1) There are three consecutive positive integers, such that the largest
is 44 less than twice the smallest. What is the value of the smallest
of these three consecutive integers?

The roots of the equation is x = -20

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The leading coefficient of the equation is -1

And , the constant term is -20

Now , according to rational root theorem ,

So , the equation is

-x - 20 = 0

Adding x on both sides of the equation , we get

x = -20

Therefore , the value of x is -20

Hence , the equation is x = -20

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A triangle represents 1/4 of the trapezoid, a diamond represents 1/2 of the trapezoid, and a hexagon represents 1/1 of the trapezoid.

Each shape represents a different part of the overall trapezoid.

The triangle represents 1/4 of the full trapezoid. This is because the trapezoid has four triangles, all of the same size. So each triangle is 1/4 of the whole trapezoid. The diamond represents 1/2 of the full trapezoid. This is because the trapezoid has two diamonds, each of the same size. So each rhombus is 1/2 of the whole trapezoid.

The hexagon represents 1/1 of the whole trapezoid. This is because the trapezoid has only one hexagon, which is the same size as the entire trapezoid. So the hexagon is 1/1, the whole trapezoid.

In summary, a triangle represents 1/4 of a trapezoid, a diamond represents 1/2 of a trapezoid, and a hexagon represents 1/1 of a hexagon. Using these fractions, we can determine the value of each shape relative to the overall trapezoid.

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The magnitude of the horizontal and vertical components are 21.33 m/s and 38.48 m/s

From the question, we have the following parameters that can be used in our computation:

Velocity = 44 meters per second

Direction = S 61° E

This means that

V = 44 and angle = 61°

The direction angle is 61° from the positive x-axis (E), so we can use the following trigonometric relationships to find H and V:

H = 44 * cos(61°) --- horizontal

V = 44 * sin(61°) --- vertical

Using a calculator, we can find that:

H = 21.33 m/s

V = 38.48 m/s

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Answer:

2(-3x+2)^2 -1

Step-by-step explanation:

so first you would find that f(g(x)) = f(-3x+2)

next plug in

f(-3x+2) = 2x^2-1

to every x

f(-3x+2) = 2(-3x+2)^2-1

Based on the information provided, it's not possible to say who is winning without knowing the specific game and how points are scored and awarded.

The statement "has -6 points give or take 4 points" doesn't provide a specific range of points that your friend could have, so we can't use this information to determine a winner.

Additionally, using a number line to compare two points of -3 and -6 is not helpful in determining who is winning in the game because it only shows their relative values, not the actual rules of the game and how points are scored.

It would be best to ask the friend to clarify their score and the rules of the game to determine who is winning.

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The area of Gavin's bedroom is 120 square feet.

Square feet can be defined as the area of a square with sides of 1 foot.

Let B be the area of Gavin's bedroom in square feet.

According to the problem, the area of Gavin's kitchen is 10 square feet more than one-third of the area of his bedroom. So we can write:

Area of kitchen = (1/3)B + 10

We also know that the area of the kitchen is 50 square feet. So we can set up an equation:

(1/3)B + 10 = 50

Subtracting 10 from both sides, we get:

(1/3)B = 40

Multiplying both sides by 3, we get:

B = 120

Therefore, the area of Gavin's bedroom is 120 square feet.

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The temperature conversion from Celsius to Fahrenheit is calculated using the following formula: Fahrenheit = (Celsius x 1.8) + 32. Increasing the Celsius temperature by 1 degree will result in an increase of 1.8 degrees Fahrenheit.

To convert a temperature of 36 degrees Celsius to Fahrenheit, we first multiply 36 by 1.8 to get 64.8, then add 32 to that result to get 96.8 degrees Fahrenheit. In other words, 36 degrees Celsius is equal to 96.8 degrees Fahrenheit. To better understand this conversion, it helps to remember that 0 degrees Celsius is equivalent to 32 degrees Fahrenheit. The two scales are offset by 32 degrees, meaning that for every degree Celsius, the equivalent Fahrenheit temperature is 1.8 degrees higher. For example, 10 degrees Celsius is equivalent to 50 degrees Fahrenheit (10 x 1.8 = 18 + 32 = 50). Thus, increasing the Celsius temperature by 1 degree will result in an increase of 1.8 degrees Fahrenheit.

