if ∆DEF ~ ∆ABC, AB/AC =2/3 and DF=6cm then find the length of DE​

Answer:

taking your points

Step-by-step explanation:

The constant of proportionality is 180.

Answer:

[tex]10^{\circ}[/tex]

Step-by-step explanation:

Supplementary angles have measures that add to [tex]180^{\circ}[/tex].

For the polygon ABCDEFG, the measurement of ∠B is option D: 141°.

What is a polygon?

In a two-dimensional plane, a polygon is a closed object formed of line segments rather than curves. Polygon is a word that combines the words poly (which meaning numerous) and gon (means sides).

The polygon ABCDEFG has angle measurements as -

Measurement of ∠BCD = 148°

Measurement of ∠DEF = 142°

Measurement of ∠EFG = 130°

Measurement of ∠FGA = 129°

Measurement of ∠GAB = 120°

Measurement of ∠CDE = 90°

Let the measurement of ∠ABC be x° .

In a heptagon (or polygon having seven sides) the sum of all angles is 900°.

So, for polygon ABCDEFG the equation will be -

∠BCD + ∠CDE + ∠DEF + ∠EFG + ∠FGA + ∠GAB + ∠ABC = 900°

Substitute the values in the equation -

148° + 90° + 142° + 130° + 129° + 120° + x = 900°

148° + 90° + 142° + 130° + 129° + 120° + x = 900°

759° + x = 900°

x = 900° - 759°

x = 141°

Therefore, the value of x is obtained as 141°.

To learn more about polygon from the given link

https://brainly.com/question/26583264

#SPJ1

The occupant load of a one room daycare that is 20' by 30' is 17 people.

The occupant load of the daycare room can be determined by using the formula:

Occupant load = Area of room / Occupant load factor

From the case, we know that the area of the room is 20' x 30', then:

Room area = 600 square feet.

The occupant load factor for a daycare is typically 35 square feet per person. This means that each person in the daycare should have at least 35 square feet of space.

Using the formula, the occupant load of the one room daycare is:

Occupant load = 600 square feet / 35 square feet per person = 17.14 people

Therefore, the occupant load of the one room daycare is 17 people. This means that the daycare can safely accommodate 17 people at one time.

Learn more about Occupant Load here: brainly.com/question/29673678

#SPJ11

One example is 70:2. In the case of any non-zero number, this is a ratios of the form 35*k/k.

An set of points of numbers “ a ” and  “ b", represented as a / b, is a ratio if b is not equal to 0. The proportion is an expression that sets two ratios at the same value. If there are two boys and five girls, for instance, you may express the ratio as 2:5.

We got the word "ratio" directly from the Latin word, which is also called "suitable ratio." The mathematics and English ratios were derived from the Latin ratio, which had multiple meanings, ranging from "cause" to "calculated" to "proportion."

To know more about ratio visit:

https://brainly.com/question/13419413

#SPJ1

The S = 37.2^0

Below has been attached a diagram with the meaning of this problem. So we have a right triangle whose Opposite side (s) measures 18.9 and whose Adjacent side (r) measures 24.9. So, these two sides are related in the following form:

[tex]tan(S)=\frac{\text{Opposite side}}{\text{Adjacent side}} =\frac{s}{r} \\\\tan(S)=\frac{18.9}{24.9} \\\\tan(S)=0.76\\\\S=arctan(0.76)\\\\S=37.23^o\\\\\text{Roundding off:}\\\\\boxed{S=37.2^o}[/tex]

Therefore, the S = 37.2^0

Learn more:

Angles in triangles: brainly.com/question/4400594

#SPJ4

The circumference of a circle with a diameter of 11 inches using  π as 22/7 is 34.86 inches.

To find the circumference of a circle, we can use the formula:

C = πd

where C is the circumference, π is a mathematical constant (approximately 22/7), and d is the diameter of the circle.

The diameter of a circle is a straight line that passes through the center of the circle and touches two points on the edge of the circle. In this problem, we are given that the diameter of the circle is 11 inches.

To find the circumference, we can substitute this value for d in the formula:

C = πd = π(11 inches)

We can simplify this by using the approximation π ≈ 3.14 (or more precisely, π ≈ 22/7), to get:

C ≈ (3.14)(11 inches) = 34.54 inches

or

C ≈ (22/7)(11 inches) = 34.86 inches

So the circumference of the circle is approximately 34.54 inches or 34.86 inches, depending on which approximation of π is used.

