in the given figure,AB is parallel to CD and angle EAB =50°,angle ECD =100°,find angle AEC
​

The measure of angles a, b, c, d and e are 54°, 18°, 108°, 81° and 99°.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, workers in an office of 40 staff were asked their favorite type of take-away.

Fraction of a person = 1 degree

Here, 360° = 40 people

So, 1 degree = 40/360 =1/9

Now, angle a =6/40 ×360

= 54°

Angle b= 2/40 ×360

= 18°

Angle c= 12/40 ×360

= 108°

Angle d = 9/40 ×360

= 81°

Angle e =11/40 ×360

= 99°

Therefore, the measure of angles a, b, c, d and e are 54°, 18°, 108°, 81° and 99°.

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The volume of the piece is: 4489.33

To find the volume of this piece, we need to subtract the volume of the cylindrical hole from the volume of the sphere.

The volume of the sphere is given by the formula: V = (4/3) * pi * r^3

Where r is the radius of the sphere, so in this case: V = (4/3) * pi * (7cm)^3 = 1436 * 3.14 cm^3 = 4511.32 cm^3

The volume of the cylinder is given by the formula: V = pi * r^2 * h

Where r is the radius of the cylinder and h is the height of the cylinder, since the hole is drilled through the center of the sphere, the height of the cylinder is equal to the radius of the sphere, so: V = 3.14 * (1cm)^2 * 7cm = 21.99 cm^3

So the volume of the piece is: 4511.32 - 21.99 = 4489.33 cm^3

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The expressions which are having common denominator 24 are

13/24  +  7/12 , 1/8  -  5/3 and for 10 are 5 - 7/10 , 3/2 -  4/5 and for 12 are

7/6  -  5/12, -3/4 - 2/3.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and constants.

Given ,

So given expressions are,

13/24  +  7/12   =  13+ 7*2 / 24  = 13+14 / 24 = 27/24

7/6  -  5/12 = 7*2 - 5 / 12  = 14-5/12 = 9/12

-3/4 - 2/3 = - (3/4 + 2/3 ) = - ( 9 + 8 / 12) = -17/12

5 - 7/10  = 5*10 - 7 / 10  =  50 - 7 / 10 = 43/10

1/8  -  5/3   = 3 - 8*5 / 24  = 3-40 / 24 = -37 / 24

3/2 -  4/5 = 3*5 - 2*4 / 10  = 15-8 / 10  = 7/10

Therefore, The expressions which are having common denominator 24 are 13/24  +  7/12 , 1/8  -  5/3 and for 10 are 5 - 7/10 , 3/2 -  4/5 and for 12 are 7/6  -  5/12, -3/4 - 2/3.

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The measure of angle m∠CBD is equal to 55°

We shall first find the measure of the angle m∠CDB so that we can evaluate for the measure of angle m∠CBD using the sum of interior angles of a triangle theorem as follows:

m∠ADB and m∠CDB are on a straight line and their sum is equal to 180° so;

m∠CBD + 80° = 180° {sum of angles on a straight line}

m∠CDB = 180° - 80° {subtract 80° from both sides}

m∠CDB = 100°

m∠BCD + m∠CDB + m∠CBD = 180° {sum of interior angles of a triangle}

25° + 100° + m∠CBD = 180°

125° + m∠CBD = 180°

m∠CBD = 180° - 125° {subtract 125° from both sides}

m∠CBD = 55°

In conclusion, the measure of angle m∠CBD is equal to 55°.

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The equation for the situation described in your problem would be y  is $10x + $2.50  .

To utilize substitution to resolve an equational system:

Divide one of the two variables in one of the equations.

Substitute the expression that the isolated variable's equivalent from Step 1 into the other equation.

Solve the linear equation for the last variable.

system of equations, simultaneous equations Algebraic equations involving two or more must be solved cooperatively (i.e., the solution must satisfy all the equations in the system). For a system to have a single solution, the number of equations must equal the number of unknowns. Even then, a solution is not guaranteed.

