Two fractions have denominators of x^2+ 6x + 9 and x^2. What is the Least Common Denominator?

Answer:

97.27 yd²

Step-by-step explanation:

First let's find the area of the right triangle on the left side. To do that, multiply 6x5, then divide the product by 2, since a right triangle is half a rectangle.

6x5=30

30/2=15

Area of triangle=15 yd²

Find area of the middle rectangle. So multiply the length by the width.

9x6=54

Area of rectangle=54 yd²

Find area of the half circle. Formula for area of circle is \(A=\pi r^{2}\). Pi is about 3.14, and radius (\(r\)) is 3. Radius is half of the diameter of circle, and the 6 on the left says the diameter of circle.

\(\pi\)x\(3^{2}\)≈28.27

Area of circle is about 28.27 yd²

Add up the three areas.

15+54+28.27=97.27

Answer:

Step-by-step explanation:

The segment sum theorem tells you the whole is the sum of the parts. That can be used to write an equation for y.

  RS +ST = RT

  (5y +5) +(4y +8) = 67

Simplifying, we get ...

  9y +13 = 67

  9y = 54 . . . . . . . . subtract 13

  y = 6 . . . . . . . . . divide by 9

RS = 5y +5 = 5·6 +5 = 35

ST = 4y +8 = 4·6 +8 = 32

The values of interest are ...

The given fractions are sorted in ascending order following the rules of sorting fractions.

What are fractions?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. The number of components of a specific size is expressed as a fraction.

Some of the rules for arranging fractions are as follows:

Now following the above rules, we can solve each question.

        We will make the denominators the same.

      The LCM of 40, 40, 20,4,5 = 40

     So the fractions become,

         \(\frac{21}{40} , \frac{29}{40} ,\frac{34}{40},\frac{30}{40},\frac{32}{40}\)

      Now sort them.

     \(\frac{21}{40} , \frac{29}{40} ,\frac{30}{40},\frac{32}{40},\frac{34}{40}\)

  2. \(\frac{7}{9} , \frac{2}{9} ,\frac{5}{6},\frac{13}{18},\frac{3}{18}\)

   LCM of 9,6,18 = 18

    So the fractions become,

      \(\frac{14}{18} , \frac{4}{18} ,\frac{15}{18},\frac{13}{18},\frac{3}{18}\)

    Now sort them.

  \(\frac{3}{18} , \frac{4}{18} ,\frac{13}{18},\frac{14}{18},\frac{15}{18}\)

3.  \(\frac{9}{4} , \frac{4}{3} ,\frac{5}{3},\frac{7}{4},\frac{7}{5}\)

     LCM of 4,3,5 = 60

   \(\frac{135}{60} , \frac{80}{60} ,\frac{100}{60},\frac{105}{60},\frac{84}{60}\)

Now sort them.

\(\frac{80}{60} , \frac{84}{60} ,\frac{100}{60},\frac{105}{60},\frac{135}{60}\)

4. \(\frac{17}{7} , \frac{23}{7} ,\frac{24}{5},\frac{17}{5},\frac{11}{35}\)

LCM of 7,5,35 = 35

\(\frac{85}{35} , \frac{115}{35} ,\frac{168}{35},\frac{119}{35},\frac{11}{35}\)

Now sort them.

\(\frac{11}{35} , \frac{85}{35} ,\frac{115}{35},\frac{119}{35},\frac{168}{35}\)

Therefore the above fractions are sorted in ascending order.

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Answer:

I think that that angle would also be 102 degrees.

Answer:

I believe it's

Step-by-step explanation:

A

however I could be wrong

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The numerical values (numbers) which makes the table show a proportional relationship between x and y are as follows:

x                     y___

2                    0.6

5                    1.5

8                    2.4

A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.

Mathematically, a direct proportion can be represented by the following equation:

y = kx

Where:

Next, we would determine the numerical value of the constant of proportionality (k) as follows:

y = kx

k = y/x

k = 0.6/2

k = 0.3

When y = 1.5, the value of x is given by:

x = y/k

x = 1.5/0.3

x = 5.

