Is the square root of 2 equal to 2?

Answer:

19.25 feet

Step-by-step explanation:

Let x be the width of the rectangle in feet. Then, the length of the rectangle is x + 3.5 feet. Since the area of a rectangle is equal to its length times its width, we know that the area of the rectangle is (x + 3.5) * x = 65 square feet.

We can solve for x by setting up the equation (x + 3.5) * x = 65 and then solving for x. This gives us the following:

x^2 + 3.5x - 65 = 0

To solve this quadratic equation, we can use the quadratic formula:

x = (-b +/- sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = 3.5, and c = -65, so we have:

x = (-3.5 +/- sqrt(3.5^2 - 4(1)(-65))) / 2(1)

Solving for x, we get:

x = (-3.5 +/- sqrt(12.25 + 260)) / 2

Therefore, the width of the rectangle is x = (-3.5 +/- 19.25) / 2 = -0.75 or 15.75 feet. Since the length of the rectangle is x + 3.5 feet, this means that the length of the rectangle is (-0.75 + 3.5) feet or (15.75 + 3.5) feet, which is equal to 2.75 feet or 19.25 feet.

However, we know that the length of the rectangle must exceed its width by 3.5 feet, so the only solution that is physically possible is x = 15.75 feet and the length of the rectangle is 19.25 feet. Therefore, the length of the rectangle is 19.25 feet.

The fractional notation ¾ is equal to 0.75.

â…” is a fractional notation that refers to the fraction 3/4, which is equal to 0.75. To understand this fraction, the denominator (bottom number) must be multiplied by the numerator (top number). In this case, 4 multiplied by 3 is equal to 12. Then, divide the numerator by the denominator to find the fractional value. In this example, 3 divided by 4 is equal to 0.75, which is the same as 3/4.

The formula for finding a fractional value is:

Fractional Value = Numerator / Denominator

To calculate the fractional value of 3/4, the numerator is multiplied by the denominator to get 12. Then, the numerator is divided by the denominator to get the fractional value:

Fractional Value = 3 / 4

Fractional Value = 3 * 4 / 4

Fractional Value = 12 / 4

Fractional Value = 0.75

Therefore, the fractional notation ¾ is equal to 0.75.

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Answer:

Monomial, Binomial,Trinomial,Quadratic equation,Linear equations

Step-by-step explanation:

Answer:

I think it's a vertical line.

The equation of line with slope 1/3 and intercept 5 is y = 1/3 x + 5.

The general equation of a straight line is y = mx + c, where m is the gradient or slope, and y = c is the value where the line cuts the y-axis. This number c is called as intercept.

According to the questions,

slope = m = 1/3

and

y-intercept = c= 5

We know that,

The general equation of a straight line is y = mx + c

y = 1/3 x+ 5

The required equation of a line is y = 1/3 x+ 5

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The domain and scope of the identity function are the same. Equation for the identity function is  f(x) = x, or y = x.

An statement, rule, or law in mathematics that specifies the connection between an independent variable and a dependent variable (the dependent variable). A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. Y=X2 is an illustration of this. You only receive one output for y if you enter anything for x. The fact that x is the input value leads us to argue that y is a function of x.

identity function are the same.

Equation for the identity function is

f(x) = x, or y = x.

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3x - 5y=-9 has a [tex]\frac{-3}{5}[/tex] slope.

A line's steepness can be determined by looking at its slope. To find the slope of a line, you need to have the equation of the line in the form y = mx + b, where m is the slope and b is the y-intercept (the point at which the line crosses the y-axis).

To put the equation 3x - 5y = -9 in this form, you can start by isolating the y term on one side of the equation:

3x - 5y = -9

-5y = -3x - 9

y = (-3/5)x - (9/5)

The slope of the line is therefore -3/5.

The complete question is:-

What is the slope of 3x - 5y =- 9?

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Answer: 40 glasses of syrup

Step-by-step explanation:

Mode is the most common value in the dataset.

The idea is to sort the array in descending order and then return the second element which is not equal to the largest element from the sorted array.

In order to have as few implementation dependencies as feasible, Java is a high-level, class-based, object-oriented programming language.

// Java program to find second largest element in an array

import java.util.*;

class GFG{

// Function to print the

// second largest elements

static void print2largest(int arr,int arr_size)

{

int i, first, second;

// There should be

// atleast two elements

if (arr_size < 2)

{

  System.out.printf(" Invalid Input ");

  return;

}

// Sort the array

Arrays.sort(arr);

// Start from second last element

// as the largest element is at last

for (i = arr_size - 2; i >= 0; i--)

{

  // If the element is not

  // equal to largest element

  if (arr[i] != arr[arr_size - 1])

  {

   System.out.printf("The second largest " +

                      "element is %d\n", arr[i]);

   return;

  }

}

System.out.printf("There is no second " +

                  "largest element\n");

}

// Driver code

public static void main(String[] args)

{

int arr[] = {12, 35, 1, 10, 34, 1};

int n = arr.length;

print2largest(arr, n);

}

}

The idea is to sort the array in descending order and then return the second element which is not equal to the largest element from the sorted array.

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To graph the equation y= −4/5x on the coordinate plane, we can plot two points that satisfy the equation and then draw a straight line through those points. For example, we could choose the points (-1, 4/5) and (2, -8/5), which both satisfy the equation. To plot these points, we first locate the point (-1, 4/5) on the coordinate plane. This point is 1 unit to the left of the y-axis, and 4/5 units above the x-axis. We can then draw a straight line through this point and the point (2, -8/5), which is 2 units to the right of the y-axis and 8/5 units below the x-axis. This line will be the graph of the equation y= −4/5x.

Here is a visual representation of the process:

 (0,0)

  |

  |

  |

  |     (2, -8/5)

  |     *

  |

  |     (1, 4/5)

  |     *

  |

  |

  |

  |

  +-----------------------------------> (x, y)

Variance's square root is always the standard deviation. √25 thus equals 5.

Saying that the median is 7, the mode is 2, and the variance is squared does not make much sense.

However, it makes sense to state that the data's median, mode, and standard deviation are 7, 2, and 4, respectively.

Thus,

√25 = 5.

Variance's square root is always the standard deviation.

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Answer:

B

Step-by-step explanation:

Credits increase the value of liability, equity, revenue and gain accounts.

Answer:

A. Decrease in assets

Step-by-step explanation:

In this case, the business sold the truck, which represents a decrease in the business's assets. Therefore, the Truck account is credited and the Cash account is debited.

By using mean formula, the mean number of letters given to each house is 2.1.

The mean, also known as the average, is a statistical measure that represents the central tendency of a set of data. It is calculated by adding up all the values in the data set and dividing by the number of values.

Central tendency is a statistical measure that describes the center of a data set. It is a way to summarize the data and to describe the typical or most common values in the data set.

1x14+2x17+3x0+4x9=84

14+17+9=40

mean = 84/40 = 2.1

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Answer:

C -3/2

Step-by-step explanation:

The slope is the change in y over the change in x.  You find the change by subtracting

The y's are -4 and 5 (-2,5) (4,-4)

The x's are 4 and -2 (-2,5) (4,-4)

[tex]\frac{-4 -5}{4 - -2}[/tex] = [tex]\frac{-9}{4+2}[/tex]  Subtracting a negative is the same as adding a positive

[tex]\frac{-9}{6}[/tex]  Divide the numerator and denominator by 3

[tex]\frac{-3}{2}[/tex]

The Median of the following observation 65,75 and 80 is 75.

Median is one indicator of central tendency. The value that falls in the middle of the given range of integers is known as the median. In a given data sample, it divides the higher half from the lower half. A minimum of half of the observations fall below or are equal to the median, and a minimum of half of the observations fall above or are equal to the median.

If a data collection has an odd number of observations, the median can be determined as follows:

Step 1: sort the information into ascending or descending order.

Step 2: The middle observation is the median of the given data if the number of observations (let's say n) is odd.

Median = [tex](\frac{n+1}{2} )^{th}[/tex] Observation.

Here n = 3, (3+1)/2 = 2 nd term is the median.

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The two equations are 1.5x+1.25y = 30 and x+y = 22 and values of x and y are 10 and 12 respectively.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, Davin is raising money for a school trip by selling candy bars and packs of cookies. The price of each candy bar is $1.50 and the price of each pack of cookies is $1.25. Yesterday, Davin made $30 from selling a total of 22 candy bars and packs of cookies.

Let x represent the number of candy bars sold, and y be the number of pack of cookies sold,

Establishing the equations,

1.5x+1.25y = 30

x+y = 22

Solving the equations, we get.

x = 10 and y = 12

Hence, the number of candy bars sold 10 and the number of pack of cookies sold is 12

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Answer:

between 1 and 10 percent

The measure of the angle when a cannonball is shot will be 60°.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

A cannonball is shot with a speed of 90 m/s. Assuming its upward speed at the highest point of its curve is 0 m/s and the flat speed at the highest point of its bend is 45 m/s.

We know that in projectile motion, the horizontal velocity does not change.

Let 'x' be the angle it shot. Then the cosine of the angle x is the ratio of horizontal velocity to the resultant velocity when it is shot. Then we have

cos x = 45 / 90

cos x = 1/2

cos x = cos 60°

x = 60°

The proportion of the point when a cannonball is shot will be 60°.

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The equation of the amount to be paid by anyone using the ride in slope intercept form is; y = 0.5x + 10

The general form of the equation of a Line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

Now, we are told that;

Amount charge by Winter Wonderland per child = $0.50

We are told that there is a separate entrance fee.

Amount of times todd sled down the hill = 16 times

Amount paid by todd = $18

Thus, using the slope intercept form, we have;

18 = 0.5(16) + b

18 = 8 + b

b = 10

Thus, the equation of this amount to be paid in slope intercept form is;

y = 0.5x + 10

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As per the given suspended mass, the function that makes values of both x and θ develop the maximum possible moment at A is written as  14715 Nm (clockwise)

While looking into the given question, we have identified the following values, adjusted for any angle 00 ≤ θ ≤ 900 any extension 0 ≤ x ≤ 5 m.

Now, Let us consider an equation to calculate the moment using θ and x as variables around point A.

=> ((9−1.5) + x) (cosθ) (120) (9.81)

When we simplifying the given equation gives us:

=> MA ​= (7.5+x) 1177.2 cosθ

 Here the maximum moment will develop if θ = 0 and x=5 m.

Now, by substituting these values gives us:

=> MA​=(7.5+x)1177.2cosθ

=> MA​=(7.5+5)1177.2cos00

Therefore, the value of MA is written as, 14715 Nm (clockwise)

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Answer: D.

Step-by-step explanation:

You can start out with the form AX = B and solve for matrix X that would yield the answer

Then X = (A^-1)(B)

A = [1    -1]

      [1     1]

A^-1 = (1/(1 - (1)(-1)))*[1    1]

                             [-1   1]

which can be written as (1/2) * [1    1]

                                                  [-1   1]

B = [26]

     [6]

(A^-1)(B) = (1/2)*[1    1] [6]

                        [-1   1] [26]

= (1/2)*[32]

          [20]

= [16]

  [10]

The common factor of equations 2x , 3x² and 4 is 1

What is an Equation?

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 , B and C

The value of A = 2x

The value of B = 3x²

The value of C = 4

Now , on simplifying the equations , we get

A = 1 x ( 2 × x )

B = 1 x ( 3 × x × x )

C = 1 x ( 4 )

So , the common term in the equations A , B and C is 1

Therefore , the common factor is 1

Hence , the common factor of the equations is 1

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The leading coefficient is the number that appears before the variable with the highest exponent in a polynomial. It can be either a positive or a negative number.

The leading coefficient is the coefficient, or number, that appears before the variable with the highest exponent in a polynomial. This coefficient helps determine the end behavior of a graph, which means it can either be a positive or a negative number. For example, if the leading coefficient is a positive number, then the graph will have an upward trend on either side of the y-axis, or the x-axis. If the leading coefficient is a negative number, then the graph will have a downward trend on either side of the y-axis, or the x-axis. Additionally, the leading coefficient can also help determine the degree of a polynomial. For example, the leading coefficient of a polynomial with a degree of two will always be a positive number, while the leading coefficient of a polynomial with a degree of three will always be a negative number. In conclusion, the leading coefficient can be either a positive or a negative number and plays an important role in determining the end behavior of a graph and the degree of a polynomial.

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The length of a leg of an isosceles right triangle can be found using the concept of Pythagoras' theorem by the formula sqrt (hypotenuse ^ 2 / 2) = x.

Since, two sides of an isosceles triangle are equal, let us consider the two equal sides as 'x' and let the hypotenuse of the triangle be 'h'.

Being a right triangle, by Pythagoras' theorem,

h ^ 2 = x ^ 2 + x ^ 2

h ^ 2 = 2x ^ 2

Hence, we can find the length of a leg of an isosceles triangle by:

sqrt (h ^ 2 / 2) = x

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When the original graph is mirrored around the line y = x, the inverse function's graph may be determined, the domain of the inverse, f-1(x), corresponds to the range of the original function (x), the x intercept of f-1(x) is the y intercept of f, and the range of the inverse f-1(x) is the domain of f(x) (x).

The intercept theorem, also referred to as Thales' theorem, the basic proportionality theorem, or the side splitter theorem, is a crucial concept in basic geometry that discusses the ratios of different line segments that are produced when two intersecting lines are intercepted by a pair of parallels.

It is equivalent to the ratios in similar triangles theorem. It is typically credited to the Greek mathematician Thales. Despite the fact that its first known demonstration may be found in Euclid's Elements, it was known to the ancient Babylonians and Egyptians.

Similarity and the intercept theorem go hand in hand. It is equivalent to the idea of similar triangles in that it may be used to demonstrate both the qualities of similar triangles and the intercept theorem.

Hence, When the original graph is mirrored around the line y = x, the inverse function's graph may be determined, the domain of the inverse, f-1(x), corresponds to the range of the original function (x), the x intercept of f-1(x) is the y intercept of f, and the range of the inverse f-1(x) is the domain of f(x) (x).

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To solve the system of equations using substitution method for three variables minimum three equations are required using following steps:

1. Get the value third variable in form of other two and substitute in other two equations.

2. Now get the value of second variable in first variable and get the value of all three variables.

Let us consider three system of equations in three variable are :

x + y + z = 0   __(1)

2x + 3y + z = 2 __(2)

3x + 2y + 2z = 1  ____(3)

Get the value of z in form of x and y from (1) and substitute in (2) and (3)

z = -(x + y)

2x + 3y -(x + y) = 2

⇒x +2y = 2   __(4)

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

⇒3x + 2y -2x -2y =1

⇒x = 1

Now substitute in (4)

1 + 2y = 2

⇒ y = 1/2

Now substitute the value of x and y in (1)

z = - ( 1 + 1/2)

⇒z = -3/2

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Answer:

A = πx² cm²

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius)

Given circumference C = 2πx , and C is calculated as

C = 2πr , then equating gives

2πr = 2πx ( divide both sides by 2π )

r = x

Then

A = πr² = πx² cm²

The ranked probability score (RPS) is a metric used to assess how well predicted events match probability distributions.

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Answer:

A' = (1, -1)

B' = (2, 1)

C' = (4, 0)

D' = (3, -4)

Step-by-step explanation:

don't speak this language. however, I assume it says translate the quadrilateral by the column vector.

A = (-4, 3)  ∴  A' = (1, -1)

B = (-8, 5)  ∴  B' = (2, 1)

C = (-1, 4)  ∴  C' = (4, 0)

D = (-2, 0)  ∴  D' = (3, -4)

Answer: 19.625 ft^2

Step-by-step explanation: To calculate the area of a circle you have to use Area=pi*r^2, so the radius is 2.5 ft, Area = 3.14*2.5^2 = 19.625 ft^2

Answer:

Step-by-step explanation:

Done the I-ready.