The following equation would apply to the scenario in your problem:

y =$10x + $2.50  

y = $2x + $4.00

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The true statement is,  c.) Prism B has a greater volume than Prism C.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

Prism A is a rectangular prism with a height of six inches, length of three inches, and a width of two inches.

Prism B is a rectangular prism with a height of three inches, length of five inches, and a width of two inches.

Prism C is a rectangular prism with a height of two inches, length of seven inches, and a width of two inches.

now,

volume of prism=V = B*H

where, B is the area of base.

so, by calculating we get,

V-prism A= 36 inch^3

V-prism B= 30inch^3

V-prism C=28 inch^3

Hence, c.) Prism B has a greater volume than Prism C.

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Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Multiply the numbers:

-5x*15x + 12x - 4x.

Which should get you: -75xx + 12x - 4x

Then combine exponents : -75xx + 12x - 4 = -75x^2 + 12x - 4x

Combine like terms: -75x^2 + 8x

Then find common factor with is -1

Lastly, rewrite in factored form : -1(75x^2 + 8x) = -1(75x - 8)x

Colin had $23 to spend on four raffle tickets after buying them had $11. So each raffle ticket cost is $3 and the equation is 4x + 11 = 23.

Colin had $23 to spend on four raffle tickets after buying them had $11

We have to determine how much each raffle ticket cost and the equation.

Let the cost of one raffle is x.

So the cost of four raffle is 4x.

Colin has total $23.

Colin has left money = $11

So the required equation should be

4x + 11 = 23

Now solving the equation

Subtract 11 on both side, we get

4x = 12

Divide by 4 on both side, we get

x = 3

The cost of one raffle is $3.

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Answer:

no solutions

Step-by-step explanation:

8(2w - 3) = 4(4w - 8)

Use distributive property.

16w - 24 = 16w - 32

subtract 16w from both sides.

-24 = -32

When the variable falls out of the equation as you are working on it, and you're left with a false statement, there is no solution.

Answer:

no solution

Step-by-step explanation:

to find the value of w, we have to isolate it on one side of the equation.

first, we distribute the numbers outside of the parentheses and multiply them to each term on the inside. this gives us:

16w - 24 = 16w - 32

next, we move 24 to the other side of the equation by adding 24 to both sides. by doing this, we get rid of 24 on the left side by making its value 0, and we add it to -32 on the right side. this gives us:

16w = 16w - 8

after this, we do the same with the 16w on the right side and subtract it from both sides. however, you might notice that there's a problem here.

when you try to move the 16w on the right side to the left side, you subtract 16w from itself, which gets rid of the variable entirely. whenever this happens, there are no values of the variable that make the equation possible- meaning that the answer is no solution.

hope this helped, good luck!

Answer:

8

Step-by-step explanation:

x= 24/3 = 8

Answer:

[tex] \sf \: x = 8[/tex]

Step-by-step explanation:

Given equation,

→ 3x = 24

Now the value of x will be,

→ 3x = 24

→ x = 24 ÷ 3

→ [ x = 8 ]

Hence, the value of x is 8.

The rate of petrol in this case is R9 per liter.

What is rate?

In mathematics, rate is a measure of how one quantity changes in relation to another quantity. It is often expressed as a ratio or fraction, where the numerator represents the amount of change in the first quantity and the denominator represents the amount of change in the second quantity.

The rate of petrol can be expressed as the cost per liter. To find the cost per liter of petrol in this case, we can divide the total cost by the total amount of petrol:

Cost per liter = Total cost / Total amount

For the given scenario, we have 20 litres of petrol for R180. So the rate can be calculated as:

Rate = Total cost / Total amount = R180 / 20 litres

Simplifying the expression, we get:

Rate = R9 per litre

Therefore, the rate of petrol in this case is R9 per liter.