When y = 2.4, the value of x is given by:

x = y/k

x = 2.4/0.3

x = 8.

In conclusion, the values of x are 5 and 8 while the value of y is 2.4.

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The correct answer is: O Yes, distance and angle measure are preserved.

When a triangle ABC is reflected across the line y = x, the pre-image and image are congruent.

This is because the line y = x is the perpendicular bisector of the segment joining each corresponding point of the pre-image and image.

Reflection across the line y = x is a type of transformation known as an isometry, which preserves both distance and angle measure.

Here's why:

Distance preservation:

When a point is reflected across the line y = x, the distance between the original point and its reflection remains the same.

This holds true for all corresponding points of the triangle.

Therefore, the distance between any two corresponding points in the pre-image and image triangle will be equal, resulting in distance preservation.

Angle preservation: When a line segment is reflected across the line y = x, the angle between the line segment and the line y = x is preserved. This means that the corresponding angles in the pre-image and image triangle will be congruent.

Since both distance and angle measure are preserved during reflection across the line y = x, the pre-image and image triangles are congruent.

It's important to note that congruence under reflection across a line holds only when the line of reflection is the same for both the pre-image and image.

If the line of reflection were different, the triangles would not be congruent.

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Answer:

The answer toy our problem is, The maximum number of days by which the completion of work can be delayed is 15.

Step-by-step explanation:

We are given that the penalty amount paid by the construction company from the first day as sequence, 4000, 5000, 6000, ‘ and so on ‘. The company can pay 165000 as penalty for this delay at maximum that is

 \(S_{n}\)​ = 165000.

Let us find the amount as arithmetic series as follows:

4000 + 5000 + 6000

The arithmetic series being, first term is \(a_{1}\) = 4000, second term is \(a_{2}\) = 5000.

We would have to find our common difference ‘ d ‘ by subtracting the first term from the second term as shown below:

\(d = a_{2} - a_{1} = 5000 - 4000 = 1000\)

The sum of the arithmetic series with our first term ‘ a ‘ which the common difference being, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) ( ‘ d ‘ being the difference. )

Next we can substitute a = 4000, d = 1000 and \(S_{n}\) = 165000 in “ \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\) “ which can be represented as:

Determining, \(S_{n} = \frac{n}{2} [ 2a + ( n - 1 )d ]\)

⇒ 165000 = \(\frac{n}{2}\) [( 2 x 4000 ) + ( n - 1 ) 1000 ]

⇒ 2 x 165000 = n(8000 + 1000n - 1000 )

⇒ 330000 = n(7000 + 1000n)

⇒ 330000 = 7000n + \(1000n^2\)

⇒ \(1000n^2\) + 7000n - 330000 = 0

⇒ \(1000n^2\) ( \(n^2\) + 7n - 330 ) = 0

⇒  \(n^2\) + 7n - 330 = 0

⇒ \(n^2\) + 22n - 15n - 330 = 0

⇒ n( n + 22 ) - 15 ( n + 22 ) = 0

⇒ ( n + 22 )( n - 15 ) = 0

⇒ n = -22, n = 15

We need to ‘ forget ‘ the negative value of ‘ n ‘ which will represent number of days delayed, therefore, we get n=15.

Thus the answer to your problem is, The maximum number of days by which the completion of work can be delayed is 15.

Therefore, the product of 5 and fraction (-2/3) is -10/3.

A fraction is a number that represents a part of a whole. It consists of two numbers separated by a horizontal or diagonal line, called a fraction bar. The number above the fraction bar is called the numerator, and the number below the fraction bar is called the denominator. The numerator represents the part of the whole that we are interested in, and the denominator represents the total number of equal parts into which the whole is divided.  Fractions can be used to represent ratios, proportions, percentages, and many other mathematical concepts. They can be added, subtracted, multiplied, and divided using specific rules and procedures. Fractions can be proper (when the numerator is less than the denominator), improper (when the numerator is greater than or equal to the denominator), or mixed (when the fraction is represented as a whole number and a proper fraction).