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The Point A on the number line is 2 1/2

From the question, we have the following parameters that can be used in our computation:

The number line

On the number line, we have

A = Halfway between 2 and 3

Using the above as a guide, we have the following:

A = (2 + 3)/2

Evaluate

A = 2 1/2

Hence, the position is 2 1/2

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To solve the exponential equation 23^x = 6, take the logarithm base 23 of both sides to get x = log base 23 of 6.

Angie, to solve the exponential equation 23^x = 6, you need to find the value of x such that when you raise 23 to the power of x, you get 6. To do this, you can use logarithms.

In particular, you can use the logarithmic function log_23. The log_23 of a number y is the exponent x such that 23^x = y. So, to solve the equation 23^x = 6, you can take the log_23 of both sides:

log_23(23^x) = log_23(6)

x = log_23(6)

The right side of this equation can be evaluated using a calculator or logarithmic tables. Once you have the value of x, you will have solved the exponential equation.

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Answer:

For question 2, Ethan needs 3 cups of milk to make the batter for 3 times as many cakes.

For question 3, Isabella needs 5/4 of a gallon of the food to make 5 gallons of the mixture.

The radius of the cylinder is approximately 5.88 inches.

What are equivalent equations?

Equivalent equations are algebraic equations that are having identical roots or solutions.

We can solve the given equation to find the radius of the cylinder using the volume and height information

3.14 * 11 * r² = 1243.44

First, divide both sides by 3.14*11 to isolate r²:

[tex]r^2 = 1243.44 / (3.14 * 11)[/tex]

r² ≈ 34.585

Taking the square root of both sides, we get:

r ≈ 5.88

Hence, the radius of the cylinder is approximately 5.88 inches.

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Answer:

scalene, right triangle

Step-by-step explanation:

Determine whether it is a triangle and the triangle's type:

Answer: scalene, right triangle

z = - 4, represents the solution of the inequality → z² + 2 < 6.

An inequality is used to compare numbers or expressions. For example -

2x + 4 > 6       4x + 6 < 8            y > 9          x < 1

All the above expressions mentioned above represent inequalities.

Given is the inequality as -

z² + 2 < 6

The given inequality is -

z² + 2 < 6

Subtract {2} from both side we get -

z² < 4

z < ± 2

Therefore, z = - 4, represents the solution of the inequality → z² + 2 < 6.

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Answer:

Your answer would be (x, y) = (0, 0)

Step-by-step explanation:

Please refer to the screenshot underneath.

Seraphina's speed has increased by a factor of around 23% compared to the first hour.

What Is a Change in Percentage?

The ratio of the difference in the amount to its starting value multiplied by 100 is known as the percentage change. When a number's final value is determined by increasing or decreasing a percentage of its starting value, the percentage change of that quantity will always change.

How can you determine the percentage to the closest tenth?

Rounding to the closest tenth entails adding one integer after the decimal point. The number in the thousandths place, or the second number from the right of the decimal, must be considered while rounding. If the amount is five or more, we add one percent to the number in the tenth position.

Percent Change Formula = [tex]\frac{ (Final value -Initial value)}{ (Initial value)}[/tex]× 100

Percent Change               = [tex]\frac{(74-60)}{60}[/tex]× 100

…                                     = [tex]\frac{14}{60}[/tex] × 100

...                                     ≈ 0.23333 × 100

Percent Change             ≈ 23.33%

The pace of Seraphina increased by around 23% in the second hour compared to the first.

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Both clusters are relevant to her career.

Cluster is derived from the old english word clyster, which means a group. Cluster is now used as both a noun and a verb.

The army sergeant who works as a trauma surgeon is probably in the Health Services and Government and Public Administration clusters.

Health Services occupations include diagnosing, treating, and preventing illnesses and injuries, while Government and Public Administration occupations include planning, managing, and providing government functions and services. The individual is a member of the military, which is a government organisation, and a trauma surgeon, which is a part of the healthcare industry. As a result, both clusters are pertinent to her career.

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The solutions for the system of equations: 7x - 4y = -12 and x - 2y = 4, x - y = 4 and 2x + y = 5, 4x - 3y = 17 and 2x - 5y = 5, 5x + 6y = -6 and 7x - 3y = -54

by elimination are respectively:

x = -4, y = -4

x = 3, y = -1

x = 5, y = 1

x = -6, y = 4

we shall write the equations as:

7x - 4y = -12...(1)

x - 2y = 4...(2)

multiply equation (2) by 7 to get equation (3)

7x - 14y = 28...(3)

subtract equation (1) from (3) to eliminate x

7x - 14y - 7x + 4y = 28 + 12

-10y = 40

divide through by -10

y = -4

put the value -4 for y in equation (2) to get y

x - 2(-4) = 4

x + 8= 4

x = -4

x - y = 4...(1)

2x + y = 5...(2)

Add equations (1) and (2) to eliminate y

2x + y + x - y = 5 + 4

3x = 9

divide through by 3

x = 3

put the value 3 for x in equation (1) to get y

3 - y = 4

y = -1

4x - 3y = 17...(1)

2x - 5y = 5...(2)

multiply equation (2) by 2 to get equation (3)

4x - 10y = 10...(3)

subtract equation (3) from (1) to eliminate x

4x - 3y - 4x - 10y = 17 - 10

7y = 7

divide through by 7

y = 1

put the value 1 for y in equation (2) to get y

2x - 5(1) = 5

2x - 5 = 5

x = 5

5x + 6y = -6...(1)

7x - 3y = -54...(2)

multiply equation (1) by 7 to get equation (3) and equation (2) by 5 to get equation (4)

35x + 42y = -42...(3)

35x - 15y = -270...(4)

subtract equation (4) from (3) to eliminate x

35x + 42y - 35x + 15y = -42 + 270

57y = 228

divide through by 57

y = 4

put the value for y in equation (1) to get x

5x - 6(4) = -6

5x + 24 = -6

x = -6

Therefore, the solutions for the system of equations: 7x - 4y = -12 and x - 2y = 4, x - y = 4 and 2x + y = 5, 4x - 3y = 17 and 2x - 5y = 5, 5x + 6y = -6 and 7x - 3y = -54

by elimination are:

x = -4, y = -4

x = 3, y = -1

x = 5, y = 1

x = -6, y = 4

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Answer:

6

Step-by-step explanation:

A. (8 * t) + (8 * 8) is equivalent to 8t + 64

B. 4t + 8 + 4t is equivalent to 8t + 8

C. 4(2t + 2) is equivalent to 8t + 8

D. 8t + 64 is equivalent to 8t + 64

E. 8t + 16 is equivalent to 8t + 16

F. (8 + t) + (8 + 8) is equivalent to 16 + t.

So the expressions that are equivalent to 8(t + 8) are B and C, the expression that is equivalent to 8t + 8 is E, and the expression that is neither is F.

In the given problem, we are comparing the given expressions to see if they are equivalent to 8(t + 8), 8t + 8, or neither.

Expression A: (8 * t) + (8 * 8) = 8t + 64

This expression is equivalent to 8t + 64, which is not the same as 8(t + 8) or 8t + 8.

Expression B: 4t + 8 + 4t = 8t + 8

This expression is equivalent to 8t + 8, which means that adding up 4t and 8, and then adding 4t again to the result is the same as multiplying 8 with t and adding 8 to the result.

Expression C: 4(2t + 2) = 8t + 8

This expression is also equivalent to 8t + 8, which means that multiplying 2t + 2 with 4 is the same as multiplying 8 with t and adding 8 to the result.

Expression D: 8t + 64 = 8t + 64

This expression is the same as 8t + 64, which is not equivalent to either 8(t + 8) or 8t + 8.

Expression E: 8t + 16 = 8t + 16

This expression is the same as 8t + 16, which is not equivalent to either 8(t + 8) or 8(t + 8).

Expression F: (8 + t) + (8 + 8) = 16 + t

This expression is not equivalent to either 8(t + 8), 8t + 8, or neither.

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--The question is incomplete, answering to the question below--

"Drag each expression to show whether it is equivalent to 8(t + 8), 8t + 8, or neither.

