. Each node is connected to other nodes by edges. Graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. They are also very useful for visualizing relationships between data points in a variety of fields.

The translation of the parent graph of f(x)=√x+3+2 is a vertical shift upward 3 units, followed by a horizontal shift to the right 2 units. This is represented by the bold line in the graph. In terms of the equation, the translation is represented by the addition of the 3 and the 2 to the function. The 3 causes the graph to shift vertically upward and the 2 causes the graph to shift horizontally to the right. As a result, the graph of f(x)=√x+3+2 is shifted 3 units up and 2 units to the right from the parent graph of f(x)=√x.

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complete question:

Below, the graph of f(x) = √x +3 + 2 is sketched in bold. Its parent function f(x)=√x is represented

by the thin curve.

1) Describe the

translation of the parent

graph.

2) How does the translation relate to the equation?

Which equation represents the relationship between x and y?

A. y = x + 25
B. y = 25x
C. x =25y
D. x = y +25

Answers

I’m not really sure but I think it is y=25x

Mashika: We already know from polling data that some segments of the electorate provide significant support to Ms. Puerta. If those segments also provide significant support to Mr. Quintana, then no segment of the electorate that provides significant support to Mr. Quintana provides significant support to Mr. Ramirez.

Salim: But actually, as the latest polling data conclusively shows, at least one segment of the electorate does provide significant support to both Mr. Quintana and Mr. Ramirez.

Among the following statements, which is it most reasonable to infer from the assertions by Mashika and Salim?

A. At least one segment of the electorate provides significant support neither to Mr. Quintana nor to Mr. Ramirez.
B. At least one segment of the electorate provides significant support to Ms. Puerta but not to Mr. Quintana.
C. Each segment of the electorate provides significant support to Ms. Puerta.
D. Each segment of the electorate provides significant support to Mr. Quintana.
E. Each segment of the electorate provides significant support to Mr. Ramirez.

Answers

Answer:

D. Each segment of the electorate provides significant support to Mr Quintana

Step-by-step explanation:

From the question, we have the following logic statement;

If those segment that provide significant support to Ms Puerto also provide support to Mr. Quintana then no segment of the electorate that provides significant support to Mr. Quintana provides significant support to Mr. Ramirez

Counter to the If Then Logic structure

At least one segment of the lectorate provides significant support to Mr. Quintana and Mr. Ramirez

Therefore, there is at least one segment that provides support to Mr. Quintana but not to Ms. Puerta

The segments that provide support to Ms. Puerta do not provide support to Mr. Ramirez

Mr. Quintana's support includes those from the supporters of Ms. Puerta and those from the supporters of Mr. Ramirez

Therefore, each segment of the electorate provide significant support to Mr. Quintana.

75 000 in standard form

Answers

Answer:

7.5×10^4

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Hope this helps <3

Answer: 7.5

Step-by-step explanation:

This Stem-and-Leaf Plot is missing one data item. If the mode of the data set is 71, what is the value of the unknown data item?

This Stem-and-Leaf Plot is missing one data item. If the mode of the data set is 71, what is the value

Answers

Using the mode concept, according to the stem-and-leaf plot, the missing value is of 71.

What is the mode of the data-set?

It is the value that appears the most times in the data-set.

In this problem, following the key format of the stem-and-leaf plot, disconsidering the missing value, the values 71 and 64 each appear 3 times.

However, the mode is 71, meaning that is should appear more times than 64, which means that the missing value is of 71.

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Answer:

The missing value is 71

Step-by-step explanation:

please help me! I will give brain list to whoever shows their work correctly with the correct answer. Please help this is due today!

please help me! I will give brain list to whoever shows their work correctly with the correct answer.

