there is 1 bus for every 32 students on a field trip.there are 96 student on the field trip. How many buses are needed

The name of a triangle when all 3 sides are the same length is Equilateral Triangle

A triangle is said to be equilateral if each of its three sides is the same length. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others.

Equilateral Triangle Properties

Equal on all three sides.

The sum of the three congruent angles is 60 degrees.

It has three regular sides and is a polygon.

The equilateral triangle is divided into equal halves by the perpendicular that is traced from its vertex to the other side. Additionally, the perpendicular's origin vertex's angle is split into two equal angles of 30 degrees each.

The centroid and ortho-centre are located at the same location.

The median, angle bisector, and altitude of an equilateral triangle are all the same.

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Therefore , the solution of the given problem of equation comes out to be 1225 boats registrations done in year 2013.

The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.

Here,

Given :

Let x be the number of boats:

t is number of years

In 1996 and 1997

=> 797 -751 = 46 boats increased

In 1997 and 1998

=> 806 -797 = 9 boats increased

So ,

the equation which can signify  the given information :

=> 2002 + t = 923 +x

So ,At 2013

=> 2013 = 1225 boats registrations done.

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1. |5+m|<13 is an "or" compound inequality. 2. 4|y + 6| ≥ 3 is neither compound inequality. 3. null set.

1. The inequality is given in the question, is as follows:

|5+m| < 13

The absolute value of the expression "5+m" is less than 13.

To solve the inequality, we need to split the inequality in two separate inequalities: 5+m < 13 and -5-m < 13.

Thus, |5+m|<13 is an "or" compound inequality.

2. 4|y + 6| ≥ 3 is neither compound inequality because we have just one inequality.

3. The absolute value of a number is always positive, so it is impossible for |g - 3| = -2. So the answer is c. null set.

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Given that the one side of a right-angled triangle is 12 and its angle is 19, the value of c is 36.85.

Trigonometry, a branch of mathematics, studies how triangle side lengths and angles relate to one another. Around the third century BC, the use of geometry in astronomical study led to the first appearance of the area. The study of specific trigonometric functions and how they could be applied to calculations is a topic covered in the branch of mathematics known as precise techniques. Trigonometry includes six well-known trigonometric operations. The names and acronyms for each are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle properties, specifically of right triangle properties. But geometry is the study of geometric figures and their features.

given

a/sinA = c / sinB

12 / sin19 = c / sin90

36.85 = c /1

c = 36.85

Given that the one side of a right-angled triangle is 12 and its angle is 19, the value of c is 36.85.

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If Elena earn y = 8.40x dollars where x represent how many hours she work and Jada earn $7 per hour, it would take Elena approximately 17.86 hours and Jada approximately 21.43 hours to earn $150

To find out how many hours it would take for Elena to earn $150, we need to solve the equation:

y = 8.4x

150 = 8.4x

x = 150/8.4

x ≈ 17.86 hours

So it would take Elena approximately 17.86 hours to earn $150.

To find out how many hours it would take for Jada to earn $150, we divide 150 by her hourly rate:

= $150 /( $7/ hour)

≈ 21.43

So it would take Jada approximately 21.43 hours to earn $150.

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(x - 4) is a factor of the expression 5x³ − 7x² − ax − 28, when a = 28

Here we are given the expression 5x³ − 7x² − ax − 28

now we need to find a value of a for which (x - 4) is a factor of

5x³ − 7x² − ax − 28

This implies that 5x³ − 7x² − ax − 28.must be divisible by (x - 4)

On dividing 5x³ − 7x² − ax − 28. by x - 4 will give us

[tex]x-4) \overline{5x^{3}-7x^{2}-ax-28.}(5x^{2}+14x+(56-a)\\{\hspace{1cm} 5x^{3}-20x^{2}\\\\\hspace{2cm}\overline{14x^{2}-ax}\\{\hspace{2cm}14x^{2}-56x\\\\{\hspace{3cm} \overline{(56 - a)x - 28}\\{\hspace{3cm} (56-a)x-(56-a)\\{\hspace{5cm} \overline{28-a}[/tex]

Since (x - 4) is a factor of 5x³ − 7x² − ax − 28, there should not be any remainder left

Hence, 28 - a = 0

or, a = 28

Hence (x - 4) is a factor of 5x³ − 7x² − ax − 28, when a = 28

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Correct Question

Find the value of a such that (x−4) is a factor of 5x³ − 7x² − ax − 28.

The value of k are the graphs (equations) equal is k = -3/2

Equations are mathematical expressions that show the relationship between two variables.

