Three consecutive even integers have the property that when the product of the first two is taken, the result is four less than the square of the third one. What are the integers?​

Index contours are usually drawn darker than the other contours.

Index Contours are darker and wider than the other regular contour lines for ease of identification. They are labeled with elevation and also have their altitude value mentioned on the dark lines and these values represent the altitudes of the particular contours. Index contours appears after every fifth contours. If the number with contours will increase then its elevation will also increase and similarly if the number associated with contours starts to decrease then its elevation also decreases.

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Answer:

15-p

Step-by-step explanation:

15-p

the solution for the  given equation is  x= 1/2

an equation could be a formula that communicates the balance of two expressions, by interfacing them with the equals sign. Understanding an equation containing factors comprises deciding which values of the factors make the equality true. The factors for which the equation must be fathomed are moreover called unknowns, and the values of the unknowns that fulfill the balance are called solutions of the condition. There are two sorts of equations such as conditional and identities equations. An identity is genuine for all values of the factors. A conditional equation is as it were genuine for specific values of the factors

since the  given expression is :

`(2-4)=2(-5+1)x²

so solving for the simple  arithmetic expression on both sides  :

=>-2 =2(-4)x²

=> -2 = -8x²

=>2/8=x²

=>1/4= x²

=>x= 1/2

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The maximum number of hikers who could have walked between 6 miles and 17 miles is 19.

We need to find the maximum number of hikers who could have walked between 6 miles and 17 miles.

When the derivative equals 0, rearrange the function using elementary algebraic principles to find the value for x. The x-coordinate of the function's vertex, which is where the maximum or lowest will occur, is provided in this answer. the solution back into the original function to determine the minimum or maximum.

From the table, we can see

Between intervals 5≤x<10 there are 2 hikers

Between intervals 10≤x<15 there are 9 hikers

Between intervals 15≤x<20 there are 8 hikers

So, total number of hikers = 2+9+8

= 19

Hence, the maximum number of hikers who could have walked between 6 miles and 17 miles is 19.

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The equation of the line parallel to the equation y = - 2 / 3 x + 5 is 2x - 3y = 21

The equation of a line can be represented in different form such as slope intercept form, point slope form, standard form and general form.

Lines are parallel when they have the same slope.

Using slope intercept form,

y = mx + b

where

Therefore,

y = - 2 / 3 x + 5.

The slope of the equation is - 2 / 3.

Hence, let's find the equation that has the same slope as - 2 / 3. First, we will have to represent the equation in slope intercept form.

2x - 3y = 21

add 2x to both sides of the equation

2x + 2x - 3y = 21 + 2x

- 3y = 2x + 21

divide both ides by - 3

- 3y  / - 3 = 2x / -3 + 21 / - 3

y = - 2 / 3 x - 7

Therefore, the slope is - 2 / 3 , the equation is 2x - 3y = 21

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Thus, the number of ways in which  to choose 4 letters, without replacement, from 17 distinct letters is 57,120.

Total distinct letters are 17.

There are 17 alternatives for the initial letter if there are 17 letters.

There are just 16 alternatives left once you remove the letter.

Each time you remove a letter, the bag contains one fewer letter.

Number of ways = 17 x 16 x 15 x 14

Number of ways =  57,120

Thus, if the sequence of the alternatives is irrelevant, there are 57,120 options.

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The values of x, y and z are 4, 1 and - 6 respectively.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied

We have the following equations -

8x + y + 4z = 9

4x - 3y + z = 7

8x - 4y + 5z = - 2

We have -

4x - 3y + z = 7

z = 7 - 4x + 3y

We can write -

8x + y + 4z = 9

as -

8x + y + 4(7 - 4x + 3y) = 9

8x + y + 28 - 16x + 12y = 9               ...Eq[1]

and we can write -

8x - 4y + 5z = - 2

8x - 4y + 5(7 - 4x + 3y) = -2

8x - 4y + 35 - 20x + 15y = - 2         ...Eq[2]

Plot the graph of equation [1] and [2]. We will will get -

x = 4

y = 1

Now -

z = 7 - 4x + 3y

z = 7 - 16 + 3

z = - 6

Therefore, the values of x, y and z are 4, 1 and - 6 respectively.

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Call the number of hours of labor x.

A flat rate of $500 -> just $500.
$50 for each hour of labor -> 50x (for x hours)

Therefore, we can represent the amount needed for x hours of labor as the function : 500 + 50x.

We substitute :
20 hours of labor = 500 + 50 x 20 = $1500
50 hours of labor = 500 + 50 x 50 = $3000

The total amount of milk needed for the recipes, considering the line plot, is of:

5.25 cups.

The total amount of milk needed for the recipes is obtained adding all the measures of the line plots.

The measures of the line plot given by the image at the end of the answer are given as follows:

The total amount is given by the sum of all these measures, hence:

2 x 0.25 + 1.25 + 1.5 + 2 = 5.25 cups.

The line plot is given by the image at the end of the answer.

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Answer:2

Step-by-step explanation:

1+1 es 2

The value of side AC is AC = 3.

What is right triangle?

A right triangle, also known as a right-angled triangle, an orthogonal triangle, or historically a rectangled triangle, is a triangle with one right angle, meaning that its two sides are perpendicular. Trigonometry's foundation is the relationship between the right triangle's sides and other angles.

The given triangle  ΔABC is a right angled triangle.

So, to find the side AC we can use the cosine ratio,

[tex]cosB = \frac{Adjacent side}{Hypotenuse}\\ cos65 = \frac{AC}{AB} \\cos65 = \frac{AC}{7} \\AC = 7(c0s(65)\\AC = 7(0.4226)\\AC = 2.9583[/tex]

AC ≈ 3.

Hence, the length of side AC is 3.

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Answer:

93.33%

Step-by-step explanation:

56/60 as a percentage:

56/60 = 0.93333

0.93333 as a percent:

0.93333 * 100 = 93.33%

The value of solution for a number 56/60 into a percentage is,

⇒ 93.33%

We have to given that,

To change a number 56/60 into a percentage.

Since, A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Hence, We can write as,

⇒ 56/60 × 100%

⇒ 5600/60

⇒ 93.33%

Therefore, The value of solution for a number 56/60 into a percentage is,

⇒ 93.33%

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The number problems solved by the little Monsters  of Beast Academy in March's meet is 15.

The problem is a simultaneous equation of two unknowns with two equations.

The equations are formed as follows

let the number of questions solved by little Monsters  of Beast Academy in

In November's Math Meet, the Little Monsters of Beast Academy solved $\frac{1}{5}$ of the problems = y/5

In March's Math Meet, they solved $\frac23$ of the problems = 2x/3

Hence:

y/5 + 2x/3 = 12

x + y = 30

solving the equation gives

x = y = 15

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The value of function is positive so the function have maximum value at x=3.

In the given question we have to find the maximum or the minimum value of a function.

The given function is

f(x) = -3x^2+18x+3

To find the maximum or minimum value we firstly find the value of f'(x).

f'(x) = -6x+18

Now put f'(x)=0

-6x+18=0

Subtract 18 on both side we get

-6x=-18

Divide by -6 on both side we get

x = 3

Now finding the value of function at x=3

f(3)= -3*(3)^2+18*3+3

f(3)= -3*9+54+3

f(3)= -27+54+3

f(3)= 30

Since the value of function is positive so the function have maximum value at x=3.

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The linear equation that represent the amount vaccine that remain is g = 61 - 0.061n. The vaccine remains in the body 24 hours after it was administered 59.536 mg. There were only 5mg of the vaccine remaining in the body after 918.033 hours.

What is rate?

A rate is a unique ratio where the two words are expressed in several units.

Given that the amount of vaccine is 61 mg.

The vaccine leaves the body at a rate of 6.1% per hour.

After 1 hour the body will consume 6.1% = 6.1/100 = 0.061 mg.

After n hour the body will consume 6.1%× n =  0.061n mg.

The remaining amount of vaccine is (61 - 0.061n).

The required linear equation that represent the remaining amount of vaccine is g = 61 - 0.061n.

Putting n =24 in the equation:

g = 61 - 0.061×24

g = 59.536 mg

The vaccine remains in the body 24 hours after it was administered 59.536 mg.

The graph represents that there were only 5mg of the vaccine remaining in the body after 918.033 hours.

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The correct answer is C. Jayce's fee for his 10th drive is equal to K dollars.

Based on the mentioned statements, n refers to the number of drives in a certain day. Additionally, it is mentioned that M(n) models the fee in dollars. As is seen in the equation, M(n) is equal to K. Thus, the fee in dollars is K dollars.

Now, as n is ten, thus the drive is tenth. And the fees for tenth drive is K dollars. So, the third option is correct, which states that Jayce's fee for his tenth drive is equal to K dollars.

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The 10th term of an arithmetic sequence is found as the 49.

As per the stated values in question.

Fifth term a5 = 24

8th term a8 = 39.

Let the first term be 'a' and the common difference be 'd'.

Then,

a5 = a + 4d

24 = a + 4d .....eq 1

a8 = a + 7d

39 = a + 7d .....eq 2

Solving eq 1 and 2.

3d = 15

d = 5

a = 4

Now,

a10 = a + 9d

a10 = 4 + (9 x 5)

a10 = 4 + 45

a10 = 49

Thus, the 10th term of an arithmetic sequence is found as the 49.

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By solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

An equation is a formula in mathematics that expresses the equality of two expressions by linking them with the equals sign =. In French, an equation is defined as including one or more variables, but in English, an equation is any well-formed formula consisting of two expressions coupled with an equals sign.

An equation is composed of two expressions joined by an equals sign (=). The expressions on the two sides of the equals sign are referred to as the equation's left-hand side and right-hand side. The right side of an equation is frequently considered to be zero.

Given,

2x+y=4

x-y=1

By solving above two equations we get,

2x+y=4

x-y=1

3x=5

x=5/3

y=-1+x

y=(5/3)-1

y=2/3

Therefore, by solving the equations 2x+y=4, x-y=11 we get values x=5/3 and y=2/3

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Using the compound amount formula, the amount after 40 years is 2000(107/100)^40.