To learn more about circumference click on,

https://brainly.com/question/24143262

#SPJ4

The measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

We shall first evaluate for the angle m∠B as follows:

m∠A + m∠B + m∠C = 180° {sum of interior angles of a triangle}

49° + B + 90° = 180°

B + 139° = 180°

B = 180° - 139° {subtract 139° from both sides}

m∠B = 41°

12.7/sin90° = a/sin41

a = (12.7 × sin49)/sin90° {cross multiplication}

a = 9.5848

12.7/sin90° = b/sin49

b = (12.7 × sin49)/sin90 {cross multiplication}

b = 8.3319

Therefore, the measure of the angle m∠B is equal to 41°. Using the sine rule the lengths of a and b are 9.6 and 8.3 respectively.

Know more about sine rule here: https://brainly.com/question/4372174

#SPJ1

The difference 6.96 - 0.04 is greater than 7.

Answer:

(a) (0,0)

Step-by-step explanation:
Solving with Elimination method-

Take the first equation-    3x - 2y = 6

Multiply both sides by 2
2(3x - 2y) = 2*6
6x - 4y = 12

Subtract Both the equations-

  6x - 4y = 12
- 6x - 4y = 12
=          0 = 0


The answer is (0,0)

Answer:

Step-by-step explanation:

The original price of the hat is $35. Paolo paid $28 for the hat.

So discount for the hat is $(35-28) = $7

$7 is discounted from $35. We have to find the percentage of the discount.

To find the percentage we have to divide the discount amount by the original price and then have to multiply it by 100.

So the discount percentage =

((7/35)×100) %

We can simplify 7/35 by dividing 7 and 35 both by 7. So we will get 1/5 after simplifying.

((1/5) ×100) %

(100/5)% = 20%

So the hat was discounted by 20%.

The correct answer is "It takes 15 pattern block trapezoids to create 5 hexagons."

Pattern block trapezoids are a type of geometric shape commonly used in math education. They are one of several shapes that can be used to create tessellations, or repeating patterns, on a flat surface. Pattern block trapezoids come in different sizes and are made of different colored plastic or foam, with each color representing a different size and shape. In addition to their use in creating tessellations, pattern block trapezoids are often used to teach geometry concepts such as area, perimeter, and angles. They can also be used to help students develop spatial reasoning skills and problem-solving abilities. The most common set of pattern blocks includes six shapes: the trapezoid, hexagon, square, parallelogram, rhombus, and triangle. These shapes can be combined in a variety of ways to create different patterns and designs, making them a versatile and useful tool for math education.

To learn more about pattern block click here

brainly.com/question/10064829

#SPJ4

After solving for the line with slope as -2 and point (3,-2) , the y intercept is  (0,4)  .

We use the Point Slope form of a linear equation to write the equation of a line given its slope and a point on the line.

So , the point slope form is ⇒ y - y₁ = m(x - x₁)  ;

Where m = slope , and (x₁, y₁) = point on line .

So , by using the slope (m = -2) and point (x₁, y₁) = (3, -2),

Substituting  these values and simplifying further ,

We get ; ⇒ y -(-2) = (-2)×(x - 3)  ;

⇒ y + 2 = (-2)×(x) + (-2)×(-3) ;

Subtracting 2 from both sides,

we have ;

⇒ y = -2x + 4

The y intercept of line is value of "y" when x = 0.

So , we substitute x = 0 in the equation of line y = -2x + 4  ;

that means ⇒  y = -2(0) + 4 ;

⇒  y = 4 .

Therefore, the y intercept of the line with slope "-2" and passing through the point (3, -2) is (0, 4).

Learn more about Y-Intercept here

https://brainly.com/question/16609931

#SPJ4

The worm is travelling at a speed of 0.0018 meter per second.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Total distance travelled by the worm = 1.3 m

The worm starts moving at 9 hour 12 minutes and reaches the end of the path at 9 hour 24 minutes.

Total time taken = 24 - 12 = 12 minutes

Speed = Distance / Time

Speed = 1.3 / 12

           = 0.1083 meter / minute

           = 0.0018 meter per second

Hence speed of the worm is 0.0018 meter per second.

Learn more about Speed here :

https://brainly.com/question/13680494

#SPJ9

According to the above statement, she has a 1/6 chance of rolling a 7 on the dice.

A possibility is a ratio that expresses the possibility or likely that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

When using two six-sided dice, there are 36 possibilities that might occur.

By using two dice, there are six ways to arrive to the sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), & (6, 1).

The likelihood of rolling a 7 is thus 6/36 = 1/6.

To know more about Probability visit:

https://brainly.com/question/24756209

#SPJ1

Answer:

94.2cm

Step-by-step explanation:

Diameter 30cm

π = 3.14

Circumference of a circle is given by the formula:

C = 2πr

r = radius

Radius is equal to half of the diameter

30/2 = 15cm

Sub into equation:

C = 2(3.14)(15)

C = 94.2cm

0 |-1| , 1.3 , 2, |2.7|

Step-by-step explanation:

it's right because |-1| is an absolute value and the absolute value is 1

Answer:

0,  |- 1| , 1.3,  2,  |2.7|

Step-by-step explanation:

The absolute value of any number, x,  denoted by |x| is the positive of that number

So | 2.7 | = 2.7

| - 1 | =  1

Therefore the order of the absolute values is
0,  1, 1.3, 2, 2.7 which is the same as 0,  |- 1| , 1.3,  2,  |2.7|

In a sample of 20 men, the mean height was 178 cm and a sample of 30 women, the mean height was 164 cm, then the mean height for both groups combined is approximately 172.4 cm.

To find the mean height for both groups combined, we need to calculate the weighted average of the means of each group, where the weight of each group is proportional to its sample size.

We can begin by finding the total height of all the individuals in both groups combined. The total height for the men's group would be 20 multiplied by the mean height of 178 cm, which is 3560 cm.

Similarly, the total height for the women's group would be 30 multiplied by the mean height of 164 cm, which is 4920 cm. Adding these two values gives a total height of 8480 cm for both groups combined.

Next, we need to find the total sample size, which is the sum of the sample sizes of the two groups. The total sample size is 20 + 30 = 50.

Finally, we can calculate the weighted average of the means of each group using the formula:

Weighted average = (weight of group 1 * mean of group 1 + weight of group 2 * mean of group 2) / (weight of group 1 + weight of group 2)

In this case, the weights of each group are proportional to their sample sizes. Therefore, the weighted average can be calculated as:

Weighted average = (20/50 * 178 cm) + (30/50 * 164 cm) = 172.4 cm

In summary, to find the mean height for both groups combined, we need to calculate the weighted average of the means of each group, where the weight of each group is proportional to its sample size. This is done by multiplying the sample size of each group by its mean height, adding the values, and then dividing by the total sample size.

To learn more about mean click on,

https://brainly.com/question/3699952

#SPJ4

The hypotenuse of the right triangle with legs measuring 18 in and 26 in is 31.6 in, rounded to the nearest tenth. This is calculated by using the Pythagorean Theorem, which states that a2 + b2 = c2 and plugging in the values for a and b.

The hypotenuse of a right triangle is the longest side of the triangle and is always opposite of the right angle. To calculate the length of the hypotenuse, you need to use the Pythagorean Theorem. The theorem states that a2 + b2 = c2, where a and b are the legs of the triangle and c is the hypotenuse. In this case, a is 18 inches and b is 26 inches, so the equation would be 182 + 262 = c2. Plugging in the values, we get 324 + 676 = c2, which simplifies to 1000 = c2. To find the length of the hypotenuse, we need to take the square root of 1000, which is 31.6 inches. Rounded to the nearest tenth, the hypotenuse of the right triangle with legs measuring 18 in and 26 in is 31.6 in.

Learn more about hypotenuse here:

https://brainly.com/question/29407794

#SPJ4

Answer:

The main cause of deforestation is agriculture (poorly planned infrastructure is emerging as a big threat too) and the main cause of forest degradation is illegal logging. In 2019, the tropics lost close to 30 soccer fields' worth of trees every single minute

Given that 10 bottles were bought for a total amount of $12, the price per bottle of sport drink is $1.20.

$12 divided by ten bottles equals $1.20.

By dividing the total amount paid ($12) by the quantity of bottles bought, the price per bottle of sport drink was determined (10). As a result, each bottle cost $1.20. According to the computation, the price of 10 bottles of sport drink came to a total of $12. The cost of individual goods or greater quantities of bottles can then be determined using this cost per bottle. The price per bottle can be used to compare the costs of various sport drink brands or sizes. Customers can choose and buy sport drinks with more knowledge if they are aware of the price per bottle.

Learn more about amount here

https://brainly.com/question/28970975

#SPJ4

The histogram of the magazine ranks the best paying college degrees in a country is illustrated below.

A histogram is a graphical representation of data that displays the frequency distribution of a set of continuous or discrete data

To construct a histogram, we would first need to determine the range of the data. In this case, the range would be the difference between the highest and lowest starting salaries or mid-career salaries. We would then divide the range into several intervals or "bins" of equal width.

For example, if we use a bin width of $10,000, the first bin would be $40,000-$49,999, the second bin would be $50,000-$59,999, and so on.

We would then count the number of degrees that fall into each bin and plot the counts as bars on a graph, with the bin ranges on the x-axis and the frequency counts on the y-axis. The resulting graph would be a histogram, showing the distribution of the data.

It is important to label the axes of the histogram and include a title that accurately reflects the data being presented.

To know more about histogram here.

https://brainly.com/question/30354484

#SPJ4

Complete Question:

Suppose a magazine ranks the best paying college degrees in a country. The following data show the median starting salary, the mid- career salary, and the percentage increase from starting salary to mid-career salary for the 20 college degrees with the highest mid- career salary.

Degree                     Starting Salary | Mid-Career Salary | % Increase

College Degree A      59,400                     104,000                       75 College Degree B     56,400                      101,000                        79 College Degree C     54,800                      101,000                        84             College Degree D     64,800                      104,000                        60    College Degree E      53,500                       93,400                        75           College Degree F       61,200                       87,700                        43              College Degree G       56,200                      97,700                        74            College Degree H       50,400                      87,000                        73            College Degree I         48,800                     97,800                       100                                College Degree J         60,800                     107,000                      76 College Degree K       47,500                      91,500                              

Frequency 40-49.9

Using a class width of 10, construct a histogram for the percentage increase in the starting salary.

This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.

What is inequality?

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

We can write the first inequality as x + y <= 12

This inequality represents the constraint that Mav can work at most 12 hours in total between both jobs.

The second inequality represents the constraint that Mav must earn no less than $140 in a given week, which can be written as:

15x + 10y >= 140

To graph the system of inequalities, we can plot the lines corresponding to x + y = 12 and 15x + 10y = 140 on the coordinate plane and shade the region that satisfies both inequalities.

The solution to the system of inequalities will be the values of x and y that lie in the shaded region.

One possible solution is x = 4 and y = 8, which means that Mav works 4 hours of lifeguarding and 8 hours of landscaping in a given week, earning a total of 15 * 4 + 10 * 8 = $120.

Hence, This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.

To learn more about inequality visit,

https://brainly.com/question/29166625

#SPJ1

Answer:

Step-by-step explanation:

You want inequalities, their graph, and a possible solution satisfying Mav's requirement for at most 12 total hours spent lifeguarding at $15 per hour and landscaping at $10 per hour, with an income of at least $140.

The required relations can be written ...

  x + y ≤ 12 . . . . . . . total hours

  15x +10y ≥ 140 . . . . total earnings

The inequalities need to be solved for y to match the answer format requirements.

  inequality 1: y ≤ 12 -x . . . . . . . . . . subtract x

  inequality 2: y ≥ 14 -1.5x . . . . . . divide by 10, subtract 1.5x

The attached graph shows a couple of possible solutions. The solution space is the doubly-shaded area bounded by vertices ...

  (4, 8), (12, 0), and (9 1/3, 0)

Mav will make the most money working 12 hours lifeguarding (x, y) = (12, 0).

She can just meet her income requirements by working 8 hours lifeguarding and 2 hours landscaping (x, y) = (8, 2).

One possible solution is 4 hours lifeguarding and 8 hours landscaping.

If one marble is drawn from a bag containing three red ones and one white one , then probability that it is a red one is 3/4 .

Total number of marbles in the jar is = 4 marbles ;

the number of red marbles in the jar is = 3 marbles ;

the number of white marbles in the jar is =  1 marble ;

The probability of drawing a red marble from the jar can be calculated as the number of red marbles divided by the total number of marbles in the jar:

⇒ P(red marble) = number of red marbles / total number of marbles

⇒ 3/4

⇒ 0.75

⇒ 75%

Therefore, the probability of drawing a red marble from the jar is 0.75 or 75%.

Learn more about Probability here

https://brainly.com/question/29251004

#SPJ4

The given question is incomplete , the complete question is

A jar contains four marbles: three red ones and one white ones , if one marble is drawn from the jar , find the probability that it is a red one ?

The equation -6(x+1)+8x=2(x-3) has all real numbers as solutions, meaning that any value of x will make the equation true. The equation does not have a single unique solution for x.

What is the equation in one variable?

An equation in one variable is a mathematical expression that contains a single variable, typically represented by x. The goal of solving an equation in one variable is to determine the value of the variable that makes the equation true.

To solve the equation -6(x+1)+8x=2(x-3), we can simplify the left-hand and right-hand sides of the equation and then solve for x. Here are the steps:

Distribute the -6 and 2 to the terms inside the parentheses: -6x - 6 + 8x = 2x - 6

Combine like terms on each side of the equation: 2x - 6 = 2x - 6

Subtract 2x from both sides of the equation: -6 = -6

At this point, we have a true statement (-6 = -6), but there is no variable present. This means that the equation has infinitely many solutions, and every real number is a solution to the equation.

Hence, the equation -6(x+1)+8x=2(x-3) has all real numbers as solutions, meaning that any value of x will make the equation true. The equation does not have a single unique solution for x.

To learn more about the linear equation in one variable, visit:

https://brainly.com/question/85774

#SPJ1

AB = [1 0] is the 2x2 identity matrix so, AB=I.

        [0 1]

To find a 3x2 matrix B such that AB=I, we need to solve the equation:

A × B = I

where I is the 2x2 identity matrix. We can use the hint given to us to find the columns of B.

Let B1 and B2 be the columns of B. Then we have:

A × B1 = I1

A × B2 = I2

where I1 and I2 are the columns of the 2x2 identity matrix I.

We can solve for B1 and B2 by setting up and solving the following systems of linear equations:

For B1:

1 × B1[1] + 1 × B1[2] = 1

2 × B1[1] + 1 × B1[2] = 0

1 × B1[1] + 1 × B1[2] = 0

For B2:

1 × B2[1] + 1 × B2[2] = 0

2 × B2[1] + 1 × B2[2] = 1

1 × B2[1] + 1 × B2[2] = 0

Solving these systems of equations, we get:

B1 = [-1, 1]

B2 = [1, -1]

Therefore, the 3x2 matrix B that satisfies AB=I is:

B = [-1  1]

     [ 1 -1]

     [ 0  0]

We can verify that AB is indeed equal to the 2x2 identity matrix I:

A × B = [1 2 1] × [-1 1 0] = [(-1)+2  (1)+(-1)  0+0] = [1 0]

           [1 1 1]   [ 1 -1 0]   [ 1+1  (1)+(-1)  1+0]   [0 1]

Therefore, AB = I:

AB = [1 0]

        [0 1]

Learn more about matrix at

https://brainly.com/question/28180105

#SPJ4

The question is -

For the given matrix A find a 3x2 matrix B such that AB=I, where I is the 2x2 identity matrix. [Hint: If B1 and B2 are the columns of B, then ABj = Ij.]

A =  1 2 1

       1 1 1

The side which corresponds to QS is VU, and the scale factor is 2.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

Given that, the figure on the right is a scaled copy of the figure on the left.

We need to find the corresponding side of QS and scale factor,

The figure is 90° counterclockwise rotated,

Therefore,

The corresponding sides are:

PR ~ TW

RQ ~ VT

QS ~ UV
PS ~ WU

∵ the measure of QS = 4 units and the measure of UV = 2 units

∴ scale factor = 4/2 = 2

Hence, the side which corresponds to QS is VU, and the scale factor is 2.

Learn more about scale factor, click;

https://brainly.com/question/29262154

#SPJ1

The question do not contain figure, the similar question is solved.