Answers

Step-by-step explanation:

For RIGHT trianges

sin Φ = opposite leg / hypotenuse

for THIS triangle

sin m =  6 sqrt(2) / 9   = 2/3  sqrt (2)    <=======exact value

                                   = .9428    <======four decimal value

Pleas homework due in 8 minutes plz plz help ASAP

Jacob used a simulation to predict the chance that a canal will flood in 1 of the next 6 years. A number 1 indicates a year in which the canal will flood. Numbers 2, 3, or 4 indicate a year in which the canal will not flood. The results of the simulation are shown. What is the experimental probability that a canal will flood in at least 1 of the next 6 years?

here is the table and the question

Pleas homework due in 8 minutes plz plz help ASAPJacob used a simulation to predict the chance that a

Answers

Answer:

is there like answer choices or do you just fill it in? if so then i think it would be unlikely.

Step-by-step explanation:

there’s only 7 ones which is the number that shows it will flood so 7/36 is unlikely, it has to be more than half to be likely

engineering: jet engines the fan blades on commercial jet engines must be replaced when wear on these parts indicates too much variability to pass inspection. if a single fan blade broke during operation, it could severely endanger a flight. a large engine contains thousands of fan blades, and 662 chapter 10 chi-square and f distributions safety regulations require that variability measurements on the population of all blades not exceed s2 5 0.18 mm2 . an engine inspector took a random sample of 61 fan blades from an engine. she measured each blade and found a sample variance of 0.27 mm2 . using a 0.01 level of significance, is the inspector justified in claiming that all the engine fan blades must be replaced? find a 90% confidence interval for the population standard deviation.

Answers

To determine if the inspector is justified in claiming that all the engine fan blades must be replaced, we can perform a hypothesis test using the sample variance and the given population variance threshold.

The null hypothesis (H0) is that the population variance is less than or equal to 0.18 mm2, and the alternative hypothesis (Ha) is that the population variance is greater than 0.18 mm2.

Using the chi-square distribution and a significance level of 0.01, we can calculate the critical chi-square value that corresponds to the upper tail area of 0.01.

Next, we calculate the chi-square test statistic using the sample variance, the sample size, and the population variance threshold. If the test statistic exceeds the critical chi-square value, we reject the null hypothesis and conclude that the fan blades must be replaced.

To find a 90% confidence interval for the population standard deviation, we can use the chi-square distribution and the degrees of freedom (n-1), where n is the sample size. The confidence interval will be constructed based on the chi-square values corresponding to the lower and upper tails of 0.05 each.

Performing these calculations will provide the necessary information to determine if the inspector is justified in claiming that all the engine fan blades must be replaced and to establish the confidence interval for the population standard deviation.

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You buy a car for $48,000. For each year, t, the value, V, of the car decreases by 14%.
Write a model to represent this scenario?

Answers

Answer:48.014

Step-by-step explanation:you got to say 48,000 plus 0.014 and you hit the equal button and see what u get and i hit the equal button and i got this answer 48.014 is my answer for this question

Someone pleaseeee help me!!!! I’m stuck

Someone pleaseeee help me!!!! Im stuck

Answers

Answer:

Hey there!

1/2 can also be written as 8/16.

Thus, starting from 0, count 8 tick marks, and place a point there.

3/16 is just 3/16.

Thus, starting from the 8th tick mark (where you left off in the first part) count three more tick marks to the 11th tick mark.

This shows us that 8/16+3/16=11/16.

Hope this helps :)

Answer:

so 1/2+3/16 is 11/16

Step-by-step explanation:

count the lines until u get to 11 and thts where u put the point.

hope this helps.have a good day

Dwayne ordered a set of purple and green pins. He received 35 pins in all. 28 of the pins were purple. What percentage of the pins were purple?

Answers

Answer:

28/35 = 4/5

Step-by-step explanation:

28 divided by 7 = 4

35 divided by 7 = 5

Please help me Sally hiked 6 tenths of a 3.6 mile trail. How many miles did Sally have left to hike?

Answers

Answer:Sally hiked 2.16 miles

Step-by-step explanation:

Sally hiked 6 tenths of a 3.6 mile trail.

6 tenths means 6/10

Therefore, Sally hiked   6/10 x 3.6 mile= 2.16 miles

if the population of san diego grows by 3.5% per year how long will it take the population to double?