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The linear equation for the coordinate points given is obtained as y = -3/2x + 19.5.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The coordinate points for the lines are (11,3) and (7,9).

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[9 - 3]/[7 - 11]

(6)/(-4)

3/-2

So, the slope point is obtained as m = 3/-2.

The equation becomes - y = -3/2x + b

To find the value of b substitute the values of x and y in the equation -

3 = -3/2(11) + b

3 = -33/2 + b

b = 3 + 33/2

b = (6 + 33)/2

b = 39/2

b = 19.5

So, the value for b is 19.5.

Now, the equation becomes -

y = -3/2x + 19.5

The graph for the equation is plotted.

Therefore, the equation is obtained as y = -3/2x + 19.5.

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Answer:

18.19

Step-by-step explanation:

$ = linear f(t)

$16.03 = f(40) = fixed fee + per min fee = x + 40y

$19.72 = f(81) = fixed fee + per min fee = x + 81 y

use above 2 equations to minus the other

you get:

19.72-16.03 = 41y

so y = 0.09

so x = 16.03 - 40*0.09 =12.43

so for 64 mins

cost = 12.43 + 0.09*64 =18.19

The value of x when using addition property of equality to solve the given problem is; -44

The addition property of equality is a property of equality that states that when the same quantity is added to both sides of an equation, it will produce an equivalent equation. For example, 4 = 2 + 2 is an equation due to the fact that both the right and the left-hand sides of the equal sign represent the number 4.

The equation to solve is;

-60 = x - 16

By the use of addition property of equality, we will add 16 to both sides to get;

-60 + 16 = x - 16 + 16

x = -44

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The distance covered on the yesterday was 24 miles.

Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Given that, The number of miles is 15 for today and m for yesterday. The number of hours is 2.5 for today and 4 for yesterday, the rate is same for both the days, therefore, this will represent a proportion,

Therefore, establishing the proportion,

15 / 2.5 = m / 4

15 × 4 / 2.5 = m

m = 24

Since, we got the value of m is 24 miles.

Hence, the distance covered on the yesterday was 24 miles.

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Answer: 180 kilometers

Step-by-step explanation:

Answer:

I think she runs 1 kilometer every 5 minutes

Step-by-step explanation:

According to the unitary method,

(a) Ticket cost for 5 people is $28.75

(b) The cost for ticket is $28.75 and the cost for popcorn is $53.25

In math the term called unitary method is defined as a basic concept to find the value of a single unit and then using that value to find the value of multiple units.

Here we have know that each person in a group buys a movie ticket, a drink, and a popcorn.

And the cost for each of the product is listed as Ticket is $5.75, Drink is $2.00 and Popcorn is $3.25.

Then the cost of 5 people is calculated as,

=> 5.75 x 5

=> 28.75

And the third group buys 5 tickets and 4 large bags of popcorn for $82.

Then the cost of the ticket is calculated as,

=> 82 - 28.75

=> 53.25

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Answer:

if younger one weighs 1 ton, then older one is heavier

Step-by-step explanation:

1 ton = 2000lbs

When the data have the properties of interval data and the multiplication or division of two values is meaningful, the variable has which scale of measurement is referred to as Ratio Scale.

Now, According to the question:

A scale of measurement can be defined as a classification which is used to illustrate the attributes of the values that are assigned to variables associated with a data set.

The scales of measurement.

Generally, there are four (4) basic scale of measurement for a variable and these include the following;

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If one set of the opposite sides of a quadrilateral is equal and parallel, the shape is referred to as a parallelogram.

A quadrilateral is a parallelogram if each pair of opposite angles in it is equal. The quadrilateral ABCD is a figure in which A = C and B = D. We are aware that a quadrilateral's angles add up to 360 degrees. ABCD is therefore a parallelogram.

A quadrilateral is a parallelogram if one pair of its opposite sides is both equal and parallel. A quadrilateral becomes a parallelogram if its diagonals cut each other in half.