In the given question,

Esther got a summer job and decided to set aside $2000 to prepare for retirement without making monthly contribution.

She invests in the US stock market through as index fund that averages a 7% return compounded annually over this 40 year period.

We have to find the total balance in the account after 40 years.

We have to find total balance compounded annually.

The formula of the compound amount is

A = P(1+r/100)^n

where A = Amount

P = Principal Amount

r = interest rate

n = time

From the question we know that

P = $2000, r = 7%, n = 40

Now putting the value in formula

A = 2000(1+7/100)^40

Simplifying

A = 2000(1×100/100+7/100)^40

A = 2000(100/100+7/100)^40

A = 2000((100+7)/100)^40

A = 2000(107/100)^40

You can find the amount after simplifying the amount.

Hence, the amount after 40 years is 2000(107/100)^40.

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Check the picture below.

There are 200 dogs Roscoe groom if he worked for 40 hours.

What is working time?

A person's working time is the time they are engaged in paid work. Personal housework, childcare, and pet care are examples of unpaid work that is not included in the definition of the working week.

In most cases, when someone inquires about your working hours, you should first provide the start time before providing the time you leave for home.

From the given graph we can see that for each three hours the number of dogs are increased by 15.

So, for each one hour the number of dogs increased by 5.

For 18 hours the the number of dogs are 90.

After 18 hours to complete 40 hours we need 22 hours.

So, for 22 hours the number of dogs are

22 x 5 = 110.

Therefore, the total number of dogs worked for 40 hours are,

90 + 110 = 220.

Hence, there are 200 dogs Roscoe groom if he worked for 40 hours.

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Answer:

The answer is x^{3}-2x^{2}-5x+6

Step-by-step explanation:

This is because only a Cubic Function would have such a shape. That leaves x^3 functions from there just substitute points and check

Answer:

56cm²

Step-by-step explanation:

Because this is an irregular shape, you have to split it into two shapes and find the area of each one. Then you can add those two areas together to find the total area of the figure. There are many ways you can split it but the way I did it left me with the equation (12·3)+(4·5). Then all you have to do is multiply and add which will give you a total of 56cm².

The probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68.

Given, that the weight of bags of all purpose flour is normally distributed with expected value 10 pounds and standard deviation 0.2 pounds.

As, we know that

P(X) = (1/s√2π)exp(-1/2((X-m)/s)^2)

where, m is the expected value

and s is the standard deviation.

Now, we have Expected value 10 pounds

and Standard Deviation 0.2 pounds

So,  the probability that of 10 randomly chosen bags of flour at least 2 are overweight be

P(X=0) + P(X=1) = (1/0.2√2π)exp(-1/2((0-10)/0.2)^2) + (1/0.2√2π)exp(-1/2((1-10)/0.2)^2)

P(X=0) + P(X=1) = 0.32

So, Required Probability be 0.68.

Now,  the probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68

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The time taken to label 750 books if Clare labels books at 15 books per minute is 50 minutes.

In this situation, Clare volunteers at a library during the summer and has to label 750 books and she labels books at 15 books per minute and she takes no breaks.

Let the time taken to label the 750 books be represented by x.

This will be illustrated as:

1/x = 15/750

Cross multiply

(15 × x) = (750 × 1)

15x = 750

Divide

x = 750 / 15

x = 50

The time is 50 minutes.

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Complete question

Clare volunteers at a library during the summer and has to label 750 books. Clare labels books at 15 books per minute and she takes no breaks, then it would take her minutes to finish labeling all the books.

The number of ribbons that is needed for 7 presents is 73 ribbons.

She needs 5 packages.

An expression is simply used to illustrate the relationship between the variables.

In this case, it takes 10 feet of ribbon to make 1 bow on a present and 3 feet is used to practice trying the bow, the expression 10p + 3 can be used.

The ribbons needed for 7 presents will be:

= 10p + 3

= 10(7) + 3

= 70 + 3

= 73

Since it's sold in 15 feet packages, the number needed will be:

= 73 / 15

= 5

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Answer:$2.61

Step-by-step explanation:

18=$15.66

÷6    ÷6

3=$2.61

The cost of 3 bottles of juice based on the given ratio will be $2.61.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

18 bottles cost = $15.66

1 bottle cost = $15.66/18 = $0.87/ bottle

For 3 bottles = 3 × $0.87 = $2.61

Hence "The cost of 3 bottles of juice based on the given ratio will be $2.61".

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The unit rate for the given situation is 29 students per classroom.

What is the unit rate?

A unit rate is described as a ratio comparing the first quantity to one unit of the second quantity.

Given situation is 87 students in 3 classrooms.

So, the unit rate  [tex]= \frac{87}{3}[/tex]  students/classroom

                            [tex]= 29[/tex] students per classroom

Hence, the unit rate for the given situation is 29 students per classroom.

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Answer:

Here,

2x+3x=20x

or,5x=20x

or,5x-20x=0

or,15x=0(divide both sides by -15)

hence,x=0