Answers

It will take approximately 20 years for the population of San Diego to double at a growth rate of 3.5% per year

How to calculate long will it take the population to double

To find out how long it will take for the population to double, we can use the rule of 70. The rule of 70 states that to find the approximate number of years it takes for a quantity to double, divide 70 by the annual growth rate as a percentage.

In this case, the annual growth rate is 3.5%, so we can calculate the doubling time as follows:

70 / 3.5 = 20

Therefore, it will take approximately 20 years for the population of San Diego to double at a growth rate of 3.5% per year.

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You earn $220 after working for 11 hours. What is your earning
rate in terms of dollars per hour?
$__/hr

Answers

220 divided by 11 = 20
$20/hr

Answer:

20

Step-by-step explanation:

220 / 11 = 20, so $20 per hour

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You estimate that there are 64 marbles in a jar. The actual amount is 46 marbles. Find the percent error. Round to the nearest tenth of a percent if necessary.

Answers

Answer:

percentage error = 39.1%

Step-by-step explanation:

You estimate that there are 64 marbles in a jar. The actual amount is 46 marbles. Find the percent error. Round to the nearest tenth of a percent if necessary.

Given that You estimate that there are 64 marbles in a jar.

The actual amount is 46 marbles

Actual marbles = 46

Your estimate = 64

\(\% error =\frac{estimated - actual}{actual}\)

% error = | estimate - actual | / actual × 100%

estimate amount - actual amount = 64 - 46 = 18

\(= \frac{18}{46} \times 100\\\\=0.391\times 100\\\\=39.1 \%\)

Therefore,  percentage error = 39.1%

A research center conducted a national survey about teenage behavior. Teens were asked whether they had consumed a soft drink in the past week. The following table shows the counts for three independent random samples from three major cities.

Answers

The given table represents the counts from three independent random samples taken from three major cities regarding whether teenagers consumed a soft drink in the past week.

By summing up the counts of teenagers who consumed a soft drink from all three cities and dividing it by the total number of teenagers surveyed, we can calculate the overall proportion. Dividing this proportion by the total number of teenagers and multiplying by 100 will give us the percentage of teenagers who consumed a soft drink.

For example, if the first city had a count of 150 teenagers who consumed a soft drink out of a total of 300 surveyed, the second city had 200 out of 400, and the third city had 180 out of 350, the overall proportion would be (150 + 200 + 180) / (300 + 400 + 350) = 530 / 1050. Multiplying this by 100, we find that approximately 50.48% of teenagers consumed a soft drink in the past week based on the combined sample.

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A research center conducted a national survey about teenage behavior. Teens were asked whether they had consumed a soft drink in the past week. The following table shows the counts for three independent random samples from major cities. Baltimore Yes 727 Detroit 1,232 431 1,663 San Diego 1,482 798 2,280 Total 3,441 1,406 4,847 No 177 904 Total (a) Suppose one teen is randomly selected from each city's sample. A researcher claims that the likelihood of selecting a teen from Baltimore who consumed a soft drink in the past week is less than the likelihood of selecting a teen from either one of the other cities who consumed a soft drink in the past week because Baltimore has the least number of teens who consumed a soft drink. Is the researcher's claim correct? Explain your answer. (b) Consider the values in the table. (i) Baltimore Detroit San Diego 0 0.1 0.9 1.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Relative Frequency of Response (ii) Which city had the smallest proportion of teens who consumed a soft drink in the previous week? Determine the value of the proportion. (c) Consider the inference procedure that is appropriate for investigating whether there is a difference among the three cities in the proportion of all teens who consumed a soft drink in the past week. (i) Identify the appropriate inference procedure. (ii) Identify the hypotheses of the test.

Look at the ingredients needed to make Josie's special pancakes. How much pancake mix and milk will you need if you want to double the recipe? to triple the recipe? solve this problem anyway you choose math answer

Look at the ingredients needed to make Josie's special pancakes. How much pancake mix and milk will you

Answers

Answer:

Double - 7 5/6

Explantion: 2 1/4 times 2 equal 4 1/2 for the pancake mix

1 2/3 times 2 equal 3 1/3 for the milk

So.....4 1/2 plus 3 1/3 equals 7 5/6

Triple- 11 3/4

Explantion: 2 1/4 times 3 equals 6 3/4 for the pancake mix

1 2/3 times 3 for the milk equals 5

So.... 5 plus 6 3/4 equal 11 3/4

Hope it help :)

The ratio of a rectangle's length to the rectangle's width is 6:11. If
the perimeter of the rectangle is 510 units, then what is the length of
the rectangle?