A. (8 * t) + (8 * 8)

B. 4t + 8 + 4t

C. 4(2t + 2)

D. 8t + 64

E. 8t + 16

F. (8 + t) + (8 + 8)"

Amongst the options circle shape from the Clade Race would be considered plesiomorphic.

A primitive or ancestral character state is called plesiomorphy or known as a plesiomorphic character), and a shared plesiomorphy is called a symplesiomorphy. For example, let us take an example of hair. It is a unique mammalian character that evolved with the evolution of mammals.

The term apomorphy means a specialized or derived character state which is plesiomorphy. It refers to a primitive or ancestral trait. An same as autapomorphy, it is a derived trait that is unique to one group, while a same as synapomorphy is a derived trait shared by two or more groups.

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Answer:

74.2

Step-by-step explanation:

Median is another word for average amount.

So if you add the numbers 56, 65, 77, 81, and 92 you would end up with 371.

To get an average, or the median, you take the numbers, add them together, then divide the answer by how ever many numbers you had.

In this case, you had 5, so

56+65+77+81+92=371

then divide by 5 so

371/5=74.2

The total cost will be $21 for the bowling alley.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that a bowling alley charges $3 plus tax for each pair of shoes and $4 plus tax for each player every game. If you and a friend hire a pair of shoes and bowl three games.

The total cost will be calculated as:-

Cost = ( 3 + 4 ) x 3

Cost = 7 x 3

Cost = $21

Therefore, the total cost will be $21.

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Answer:

Below

Step-by-step explanation:

There are 5280 ft in a mile...how many 5280's are there in 30 000 ?

30 000 ft  / 5280 ft/mile  = 5.68 miles

The height of 30,000 feet above sea level corresponds to 5.68 miles.

To convert feet to miles,

we can use the conversion factor 1 mile = 5280 feet.

Therefore, to find how many miles 30,000 feet corresponds to, we can divide 30,000 by 5280:

=30,000 feet / 5280 feet/mile

≈ 5.68 miles

So, 30,000 feet above sea level corresponds to 5.68 miles.

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The solution is, Dobson have to repay B. $17,600.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

The bank grants Marcus Dobson a loan for $22,000 with an APR

of 10 percent.

He agrees to a down payment of 20 percent and will repay the loan over 24 months.

so, he paid = 22000*20%

                  = $4400

so, remained loan = $ 17600

using the formula of interest , we get,

he has to repay with interest = $ 17600* 10%* 2 + $ 17600

                                                 =$ 3520 + $ 17600

                                                  =$ 21120

Hence, The solution is, Dobson have to repay B. $17,600.

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Answer:

6 grams of sugar in 3/4 liter.

Explanation:

Recall that two 1/4 portions is equal to 1/2.  So if 1/2 liter has 4 grams, 1/4 liter will have 2 grams of sugar.

Every 1/4 liter will have 2 grams of sugar.

Therefore, 3/4 liter will have 3 times as much sugar as 1/4 liter.  The amount of sugar in 3/4 liter will be 3 times 2 grams or 6 grams of sugar in 3/4 liter

No, the expression −  + 3 × 5 −  2 −a+3a 5 −a 2 is not a polynomial.

In mathematics, an expression is a combination of numbers, symbols and operations such as addition, subtraction, multiplication and division that may be evaluated to produce a single number, a variable or a set of numbers. Expressions can be complex, and often appear in the form of equations or formulas. Examples of expressions include equations, polynomials, functions, matrices and more.

A polynomial is an expression that is a sum of one or more terms, each of which is the product of a constant and a non-negative integer power of a variable. In the expression given, the exponent of the variable a is negative, which does not meet the criteria to be considered a polynomial.

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Answer:

f(n) = 10 + 3n

Step-by-step explanation:

Each of the expressions has 10 + a certain number of 3's

For example for n = 3 we have
f(3) = 10 + 3 threes = 10 + 3 x 3 = 10 + 9 = 19

For n = 4, we have

f(4) = 10 + 4 threes = 10 + 4 x 3 = 10 + 12 = 22

The others follow the same pattern

So the explicit equation is

f(n) = 10 + 3n

Testing on n = 6 we get

f(6) = 10 + 6n = 10 + 6 x 3 = 10 + 18 = 28