A rope is fixed between two trees that are 10 metres apart. When a child hangs on to the centre of the rope, it sags so that the centre is 2 metres below the level of the ends. Find the lenth of the rope.​

Therefore , the solution of the given problem of slope comes out to be  

M = 1/2.

What determines a line's steepness is its slope. Gradient overflow is a mathematical expression for the gradient. The slant is the proportion of both the vertical difference (rise) over the distance between two locations to the lateral change (run) over the same distance. Hill form of an equation is used to express a straight line's equation, which is written as y = mx + b. A point on the line where the slope is m, b equals a, and the y-intercept is placed is (0, b). An illustration would be the slope and y-intercept of the formula y = 3x - 7 (0, 7). At the location of the y-intercept, the line has a slope of m, b, and c.

Here,

Given : (0,-3) and (-2,-4)

Thus,

To calculate the slope ,

We use formula:

=> M = y2 -y1 /x2-x1

=> M = -4 -(-3) / -2 - 0

=> M = -1 /-2

=> M = 1/2

Therefore , the solution of the given problem of slope comes out to be  

M = 1/2.

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Answer:

7) perpendicular

8) perpendicular

Step-by-step explanation:

If the equations are in the form:

y = mx + b

(they all are in this form in these questions)

the m, the number in front of the x, is the slope.

If the slopes are the "negative reciprocals" (opposite signs and flipped over from each other) of each other, then the lines are perpendicular.

You can also do a quick check by, if the m values are multiplied together you should get -1.

1/3 • - 3 = -1

1 • -1 = -1

1/3 and -3 have opposite signs and are reciprocals (flipped over)

1 and -1 are opposite signs. It isn't very obvious maybe that they are reciprocals, but they are. Like 1/1 flipped over is 1/1.

The number 59 in the equation represents the following:

"A student's expected quiz score if they spent no time on their homework"

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

y=59+6x

When x=0, y=59+6*0 = 59+0 = 59

This means,  y=59 is the  student's expected quiz score if they spent no time on their homework.

The number 59 in the equation represents the following:

"A student's expected quiz score if they spent no time on their homework"

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Answer:

y = 3/2x - 3

Step-by-step explanation:

first find slope (m):

m = (-3/2 -(-15/2)) / (1 - (-3)) = (12/2) / 4 = 6/4 = 3/2

plug the point (1, -3/2) into the point-slope form (y-y1) = m(x-x1):

y - (-3/2) = 3/2(x-1)

y + 3/2 = 3/2x -3/2

now put it in slope-intercept form y = mx + b:

y = 3/2x -6/2

y = 3/2x - 3

The value of d in the equation is 13 and it is equal to the number of dresses made by her.

The total amount paid by Mr. Hubble to make some custom dresses is 1677 dollars.

The price paid to make one dress is 129 dollars.

The equation that represents this situation is given to be 1677 = 129d

Where d is the number of dresses made,

Now, using simple algebra,

1677 = 129d

d = 1677/129

d = 13

So, she has made a total number of dress she made is 13 and the value of d is the equation is also 13.

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The length AB of the roof is 3.20 m.

What is the Pythagorean theorem.

The Pythagorean theorem is one that can be used to determine the value of the unknown side of a right triangle when given two of its sides.

The theorem states that;

/Hyp/^2 = /Adj/^2 + /Opp/^2

Considering the given picture of the shed, draw a perpendicular to B from a point C on parallel line A. So that the length of AB can be referred to as the hypotenuse of triangle ABC.

Now applying the Pythagorean theorem, we have;

/Hyp/^2 = /Adj/^2 + /Opp/^2

/AB/^2 = /2/^2 + /2.5/^2

            = 4 + 6.25

/AB/^2 = 10.25

AB = (10.25)^ 1/2

AB = 3.20

Thus, the length of AB of the roof is 3.20 m.

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Fuel consumption is 53.957 miles per gallon for a car moving at  a speed of 60 miles per hour using least square Regression .

A statistical word for models that evaluate the connections between variables is regression. A single dependent variable Y and one or more independent variables X are studied using a linear regression model.

A technique for employing a goodness-of-fit criterion to fit a curve—not necessarily a straight line—through a collection of points. Regression that is most frequently used is linear regression. Recursion is occasionally used interchangeably with the word regression.

Y = mX + b, where X is the predictor (independent) variable, m is the estimated slope, and b is the expected intercept, is the formula for simple linear regression.

Calculation of Fuel Consumption in 60 miles per hour.

given the least square regression line is

y = 55.3286 - 0.02286x

so, y = 55.3286 - 0.02286 * 60 = 53.957 miles per gallon.

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The correct factorization are as follows:

(a) x² + x = x(x + 1)

(b) 3x-9x² = 3x(1 - 3x)

(c) 7x³ - 35x = 7x(x^2 - 5)

(d) 4x³ + 24x² = 4x^2(x + 6)

What do you mean by "factorization"?

The most crucial step in factorization is to identify the terms points of commonality. Divide each term by the common factor between them, then multiply the result by the entire expression to maintain the value.

One of the key techniques for reducing an algebraic or quadratic equation to a simple form is factorization. Thus, one should be familiar with factorisation formulas in order to simplify the complex problem.

Additionally, you can always multiply your response to see if you end up with the same result as your starting point.

Step by step solution:

(a): x² + x, [Here both terms have 'x' in common]

=x( (x²/x) + (x/x) )

= x(x+1)

(b): 3x - 9x², [Here both terms have '3x' in common]

=3x( (3x/3x) - (9x²/3x) )

= 3x(1-3x)

(c): 7x³ - 35x, [here both terms have '7x' in common]

=7x( (7x³/7x) - (35x/7x) )

= 7x(x²-5)

(d): 4x³+ 24x² [here both terms have 4x² in common]

=4x²( (4x³/4x²) + (24x²/4x²) )

= 4x²(x+6)

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Answer:340 cm long

Step-by-step explanation: multiply 7 x 10 then 70 x 12

Using multiplication we know that the product of 3 * - 4 is -12.

One of the four fundamental arithmetic operations, along with addition, subtraction, and division, is multiplication.

A product is the output of a multiplication operation.

The addition method, lengthy multiplication, grid method, and drawing lines are four different ways to multiply.

So, we have:

3 * -4

Here, we know that 3 is a positive number and -4 is a negative number.

And so the product will be a negative number.

Now, calculate the product as follows:

3 * -4

-12

Therefore, using multiplication we know that the product of 3 * - 4 is -12.

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The Iroquois perform rituals in "The World on Turtle's Back" to honour the twins, demonstrating their belief that they must carry out specific rituals in order to preserve the Earth.

A ritual is a set sequence of actions involving gestures, words, actions, or objects. The customs of a group, including a religious group, may dictate rituals. Formalism, traditionalism, invariance, rule-governance, sacral symbolism, and performance are characteristics of rituals but not what defines them.

All known human societies have rituals. In addition to the rites of passage, atonement, and purification, oaths of allegiance, dedication ceremonies, coronations, presidential inaugurations, marriages, funerals, and other ceremonies, they also include the worship rites and sacraments of organised religions and cults. Even routine behaviours like shaking hands and saying "hello" can be categorised as rituals.

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Answer:

polygon has 12 sides

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

the sum of the interior angles of a polygon is

sum = 180° (n - 2 ) ← n is the number of sides

given the sum of the interior angles is 5 times sum of exterior angles, then

sum = 5 × 360° = 1800° then

180° (n - 2) = 1800 ( divide both sides by 180 )

n - 2 = 10 ( add 2 to both sides )

n = 12

Thus the polygon has 12 sides

The numerical coefficient of xy in the given expression 6xy is 6.

In mathematical terms, a coefficient is a numerical value that is multiplied by a variable in an algebraic expression. The coefficient is the number that appears in front of the variable.

For example, in the expression 3x, the coefficient is 3. In the expression 2[tex]y^2[/tex], the coefficient is 2. In the expression -5[tex]z^3[/tex], the coefficient is -5.

In the case of a constant term in an expression, the coefficient is the constant term itself.

For example, in the expression 3x + 4, the coefficient of x is 3 and the coefficient of the constant term 4 is 4.

Here, in the expression 6xy, the numerical coefficient of xy is 6.

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Answer:

The least common denominator is 8, you need to multiply the 3 by 2.

Answer:

8

Step-by-step explanation:

The quantities which are proportional to 12/4 are 36/12 and 3/1 .

What is proportional ?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.

The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.

12/4 ⇒ 3/1

          = 24/9

          = 8/3

The quantity 12/4 is not proportional to 48/18

        = 18/6

        = 3/1

The quantity 12/4 is proportional to 36/12

       = 7/3

The quantity 12/4 is not proportional to 35/15

       = 12/8

       = 6/4

       = 3/2

The quantity 12/4 is not proportional to 24/16

The quantity 12/4 is proportional to 3/1

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Answer:

2 pie over r

Step-by-step explanation:

Step-by-step explanation:

the circumference is given by:

[tex]2\pi(radius)[/tex]

in this case x is the radius hence the circumference would be:

[tex]2\pi(x)[/tex]

hope this helps :)

Answer: m= 0 ; b= 16

(5,16) (-10,16)

Step-by-step explanation:

y=16 so dont need to find y cause it already there so (5,16) (-10,16)

m=y^2- y^1 / x^2-x^1

16-16 / -10-5 = 0/-15 = 0. So m= 0

b is y-intercept and we have y=16 so b=16

Answer: To estimate the tip, you can first round the bill to the nearest ten dollars. In this case, $706.03 rounded to the nearest ten dollars is $710.

Next, you can calculate the tip by multiplying the rounded bill amount by the tip percentage, 15% in this case.

15% of $710 is 15/100 * 710 = 106.50

So the amount of the tip is approximately 106.50

It's worth mentioning that this method of approximation is not always precise, but it can be a quick and easy way to calculate an estimate when you don't need a very precise answer.

Step-by-step explanation:

Answer:

The surface area of a sphere is given by the formula:

surface area = 4 * pi * r^2

Where r is the radius of the sphere.

Using this formula, the surface area of an orange with a radius of 3.5 cm is:

surface area = 4 * pi * (3.5 cm)^2

= 4 * pi * 12.25 cm^2

= 49.0307 cm^2

The volume of a sphere is given by the formula:

volume = (4/3) * pi * r^3

Where r is the radius of the sphere.

Using this formula, the volume of an orange with a radius of 3.5 cm is:

volume = (4/3) * pi * (3.5 cm)^3

= (4/3) * pi * 42.875 cm^3

= 113.097 cm^3

Step-by-step explanation:

Given ,

To Find : The Surface Area and the volume of a spherical orange

In order to find the surface area of a spherical orange we use the formula,

[tex]SA = 4\pi r^{2}[/tex]

[tex]SA = 4X\frac{22}{7} X 3.5X3.5[/tex]

[tex]SA =[/tex] [tex]154cm^{2}[/tex]

And now to find the volume of a sphere

[tex]V = \frac{4}{3} \pi r^{3}[/tex]

[tex]V = \frac{4}{3} X \frac{22}{7} X (3.5)^{2}[/tex]

[tex]V[/tex] [tex]= 179.59cm^{2}[/tex]

Hence, the surface area is 154[tex]cm^{2}[/tex]and the volume of a sphere is [tex]179.59cm^{2}[/tex]

The given equation t = s/5 represents a proportional relationship and the value of the constant of proportionality is 1/5.

The constant of proportionality is the constant value of the ratio of two proportional values. A proportionality relation exists between two changing quantities when either their ratio or product gives a constant.

Proportional relationships are written in the form y = kx

where k is the constant of proportionality.

The given equation below which is given in the question:

t = s/5

The above equation represents a proportional relationship.

According to the given question, k = 1/5 so the answer is 1/5.

Thus, the value of the constant of proportionality is 1/5.

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If Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years then he has to pay 3009.6 back.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years.

A=P(1+rt)

Where, A is final amount, P is principal amount, r is rate of interest, t is time period.

P=3000, r=0.16%=0.16/100=0.0016, t=2

A=3000(1+(0.0016)2)

=3000(1+0.0032)

=3000(1.0032)

=3009.6

Hence, Canon needs to pay back 3009.6

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Answer: B,D

Step-by-step explanation:

We refer to the enlargement or reduction of one of two figures as a similarity transformation. For example: When one of two figures can be produced from the other and the ratio of their corresponding sides is equal, we say that the two figures are comparable. Similar figures come in a variety of sizes and shapes.

Either a geometric similarity or a matrix transformation that produces a likeness are referred to as "similarity transformations" in this context. Space items are changed into comparable things by similarity transformations. Fractals and iterated function systems are based on essential principles such as similarity transformations and the idea of self-similarity.

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In order to maintain soil fertility and productivity, soil must be protected from erosion and other forms of deterioration. Water use and watershed management are typically included.

Eliminating the existing vegetation is the first step in making a garden bed. Weeds can be manually pulled. Just be certain to remove the roots to prevent regrowth. You might want to rent a gas-powered sod cutter to get rid of the grass if you're starting with a lawn.

Better soil conservation techniques that affect both erosion and fertility include crop rotation, cover crops, conservation tillage, and installed windbreaks.

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Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day.

Two or more expressions with an Equal sign is called as Equation.

The billing cycle for the month = 28 days

Current beginning balance = x

Annual percentage rate (APR) = 24%

Monthly percentage rate (MPR) = 2% (24% ÷ 12)

Purchase on the last day = $1,400

Total finance charge for the month = $51

Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)

Finance charge for the beginning balance = $50 ($51 - $1)

The current beginning balance, x = $2,500 ($50 ÷ 2%)

Equation for current beginning balance, x = 51 - 1 ÷ 0.02

Total finance charge for the last-day purchase = $28 ($1,400 x 2%)

Savings in finance charge by purchasing on the last day = $27 ($28 - $1)

Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day.

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No, 16x2 40x 25 is not a perfect square trinomial.

Perfect squares are numbers that are the result of multiplying a number by itself. Examples of perfect squares include 4, 9, 16, 25, 36, and 49. Perfect squares are also known as "square numbers" or "whole numbers." Perfect squares are not just limited to whole numbers; some decimals and fractions can also be perfect squares.

A perfect square trinomial is an expression of the form a2 + 2ab + b2, where a and b are constants. 16x2 40x 25 does not fit this form, and is therefore not a perfect square trinomial.

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The solution to the system of linear equations is (-8, -2).

NOTE: The problem that is solved here is, 'What is the solution to this system of linear equations? Y - x = 6, Y + x = -10'

The equations with two variables and the largest exponent order of 1 each have one, zero, or an infinite number of solutions, and are referred to as linear equations.

A linear equation with two variables has the conventional form ax + by + c = 0, where x and y are the variables.

Additionally, the answers can be expressed as ordered pairs, like as (x, y). The system of linear equations in two variables is graphically represented by two straight lines, which may intersect, be parallel, or be coincident.

y - x = 6 ----> y = x + 6

y + x = -10 -----> y = - x - 10

As both the equations in terms of y, we get

x + 6 = - x - 10

By further calculation

x + x = - 10 - 6

2x = - 16

Dividing both sides by 2

x = -8

Substituting the value of x in either of the equations

y - x = 6

y - (-8) = 6

So we get

y + 8 = 6

y = 6 - 8

y = - 2

Therefore, the solution to the system of linear equations is (-8, -2).

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The provided schematic must be followed in order to answer these diamond problems. You must multiply the values on the left (x) and right (y) cells in order to find the value that belongs in the top cell.

we have,

For Diamond Problems a

x+y=1.2

xy=.32

so value of x= .8 and y = .4.

for Diamond Problems b

x= 11

x+y=25.

so y= 14 and xy=11*14=154.

for Diamond Problems c

x=-7

y=-9

so x+y=-16 and xy= 63.

for Diamond Problems d

x+y=31

xy=234

x=13 and y=18

Because puzzles engage both the left and right sides of your brain, solving them aids in the development of your problem-solving abilities. Solving puzzles with others is a terrific method to improve your communication and cooperation skills in addition to your problem-solving and critical thinking abilities.

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