Since we have the two equations  12y = -3x + 8 and 6y = kx -5, re-writing them, we have

12y = -3x + 8

3x + 12y - 8 = 0  (1)

Also, 6y = kx - 5

-kx + 6y + 5 = 0  (2)

For a pair of equations ax + bx + c = 0 (3) and a'x + b'x + c' = 0 (4) to be equal (or consistent), then

a/a' = b/b' = c/c'

Comparing with (1) and (2), with (3) and (4) above, we have that

So, using a/a' = b/b', we find k.

So, substituting the values of the variables into the equation, we have that

a/a' = b/b'

⇒ 3/-k = 12/6

Cross-multiplying, we have that

3 × 6 = -k × 12

k = -3 × 6/12

k = -3/2

So, the value of k = -3/2

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Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

When two figures or things are similar in size and shape, or when one is the mirror image of the other, they are said to be congruent.

It states that two triangles are considered to be congruent if they are identical duplicates of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equivalent to those of the first triangle.

Two line segments are said to be congruent if their lengths are identical. In addition, two congruent line segments have the same length. Two angles are congruent if they have the same measure.

Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

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Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

When two figures or things are similar in size and shape, or when one is the mirror image of the other, they are said to be congruent.

It states that two triangles are considered to be congruent if they are identical duplicates of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equivalent to those of the first triangle.

Two line segments are said to be congruent if their lengths are identical. In addition, two congruent line segments have the same length. Two angles are congruent if they have the same measure.

Angle 5 is congruent to angle 8 by (vertically opposite angle )

Angle 5 is also Congruent to Angle 4 (alternate Angles)

Angle 5 is also Congruent to Angle 1 ( corresponding Angles )

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Answer:

4 loaves of bread

Step-by-step explanation:

Cost of 1 loaf of bread = $3

Cost of 1 roll = $1

The baker needs to sell both items and it should be worth $24.

To find the linear equation,

Suppose, the baker sells

x

loaves of bread and

y

rolls.

Then the total cost of the sales has to be $24.

So, the linear equation will be:

3

x

+

1

y

=

24

.......................(A)

Now, it is given that the baker sold 12 rolls and we need to know how many loaves he has to sell.

For that, replace the

y

in equation (A) with 12 as

y

represents number of rolls sold.

Then the new equation becomes:

3

x

+

1

×

12

=

24

0r

3

x

=

24

−

12

or

3

x

=

12

Solving for

x

,

x

=

12

3

=

4

loaves

3×3×3×3×3 in exponential form is 3⁵.

When we represent a number in the exponential form then we can say that its power has been raised by an exponent. The exponential form is an easier way of representing repeated multiplication involving base and exponents.

For example, If we have to write the exponential form of a×a×a×a×a, we can write it as a base and the number of a's as the power that is

a×a×a×a×a = a⁵

Where

a is the base

5 is the power of a

We can simply write 3×3×3×3×3 in exponential form by raising the power to the base 3,

3×3×3×3×3 = 3⁵

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For y = 10x the constsnt of proportionality is 10

We know that the quantity m is proportional to quantity n if there is a constant p such that m = pn

Here, p is called as the constsnt of proportionality.

This means, the constsnt of proportionality is nothing but the ratio between two proportional quantities.

Two variables are proportonal to each others means, when the variable increase the other one would also increase at some rate and that rate is the constant of proportionality.

We have been given an equation y = 10x.

Comparing given equation y = 10x with y = kx (here k is the constsnt of proportionality)

we have k = 10

This means, the constsnt of proportionality is k = 10

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Answer:

Step-by-step explanation:

Zero Angle (0° in Measure)

Acute Angle (0 to 90° in Measure)

Right Angle (90° in Measure)

Obtuse Angle (90 to 180° in Measure)

Straight Angle (180° in Measure)

Reflex Angle (180 to 360° in Measure)

Complete Angle (360° in Measure)

Angular speed of the fan in radians per minute is 421 (crad /min) , The linear speed of the tip of a blade in inches per minute is

Suppose the dan turns at a rate of 69 revolutions per minute.

Angular speed of the fan in radians per minute is

According to the problem

w = 2zn

(a)  w = 2z * 67  

= 134z

≈ 421 crad /min)

Angular speed of the fan in radians per minute is 421 (crad /min)

The linear speed of the tip of a blade in inches per minute is

(b) v = 2z * 19 * 67

{ v = 2zrn}

=2546z

7988(cin / m * in)

The linear speed of the tip of a blade in inches per minute is 7988(cin / m * in)

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Dilation and Stretch are non-rigid transformations.

Non - Rigid transformation:

Non-rigid transformations can change the size or shape of the archetype, or both size and shape. The two transformations Strain and Shear are not rigid. The resulting image of the transform is changed in size, shape, or both.

A non-rigid transformation is a transformation that changes the length or angle of a shape's sides. Nonrigid transformations are dilation and stretching.

All types of transformations except dilation are rigid transformations.