The opposite sides of a parallelogram are equal to one another. A parallelogram's diagonals are consistently equal. The diagonals do not cross each other in a parallelogram. The diagonals in a parallelogram are always at right angles to one another.

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The angular momentum of an object can be calculated using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

In the case of the ballet dancer, we are told that they are spinning at 1.5 rev/sec, and that they can be modeled as a cylinder with a moment of inertia of 22 MR^2, a mass of 62 kg, a height of 1.6 m, and a radius of 0.16 m.

We can calculate the moment of inertia of the cylinder using the formula I = (1/2) MR^2, where M is the mass and R is the radius.

Plugging in the values we have, I = (1/2)(62 kg)(0.16 m)^2 = 3.072 kg-m^2

We can then calculate the angular momentum of the dancer by plugging in the values we have into the formula L = Iω,

L = (3.072 kg-m^2)(1.5 rev/sec) = 4.608 kg-m^2/s

So the angular momentum of a ballet dancer who is spinning at 1.5 rev/sec, modeled as a cylinder with a moment of inertia of 22 MR^2, a mass of 62 kg, a height of 1.6 m and a radius of 0.16 m is 4.608 kg-m^2/s.

Answer:

See below

Step-by-step explanation:

No table was given but it should look something like

x   y

-3  1

-2  2

-1   3

0   4

1    5

2   6

3   7

Whatever number you select for x add 4 to it and that will give you your y value

Answer:

20

Step-by-step explanation:

=12÷3[-15-5{6-8+2}]

=12÷3[-15-5{6-10}]

=12÷3[-15-5-4]

=12÷3[20-4]

=12÷3+16

=4+16

=20

If Jake finally found the gaming console on a resale platform, it was marked up 40% ,then the amount that Jake has to pay to buy it is $418.6    .

The retail price of the gaming console is = $299  ;

the markup in the price of the gaming console is = 40%  ;

then the new price of the gaming console is = 299 + 40%  of $299  ;

= 299 + 0.40 × 299      ...because 40% is 0.40

Simplifying further ,

we have ;

= 299 + 119.6

= 418.6

Therefore , Jake has to pay $418.6 for the gaming console to buy from the resale platform .

The given question is incomplete , the complete question is

A popular gaming console that retails for $299, was sold out for quite some time. Jake finally found it on a resale platform, but it was marked up 40% , Find the amount that Jake has to pay to buy it .

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Answer:

LESS THAN ONE

Step-by-step explanation:

1 1/5 - 1/3=0.86666666666

0.86666666666

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The required values of the angle ∠1 and ∠2 are  135°and 135°respectively.

An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.

We need to find angle 1 and 2

So, by using corresponding angle theorem,

∠1 = 135°

Similarly for ∠2

By using vertically opposite angle,

∠2 =135°

Thus, required value of the angle are ∠1 = 135°, ∠2 =135°.

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The asymptotes of f vertically (x)x=4, -4 are the vertical asymptotes.

An area on a graph where a function approaches infinity or negative infinity is known as a vertical asymptote. It happens when a rational function, which is a function that can be expressed as the quotient of two polynomials, has a denominator equal to zero but a numerator that is not. As a result, there is a noticeable "break" in the graph when the function becomes unbounded. For instance, when x=3, the vertical asymptote of the function 1/(x-3) exists.

As per the data given in the above question are as bellow,

The provided data are,

[tex]\mathrm{F}(\mathrm{x})=\frac{3 \mathrm{x}^2}{\mathrm{x}^2-16}[/tex]

When it comes to vertical asymptotes, the denominator is zero.

[tex]\mathrm{x}^2-16 & =0 \\\mathrm{x}^2 & =16 \\[/tex]

x= ±4

x=4,-4

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Answer:

nches. L.S.A.=2π(3)(9)=54π inches2. ≈169.64 inches2

Step-by-step explanation: