y=x2-14x+1
y=-14x+17

Based on the concept of unitary method, the amount of time he spent on the bicycle is 5.6 hours.

Unitary method:

Unitary method is used for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given,

Jim began a 182​-mile bicycle trip to build up stamina for a triathlete competition.​ Unfortunately, his bicycle chain​ broke, so he finished the trip walking. The whole trip took 5 hours.

Here we need to find the amount of time he spent on the bicycle if Jim walks at a rate of 4 miles per hour and rides at 40 miles per​ hour.

Let us consider x be the hours on the bike for distance 40x miles.

We know that, he spent 5 - x hours walking for distance 4(5 - x) miles or it can be written as

=> 20 - 4x

And we also know that those two, 40x and 20 - 4x, add to 182 miles

=> 40x + 20 - 4x + 182

=> 36x + 202

=> 36x = 202

=> x = 5.6

And the units calculation is m/h*h=m

If the value of x = 5.6 hours on the bike for 139.5 miles, then 5 - x =0.6 hours walking for 4 miles.

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To determine the degree measure of one angle of a 30-sided regular polygon.

The degree measure of one angle of a 30 sided regular polygon is 168°​.

What is a regular polygon?

A two-dimensional geometric shape with a finite number of sides is called a polygon. A polygon's sides or edges are made up of segments of straight lines that are joined end to end to create a closed shape.

The intersection of two lines is referred to as a vertex or corner, and an angle is created as a result. Regular polygons are those that have sides that are congruent.

We will use the side-angle relation of a regular polygon with any no. of sides to find total sum of interior angles that is

(Side - 2) × 180°

(30 - 2) × 180°

= 5040°

Measure of each angle of 30-gon

= 5040°/30

= 168°​

Thus, the degree measure of One angle of a 30 sided regular polygon is 168°​

Hence the answer is, The degree measure of one angle of a 30 sided regular polygon is 168°​.

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Answer:

it will increase

Step-by-step explanation:

6 is bigger than 10

The side of the cube is 6 cm.

What is the Volume of a prism?

The area that a prism takes up is referred to as its volume. A prism is a solid, three-dimensional structure with two identical faces and additional faces that resemble parallelograms. It is a polyhedron whose nomenclature is influenced by the various basic forms. Every prism has a particular base, whether it be a triangular prism (triangular base), square prism (square base), rectangular prism (rectangular base), pentagonal prism (pentagonal base), hexagonal prism (hexagonal base), or an octagonal prism (octagonal base). Consequently, because a prism is a three-dimensional form, its volume likewise exists in a three-dimensional plane. Prisms are measured in terms of their volume in cubic meters, cubic millimeters, cubic inches, or cubic feet. Following are the steps to calculate the prism's volume:

Write down the prism's dimensions as specified in step one.

Step 2: Use the formula V = B H to calculate the prism's volume. V, B, and H stand for the prism's volume, base area, and height, respectively.

Step 3: After obtaining the volume of the prism's value, add the unit of prism volume at the conclusion (in terms of cubic units).

In the question, we have given that:

Prism is made up of 120 equal cubes;

The volume of the prism is 25, 920[tex]cm^{3}[/tex];

So, we can equate the volume of 120 equal cubes with the prism's volume;

⇒ 120 × [tex](a)^{3}[/tex] = 25, 920;

⇒[tex](a)^{3}[/tex] = [tex]\frac{25920}{120}[/tex]

⇒[tex](a)^{3}[/tex] = 216;

So, the value of a is 6 cm;

That is the side of the cube is 6 cm;

Hence, The side of the cube is 6 cm.

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Answer:

See the picture below

Step-by-step explanation:

The dimensions of the rectangle are length and width are 6 and 11.6      respectively.

L = 3w - 11 ,

where,

L = length of the rectangle and

W =width of the rectangle

A=LW

Here A is Area of the Rectangle which is product of its dimensions i.e., length and breadth.

LW = 42

substituting for l:-

(3W-11)W= 42

3W^2 - 11W - 42 = 0

(3W + 10)(W - 6) = 0

W = 6 or -10/3  (ignore the negative root)

So the width is 6 and the length is 70/6= 11.6

The rectangle's length and width are therefore 6 and 11.6, respectively.

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The meters of rope used for knot tying is 10 meters.

According to the question,

We have the following information:

A cout mater bough 45 meter of rope he used two-ninth of the rope for knot tying.

So, we have the following expression for the rope used for knot tying:

45 of 2/9

We know that the word of is replaced by multiplication.

45*2/9

Now, we will first multiply the numbers in the numerator and then we will divide the obtained result by denominator.

90/9

Dividing 90 by 9:

10 meters

Hence, the meters of rope used for knot tying is 10 meters.

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Given trigonometric expression in algebraic form would be,

cos(arcsin(x - h/r)) =  ± [√(r² - (x - h)²)]/r

In this question, we need write the expression in algebraic form.

Given trigonometric expression is cos(arcsin(x - h/r))

Let y = arcsin(x - h/r)

so, sin(y) = (x - h)/r

By trigonometric identity,

sin^2(y) + cos^2(y) = 1

we have cos(y) = ±√(1 - sin²y)

cos(arcsin(x - h/r)) = ±√[1 - ((x - h)/r)^2]

                             = ± [√(r² - (x - h)²)]/r

Therefore, given trigonometric expression in algebraic form would be,

cos(arcsin(x - h/r)) =  ± [√(r² - (x - h)²)]/r

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the probability that each of the four players is dealt exactly one ace is about 0.11. this means that in a very large number of bridge deals, the percentage of deals on which each player has one ace will be very close to 11%

The probability of each of the four players is dealt exactly one ace is about 0.11

so,

the probability is always approximately the corresponding percent obtained for very large samples.

Hence it means that in a very large number of bridge deals, the percentage of deals on which each player has one ace will be very close to 11%

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The option that could be the diameter of a baseball used by a professional baseball team is A. 2 7/8 inches.

From the information, the baseball used by a professional baseball team must have a diameter that is between 2.86 inches and 2.94 inches.

In this case, 2 7/8 inches to decimal is 2.875

2 7/9 inches will be 2.778

2 8/10 will be 2.8

2 9/11 inches will be 2.818

Therefore, the correct option is A as it fits tye value given.

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Complete question

A baseball used by a professional baseball team must have a diameter that is between 2.86 inches and 2.94 inches. which of the following could be the diameter of a baseball used by a professional baseball team?

A. 2 7/8 inches

B 2 7/9 inches

C 2 9/11 inches

D. 2 8/10 inches.

6-3y=2x

-3y=2x-6

y=(2x-6)/-3

y=-(2/3)x+2


No me deja adjuntar la imagen de la gráfica, te recomiendo una página de internet llamada Desmos

X=0
y=-(2/3)(0)+2=2
(0,2)esmos


x=3
y=-(2/3)(3)+2=-2+2=0
(3,0)

x=-3
y=-(2/3)(-3)+2=2+2=4
(-3,4)

The dimensions of the cylinder will be r = 8.92 cm and h = 17.86 cm.

What is dimensions ?

Dimensions refer to the length or width of an area, region, or space in one direction.

Main Body:

Volume of cylinder = πr²h

Surface area = 2πr² + 2πrh

Given surface area = 1500 cm²

1500 = 2πr²+2πrh

h= (750/πr)-r   ----(1)

V= πr²{(750/πr)-h}

V =750r - πr³

V' = 750- 3πr²

Put V' =0

0 = 750 - 3πr²

r≈ 8.92 cm

substituting the value of r in equation (1)

we get h= 17.86 cm

Hence the dimension of cylinder are r = 8.92 cm and h = 17.86 cm

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Answer:

A- the slope is -4 and y-intercept is 3

Step-by-step explanation:

The standard form is y=mx+c (for straight line graph) while m is slope(gradient) and c is y-intercept.

So, slope is -4 and y-intercept is 3

The side length of a single cube will be 6 centimeters.

The volume of the cube will be -

V = (a x a x a) cubic units

We have the volume of Prism as V[P] = 25920 cm³ which is made up of [n] = 120 cubes of the same volume.

The volume of a single cube will be -

V[c] = V[P]/n

V[c] =  25920/120

V[c] = 216 cm³

Volume of a cube = V[c] = (a x a x a)

Equating volume, we get -

a³ = 216

a = 6 cm

Therefore, the side length of a single cube will be 6 centimeters.

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The solution of the system of equations is x = 1 and y = -1.

What is a two-variable linear equation?

If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equivalent to zero, it then is said to be a linear equation in 2 factors. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.

SOLUTION TO WORK OUT

the equations are resolved

8x + 3y = 5 & 3x − 2y = 5

EVALUATION

The equations in the given system are

8x + 3y = 5 - - - - - - - (1) (1)

3x − 2y = 5 - - - - - - - (2) (2)

Equation 1's two sides multiplied by two gives us

16x + 6y = 10 - - - - - - (3) (3)

Equation 2's two sides are multiplied by three to get

9x - 6y = 15 - - - - - - (4) (4)

Equation 3 and Equation 4 together give us

25x = 25

⇒ x = 1

Equation 1 is completed when x = 1.

8 + 3y = 5

⇒ 3y = 5 - 8

⇒ 3y = - 3

⇒ y = - 1

FINAL RESPONSE

Consequently, the needed answer is x = 1 and y = - 1.

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Answer:

Step-by-step explanation:

The Simplify the expression is -10, when we use fraction.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

=-5(∛27 *2)/3

=-5(3*2)/3

=-5(6)/3

=-10

Hence the answer will be -10 simplify the expression.

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The unit rate of weeks to pounds is 2.5 pounds in just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.

Given that,

In just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.

We have to find how many weeks are there in a pound.

A rate is a ratio that is utilized to compare the quantities of several commodities. A unit rate is a rate with one as the denominator. Whenever a rate's denominator, such as the price per unit of a certain number of items, is not 1.

So, we can write has

This is the fraction of the number of pounds and number of weeks.

=30pounds / 12 weeks

=2.5 pounds

Therefore, The unit rate of weeks to pounds is 2.5 pounds in just 12 weeks, Kristen shed 30 pounds. Every week, she lost the same amount of weight.

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The probability that one such device will work at least 15 hours at least 3 among 6 devices is 0.33 approximately.

The cumulative distribution function of X is:[tex]F(x)= 1- 10/x[/tex]  ( for x > 10)

X = the entire lifespan of a definite type of electronic device in hours, then the probability function of X,

here we use the cumulative distribution function, which is used to specify random variables,

F(X)= 1 - 10/X is cumulative distribution function,

then the probability that at least 3 devices will work for 15 hours

P(X[tex]\geq[/tex]15)= 1- P(X<15)

            = F(15)

            = 1- 10/15

            =5/15

            =0.333

Hence, the probability that one such device will work at least 15 hours at least 3 among 6 devices is 0.33 approximately.

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Considering the expression of a line, the equation of the line that passes through the points (-9,-7) and (-11,-6) is the equation of the line is y= -1/2x -23/2.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of a line can be calculated as:

m= (y₂ - y₁)÷ (x₂ -x₁)

Substituting the value of the slope m and the value of one of the points in y=mx +b, the value of the "b" can be obtained.

Being (x₁, y₁)= (-9, -7) and (x₂, y₂)= (-11, -6), the slope m can be calculated as:

m= (-6 - (-7))÷ (-11 -(-9))

m= (-6 +7)÷ (-11 +9)

m= (1)÷ (-2)

m= -1/2

Considering point 1 and the slope m, you obtain:

-7= (-1/2)×(-9) + b

-7= 9/2 +b

-7 -9/2= b

-23/2= b

Finally, the equation of the line is y= -1/2x -23/2.

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15x² - 10 = 0 is a quadratic equation which has complex solutions.

The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. There should be two solutions to quadratic equations. If you think about the discriminant formula, two roots can be real, equal, or imaginary.

Given,

Quadratic equation:

15x² - 10 = 0

15x² = 10

x² = 10/15

Roots:

x = ±√10/15

15x² - 10 = 0 is a quadratic equation which has complex solutions.

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a. The functions are classified as follows:

b. The functions are given as follows:

c. She should purchase Car 1, as it will have a higher value in nine years.

The functions are classified depending if there is an equal factor or an equal difference between consecutive terms, as follows:

Hence the functions in this problem are classified as follows:

Hence the functions are given as follows:

After nine years, the values are as follows:

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Answer:

That's right

Step-by-step explanation:

If the perimeter of the parallelogram is 102 feet, then the value of m is 12.75

The perimeter of the parallelogram = 102 feet

The perimeter of the parallelogram = 2(l + w)

Where l is the length and w is the width of the parallelogram

The length of the parallelogram = 3m

The width of the parallelogram = m

Substitute the values in the equation of the perimeter

102 = 2(3m + m)

102 = 2(4m)

102 = 8m

m = 102 / 8

Divide the terms

m = 12.75

Hence, if the perimeter of the parallelogram is 102 feet, then the value of m is 12.75

The complete question is:

The perimeter of the parallelogram is 102 feet. Find m. Write your answer as a decimal or mixed number.

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Variability provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out to clustered together. The purpose for measuring variability is to obtain an objective measure of how the scores are spread out in a distribution

Variability also measure how accurately individual score or sample represent the entire population

When the standard deviation is 0 , the scores have no variability.

Variability describes how far the data points are from each other and from the center of the distribution. In addition to measures of central tendency, measures of variability provide descriptive statistics that summarize the data.

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Proportional relationships are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."

A proportional relationship exists when each pair of data values is related in the same way, by multiplying by a factor. A proportional relationship can be identified by looking at data, an equation, or a graph. A proportional relationship with a constant of proportionality k between two quantities y and x is represented by the equation y = kx.

They pass through the source. They are linear (straight lines) and pass through the origin as well. The x to y ratio is a proportionality constant. For example, consider the following number pairs with a ratio of 2.5: 5 and 2; 10 and 4; 100 and 40; 2.5 and 1. These number pairs are all proportional to one another.

Note that an overview was his as the information is incomplete.

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[tex]{\Large \begin{array}{llll} y=ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=2\\ y=6.4 \end{cases}\implies 6.4=ab^2\implies \cfrac{6.4}{b^2}=a \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} x=5\\ y=409.6 \end{cases}\implies 409.6=ab^5\implies \stackrel{\textit{substituting from the 1st equation}}{409.6=\left( \cfrac{6.4}{b^2} \right)b^5} \\\\\\ 409.6=6.4b^3\implies \cfrac{409.6}{6.4}=b^3\implies 64=b^3\implies \sqrt[3]{64}=b\implies \boxed{4=b} \\\\\\ \cfrac{6.4}{b^2}=a\implies \cfrac{6.4}{4^2}=a\implies \boxed{0.4=a}~\hfill {\Large \begin{array}{llll} y=0.4(4)^x \end{array}}[/tex]

The correct option is (a) i.e. the slope intercept form of the given line is y = 6x-14.

The slope of the line through two points (x₁ ,y₁) and (x₁ ,y₂) can be found by using the formula below.

  m = (y₂ - y₁) / (x₂ - x₁).

The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis).

The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the y-intercept can be given as y = mx + b.

Here we have a line that passes through two points (x₁ ,y₁) = (3 ,4) and  (x₁ ,y₂) =(5 ,16).

The slope of the line m = (y₂ - y₁) / (x₂ - x₁) = (16 -4) /(5 -3) = 12/2 = 6.

 ⇒ slope m = 6.

And we know the slope intercept form  is

  y = mx + b

⇒ 4 = 6*3 + b  {with points  (3 ,4)}

⇒ b =4 - 18 = -14 ⇒ b = -14.

So the slope intercept form is y = 6x-14.

The slope-intercept form of the equation with m =6 and y-intercept as -14 was found to be

  y = 6x -14.

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NOTE : The question given here is not complete. The complete question is given below.

Question: What is the slope intercept form equation of the line that passes through (3 ,4)and (5,16)?

(a) y = 6x − 14  

(b) y = −6x +14

(c) y = −6x − 14

(d) y = 6x + 14?