Answers

Answer:

Step-by-step explanation:

90

By solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.

What are equations?

It primarily consists of a variable, sometimes with a numerical constant in addition.

Take the following illustration into consideration to quickly grasp this idea. 3x – 4 = 5. It is a simple equation of class 7.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

So, we know that the ration is 6:11 and the perimeter is 510 units.

Then, form and solve the equation as follows:

510 = 2(6x + 11x)

510 = 12x + 22x

510 = 34x

x = 510/34

x = 15

Then, the length will be:
6x

6(15)

90 units

Therefore, by solving the equation 510 = 2(6x + 11x), we know that the length of the given rectangle is 90 units.

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Consider a velocity field where the x and y components of velocity are given by u = cy/(x2+y2) and v =-cx/(x2+y2) where c is a constant. This velocity field is called vortex flow Obtain the equations of the streamlines. For the vortex flow, calculate the time rate of change of the volume of a fluid element per unit volume. For the vortex flow, calculate the vorticity. a) b) c) Hint: For convenience use polar coordinates.

Answers

a) The equations of the streamlines are: r = c sin(θ)/constant; r = -c cos(θ)/constant. b) For the vortex flow, the time rate of change of the volume of a fluid element per unit volume is zero. c) For the vortex flow, the vorticity is (2 c/r2)e_r.

a) The equations of the streamlines can be obtained by setting the velocity field equal to a constant. This means that u = cy/(x2+y2) = constant and v =-cx/(x2+y2) = constant. To simplify these equations, we can use polar coordinates where x = r cos(θ) and y = r sin(θ). Substituting these into the equations for u and v gives us:
u = c sin(θ)/r = constant
v = -c cos(θ)/r = constant
Solving these equations for r gives us the equations of the streamlines:
r = c sin(θ)/constant
r = -c cos(θ)/constant


b) The time rate of change of the volume of a fluid element per unit volume can be calculated using the divergence of the velocity field. The divergence of the velocity field in polar coordinates is given by:
∇ ⋅ u = (1/r)(∂(r u_r)/∂r + ∂(r u_θ)/∂θ)
Substituting the expressions for u_r and u_θ in terms of u and v gives us:
∇ ⋅ u = (1/r)(∂(r (u cos(θ) + v sin(θ)))/∂r + ∂(r (-u sin(θ) + v cos(θ)))/∂θ)
Substituting the expressions for u and v in terms of c, r, and θ gives us:
∇ ⋅ u = (1/r)(∂(r (c sin(θ)/r cos(θ) - c cos(θ)/r sin(θ)))/∂r + ∂(r (-c sin(θ)/r sin(θ) - c cos(θ)/r cos(θ)))/∂θ)
Simplifying this expression gives us:
∇ ⋅ u = 0
This means that the time rate of change of the volume of a fluid element per unit volume is zero for the vortex flow.


c) The vorticity of the vortex flow can be calculated using the curl of the velocity field. The curl of the velocity field in polar coordinates is given by:
∇ × u = (1/r)(∂(r u_θ)/∂r - ∂u_r/∂θ)e_r + (∂u_r/∂θ - ∂u_θ/∂r)e_θ
Substituting the expressions for u_r and u_θ in terms of u and v gives us:
∇ × u = (1/r)(∂(r (-u sin(θ) + v cos(θ)))/∂r - ∂(u cos(θ) + v sin(θ))/∂θ)e_r + (∂(u cos(θ) + v sin(θ))/∂θ - ∂(-u sin(θ) + v cos(θ))/∂r)e_θ
Substituting the expressions for u and v in terms of c, r, and θ gives us:
∇ × u = (1/r)(∂(r (-c sin(θ)/r sin(θ) - c cos(θ)/r cos(θ)))/∂r - ∂(c sin(θ)/r cos(θ) - c cos(θ)/r sin(θ))/∂θ)e_r + (∂(c sin(θ)/r cos(θ) - c cos(θ)/r sin(θ))/∂θ - ∂(-c sin(θ)/r sin(θ) - c cos(θ)/r cos(θ))/∂r)e_θ
Simplifying this expression gives us:
∇ × u = (2 c/r2)e_r
This means that the vorticity of the vortex flow is (2 c/r2)e_r.