Dilation transformations are divided into two types

Therefore non-rigid transformations are Dilation and Stretching

Dilation:

Dilation (usually denoted by ⊕) is one of the fundamental operations in mathematical morphology. Originally developed for binary images, it was expanded first to grayscale images and then to full meshes. Stretch operations typically use a structuring element to examine and expand the shapes contained in the input image.

Strechting:

A non-rigid transformation changes the size or shape of an object. Resizing (stretching horizontally, vertically, or both) is a non-rigid transformation.

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You can tell if a table shows a proportional relationship by calculating the ratio of each pair of values.

The table depicts a proportionate relationship if all of those ratios are the same.

If all of the ratios of the variables are equal, then there is a proportional link between the two variables.

In proportional relationships, one variable is, in other words, always a constant value multiplied by the other variable. The proportionality constant is the name given to the constant value. A mathematical equation of the form y=kx, where k is the proportionality constant, can be used to model any proportional relationships. The unit rate is another name for the proportionality constant.

Dustin, for instance, spends $8 each month for a music streaming service. The total cost of the service, c, and the number of months Dustin pays for the streaming service, m, are proportionate. 

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The angle also should be known to prove congruency.

It states that two triangles are said to be congruent if they are exact copies of one another and completely cover one another when superposed. In other words, two triangles are congruent if their corresponding sides and angles are equal to those of the first triangle.

It is ineffective to only know angle-angle-angle (AAA), as this can result in triangles that are similar but not congruent. There are four short cuts that can be used to check whether two triangles are congruent.

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An expression to represent the perimeter of the rectangle with  10/(x² + 11x +24) and (x+1)/(x+3) would be (x+12)(x+6)//(x+8)/(x+3).

What is the perimeter?

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.

Here, we have

Given: Sides = 10/(x² + 11x +24) and (x+1)/(x+3)

The perimeter is when you add all the sides of a shape.

In a rectangle, two sides are the same, and so are the other two. therefore, if the two sides are 10/(x² + 11x +24) and (x+1)/(x+3) the expression will be:

= 2(10/(x² + 11x +24)) + 2(x+1)/(x+3)

= 20/(x² + 11x +24) + 2(x+1)/(x+3)

= 20/(x+8)/(x+3) + 2(x+1)/(x+3)

= {20 + 2(x+1)(x+8)}/(x+8)/(x+3)

= {20 + 2(x² + 9x + 8)}/(x+8)/(x+3)

= { 20 + 2x² + 18x + 16}/(x+8)/(x+3)

= {2x² + 18x + 36}/(x+8)/(x+3)

= (x+12)(x+6)//(x+8)/(x+3)

Hence, an expression to represent the perimeter of the rectangle with  10/(x² + 11x +24) and (x+1)/(x+3) would be (x+12)(x+6)//(x+8)/(x+3).

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Answer: P

Step-by-step explanation:

Answer: x = 2, 1

Step-by-step explanation:2x^2 - 6x + 4 = 0

Firstly, simplify. Divide by 2 to get

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

Move the constant to the other side.

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

Divide the x term by 2 and square it

-3/2^2 = 9/4

Add this result to both sides.

2(x^2-3x+9/4) = 1/4.
Put the perfect sq on both sides
2(x-3/2)^2=1/4
Then solve the equation:

take the sqrt of both sides and isolate x for each solution

x-3/2= +/-1/2
x = 3/2 + 1/2
x= 3/2-1/2
x= 2, 1

On solving the provided question we can say that the ​Lateral Surface area=396cm2

The surface area of a three-dimensional object less the area of its bases is the item's lateral surface area. All of an object's sides, excluding its base and top, are considered its lateral surface. The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area.

The Lateral surface area of cylinder

=2πrh

2π×7×18=792cm2

When the height is reduced to half then using the same formula for the lateral surface area

we have

2π×7×9=396cm2

​Lateral Surface area=396cm2

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On solving the provided question we can say that the ​Lateral Surface area = 396 cm²

The surface area of a three-dimensional object less the area of its bases is the item's lateral surface area. All of an object's sides, excluding its base and top, are considered its lateral surface. The size of the lateral surface is referred to as its area. This must be distinguished from the total surface area, which consists of the base and top areas as well as the lateral surface area.

The Lateral surface area of cylinder

=2πrh

2π×7×18=792cm2

When the height is reduced to half then using the same formula for the lateral surface area

we have

2π×7×9=396cm2

​Lateral Surface area=396cm2

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Answer:

Step-by-step explanation:

x+y=56

x+12=y

2x+12=56

2x=44

x=22

y=56-22

y=34

x=22

hope this helps

Answer:

34 and 22

Step-by-step explanation:

x + y = 56   Add the two equations together

x - y = 12

2x     = 56  Divide both sides by 2

x = 34

substitute 34 for x in either of the two original equations to solve for y

x + y = 56

34 + y = 56   Subtract 34 from both sides

y = 22

Check:

x + y = 56

34 + 22 = 56  Checks

x - y = 12

34 - 22 = 12

12 = 12  Checks

The midpoint of the line segment joining (–4, –2) and (2, 8) is calculated to give: (-1, 3)

The centroid of a line segment is its middle point. Since it is equally far from both ends, it divides the region in half.

In coordinate geometry, the midpoint formula is the method for calculating the center point of a straight line given its endpoints' coordinates.

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

For points (–4, –2) and (2, 8).

X= (-4 + 2)/2 = -1

Y = (-2 + 8)/2 = 3

The midpoint is solved to be (-1, 3)

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The result after multiplication = 6/X, 1, 1/ 7

When one is divided by a number or value it is called the reciprocal of that number or value. It is also said the inverse form of the value or number. As example, reciprocal of 12 is written as 1/12.

What is the result?

There are four values 6, X, 6 and 42.

multiply the first number by the reciprocal of others.

reciprocal of X = 1/X

reciprocal of 6 = 1/6

reciprocal of 42 = 1/42

now we multiply, 6×1/X = 6/X

6×1/ 6 = 1

6×1/ 42 = 1 /7

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The piecewise-defined function for M(x), the cost for x megabytes of data used in a month [tex]$m(x)=\left\{\begin{array}{c}10, i f x \leq 2 \\ 0.1 x+9.8, i f x > 2\end{array}\right.$[/tex].

A function in mathematics from a set X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Data exceeding 2 MB is charged at a rate of $0.10 per MB; one-time fee is $10;

The cost per month for x MB of data is:

Up to 2 Mb of data utilized; $10

Data use of over 2 MB

One off charge = $ 10

Charge for data over 2 Mb is $ 0.10 per MB

The monthly charge for x MB data is:

Data ta used up to 2 Mb

$ 10

Data used more than 2 Mb

m(x) = 10 + 0.1(x-2)

m(x) = 10 + 0.1 x-0.2

m(x) = 0.1 x + 9.8

So the function is:

[tex]$m(x)=\left\{\begin{array}{c}10, i f x \leq 2 \\ 0.1 x+9.8, i f x > 2\end{array}\right.$[/tex]

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The table shows the temperature of a substance at the start of a science experiment which - 16.8°C and we were told that it changed by 3/4 of the value which therefore means that the final temperature at 2:35pm is - 29.4°C.

This is referred to as the degree of hotness or coldness of a substance and it is measured in Celsius, kelvin etc.

In this scenario we were told that the temperature - 16.8°C changed by 3/4 of the value which means that:

3/4 × - 16.8°C = - 12.6°C

The temperature at 2:35pm will therefore be  - 16.8°C - 12.6°C = - 29.4°C.

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Answer:8-b=13

Step-by-step explanation:

8-b=13

-b=13-8

-b=5

b=-5

The correct solution is shows in below.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

Given that;

1) 3/4 - 1/5 = 11/20

2) 3 1/3 - 4/7 = 2 16/21

3) 3 3/7 - 2 2/3 = 16/21

Now,

Simplify the fraction as;

1) 3/4 - 1/5 = 11/20

LHS;

⇒ 3/4 - 1/5

⇒ (15 - 4) / 20

⇒ 11/20

⇒ RHS

2) 3 1/3 - 4/7 = 2 16/21

⇒ 10/3 - 4/7

⇒ (70 - 12) / 21

⇒ 58 / 21

⇒ 2 16/21

⇒ RHS

3) 3 3/7 - 2 2/3 = 16/21

LHS;

⇒ 3 3/7 - 2 2/3

⇒ 24/7 - 8/3

⇒ (72 - 56)/21

⇒ 16/21

⇒ RHS

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We will convert between volume units by multiplication or division process depending on the standard metric units.

What is unit conversion?

Unit conversion is done either by multiplication or division process between numerical values. There are some standard metric units. By following the standard, we can convert one unit to another. As example we have a box that is 2 square feet area, now we want to know the area in inches. So, we will multiply it by 144 to convert in square inches.

How do we convert between volume units?

We convert between volume units either by multiplication or division process depending on the standard unit. If we find a volume in liter and we can convert it in cubic meter by multiplying the number by 0.001. Assume, we measured a volume in cubic feet, but someone want to know this volume in cubic meter that time we divide this value by 35.32 to convert in required unit.

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The equation for the line is y = 3/5x + 5.

What is equation ?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used.

y = mx + b

8 = 3/5(5) + b

8 = 15/5 + b

b = 5

∴ equation is y = 3/5x + 5

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