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Amelia is 3 years younger than Etta. The product of their ages is 40. How old is Amelia?

Answers

Answer:

Amelia is 5 years old

Let x be Amelia and y by Etta.

[] Amelia is 3 years younger than Etta.

x = y - 3

[] The product of their ages is 40.

x * y = 40

We can use a system of equations to solve

[] The system

a = e - 3

a * e = 40

[] Graphing

-> See attached

[] The answer is 5

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.

- Heather

Amelia is 3 years younger than Etta. The product of their ages is 40. How old is Amelia?

what is the total area of all the sides of the cube if one edge is 12 cm

Answers

we are asked to determine the surface area of a cube that has a side length of 12 cm.

To do that let's remember that a cube has 6 faces and the area of each face is its side length squared. Therefore, the total surface area is the side length squared multiplied by 6:

\(A=6(12\operatorname{cm})^2\)

Solving the operation:

\(A=864cm^2\)

181 sq cm

Step-by-step explanation:

Answer:Total surface area of cubes (TSA) = 6a2

(1) a = 3cm

TSA = 6 × 3 × 3, TSA = 54 sq.cm

(2) a = 5 cm TSA = 6 × 5 × 5, TSA = 150 sq.cm

(3) a = 5,5 cm, TSA = 6 × 5.5 × 5.5

TSA = 181.5 sq. cm

Un agricultor planta 720 naranjos, 250 matas de mandarina, 360 de mamon y 480 de níspero en el menor número posible de hileras, cada una con el mismo número de árboles, sin mezclarlos. A) ¿Cuántos arboles tiene cada hilera? B) ¿Cuántas hileras necesita?

Answers

Answer:

A) Se requiere 10 árboles por hilera.

B) El agricultor necesita 72 hileras de naranjos, 25 hileras de mandarinos, 36 hileras de mamoneros y 48 hileras de nísperos.

Step-by-step explanation:

A) A continuación, realizamos la descomposición factorial de cada número:

Naranjos

\(720 = 2 \times 2 \times 2 \times 2 \times 3\times 3\times 5\)

\(720 = 2^{4}\times 3^{2}\times 5\)

Mandarinos

\(250 = 2\times 5\times 5\times 5\)

\(250 = 2\times 5^{3}\)

Mamoneros

\(360 = 2\times 2\times 2\times 3\times 3\times 5\)

\(360 = 2^{3}\times 3^{2}\times 5\)

Nísperos

\(480 = 2\times 2\times 2\times 2 \times 2\times 3\times 5\)

\(480 = 2^{5}\times 3\times 5\)

El máximo común divisor de los cuatro números representa el número de árboles de cada hilera considerando el menor número posible de hileras, cuyo valor es \(2\times 5 = 10\). Se requiere 10 árboles por hilera.

B) El número de hileras por árbol se determina al dividir el total de cada tipo de árbol por el resultado del punto anterior:

Naranjos

\(x = \frac{720}{10}\)

\(x= 72\)

Mandarinos

\(x = \frac{250}{10}\)

\(x = 25\)

Mamoneros

\(x = \frac{360}{10}\)

\(x = 36\)

Nísperos

\(x = \frac{480}{10 }\)

\(x = 48\)

El agricultor necesita 72 hileras de naranjos, 25 hileras de mandarinos, 36 hileras de mamoneros y 48 hileras de nísperos.

Teniendo en cuenta la definición de m.c.m:

A) Se requieren 10 árboles por hilera.

B) El agricultor necesita 72 hileras de naranjos, 25 hileras de mandarinos, 36 hileras de mamoneros y 48 hileras de nísperos.

A) Para hallar la cantidad de árboles que posee cada hilera debes hallas el m.c.d entre 720, 250, 360 y 480.

El máximo común divisor, m.c.d., de dos o más números es el mayor número que divide a todos de manera exacta, es decir, es el mayor de los divisores que tienen en común dos o más números.

El mínimo común múltiplo se suele expresar con las siglas m.c.d. (a, b), siendo a y b los números.

Para calcular el mínimo común múltiplo de dos o más números, de debe descomponer los números en factores primos (son los números que sólo son divisibles por sí mismos o por el número 1). En este caso:

720= 2×2×2×2×3×3×5= 2⁴×3²×5

250=2×5×5×5= 2×5³

360=2×2×2×3×3×5= 2³×3²×5

480=2×2×2×2×2×3×5= 2⁵×3×5

El mínimo común múltiplo se obtiene escogiendo todos los factores comunes, elevados a la menor potencia. Es decir, se escoge aquellos factores que aparecen en todas las descomposiciones la menor cantidad de veces. En este caso:

mcd (720,250,360, 480)= 2×5= 10

Entonces, se requiere 10 árboles por hilera.

B) El número de hileras por árbol se determina al dividir el total de cada tipo de árbol por la cantidad de árboles que se requiere por hilera:

Naranjos: 720÷10= 72

Matas de mandarina: 250÷10= 25

Mamon: 360÷10= 36

Níspero: 480÷10= 48

El agricultor necesita 72 hileras de naranjos, 25 hileras de mandarinos, 36 hileras de mamoneros y 48 hileras de nísperos.

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two cities are 145 miles apart. a truck travels this distance in 2.5 hours. a car is 1.5 times as fast as the truck. how long does it take for the car and the truck to meet if they leave at the same time, and travel toward each other

Answers

By using the travel distance formula, we found out that it takes 1 hour for the car and the truck to meet if they leave at the same time and travel toward each other.

It is given to us that -

Two cities are 145 miles apart

Truck travels this distance in 2.5 hours

Car is 1.5 times as fast as the truck

We have to find out the time taken for the car and the truck to meet if they leave at the same time, and travel toward each other.

We know that -

\(Speed = \frac{Distance}{Time}\) ----- (1)

Let us say that the speed of the truck is given by \(S_{t}\) and the speed of the car is given by \(S_{c}\).

Now, from equation (1), we can say that the speed of the truck,

\(S_{t}=\frac{145}{2.5} \\= > S_{t}= 58 miles per hour\) ----- (2)

It is given to us that the car is 1.5 times as fast as the truck

=> \(S_{c}= 1.5 * 58\\= > S_{c}= 87 miles per hour\) ----- (3)

It is mentioned that the car and the truck leave at the same time to meet each other.

Let us say that the truck meets the car at a distance 'd'.

This implies that the distance travelled by the car to meet the truck at a given point = (145-d)  --- (4)

From equation (1), we can say that

\(Time = \frac{Distance}{Speed}\)

Also, we know that -

Time taken by truck to travel d miles = Time taken by car to travel (145-d) miles

\(\frac{d}{58}=\frac{145-d}{87} \\= > 87d = 8410-58d\\= > 145d=8410\\= > d = 58\)

Thus, the truck will travel 58 miles to meet car after they leave at the same time.

So, the time taken for the car and truck to meet =

\(\frac{58 miles}{58 miles per hour} = 1 hour\)

Therefore, according to the distance formula, it takes 1 hour for the car and the truck to meet if they leave at the same time and travel toward each other.

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Kevin drew a scale drawing of a boarding school. The scale of the drawing was 1 millimeter : 3 meters. A building at the school is 150 meters long in real life. How long is the building in the drawing?

Answers

Answer:

50 mm

Step-by-step explanation:

Using the proportion: 1mm/ 3m

1mm     xmm

3m        150m

150/3= 50

1(50)= 50

x=50mm

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