Here,

To find the product of 5 and (-2/3), we simply multiply the two numbers:

5 x (-2/3) = -10/3

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The measure of angle x to the nearest tenth of a degree is 51.8°

The figure in the image is a right triangle.

From the image;

To solve for the measure of angle x, we use one of the six (6) trigonometric ratio.

Sine = Opposite / Hypotenuse.

Plug in the given values and solve for angle x.

sin( x ) = 11 units / 14 units.

Take the sine inverse.

x = sin⁻¹( 11/14 )

x = 51.7867

x = 51.8 degrees.

Therefore, the value of x is 51.8 degrees.

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Answer:xet1234567890987654323456789

Step-by-step explanation:

87654323456789098765434567890

The fraction of the class working on the art project is;

Here, we want to calculate the fraction of the class that worked on the art project

Mathematically, at any point in time, the total fraction is 1

So, all we have to do here is to sum up the fractions that we have and subtract from 1

We have this as;

Answer:

answer is 29

Step-by-step explanation:

subtract 27 from 56 and it equals 29

The domain and the range of the function represented by the graph are [-2, 2) and (-4, 4]

In mathematics, the domain and range of a function are used to describe the set of possible input and output values of the function, respectively.

From the graph, we have the set of input values to be

Input = From -2 (closed circle) to 2 (open circle)

This means that the domain is

[-2, 2)

From the graph, we have the set of output values to be

Output = From -4 (open circle) to 4 (closed circle)

This means that the range is

(-4, 4]

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The seven ordered pairs that fit on the axes of the graph include the following:

In order to use the given polynomial function to complete the table, we would have to substitute each of the values of x (x-values) into the polynomial function and then evaluate as follows;

When the value of x = -3, the output value of this polynomial function is given by;

y = x³ + 6

y = (-3)³ + 6

y = -27 + 6

y = -21

By observing critically the graph (see attachment), we can logically deduce that it represents a polynomial function.

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In this case, the amount of the paint that she used to paint her room is 4 1/2 of the paint

Here are the general steps to follow when forming an equation from a word problem:

Read the problem carefully and identify the quantities and variables involved. Look for keywords that indicate the mathematical operation to be performed, such as "sum", "difference", "product", "quotient", "is", "was", "will be", "more than", "less than", "equal to", etc.

Translate the words into mathematical expressions and equations. Use the quantities and variables identified in step 1 to form equations. Assign variables to unknown quantities, and use algebraic symbols and operations to represent the relationships between the quantities.

Solve the equations to find the answer to the problem. Simplify the equations and solve for the unknown variable. Check your answer to make sure it makes sense in the context of the problem.

1) 5 * 19/4

= 95/4

23 3/4

2) Total weight = 3(14/3) + 5(15/2)

14 + 75/2

28 + 75/2

= 51  1/2 pounds

3) x = 45/8 *  4/5

= 9/2

= 4 1/2

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The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

In the context of this problem, the variables x and y are given as follows:

The equation for the constant is given as follows:

k = y/x.

Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.

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Answer:

a. 2³   b. 8

Step-by-step explanation:

(2*2)=2 papers cut in half

2*2*2=2 papers cut in half twice

2*2*2=2³

2³=8

The situation is 1 x 2 + (1 x 2) ³ = X. Kwami has 10 pieces of paper now.

Since Kwami had two large sheets of paper, and he cut each piece of paper in half, and then he cut the smaller pieces of paper in half two more times, to write this as a power and determine how many pieces of paper does Kwami have now the following calculation must be performed:

First, you must consider the division of the paper, and then consider the number of times that process was repeated.

So now Kwami has 10 pieces of paper.

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16.5 is 30% of 55

1650/55 = 30

Answer:

\(\sf 2\sqrt{2}\)

Step-by-step explanation:

First find h(10)

   h(x) = 2x - 8

   h(10) = 2*10 - 8

           = 20 - 8

           = 12

\(\sf g(x)=\sqrt{x-4}\\\\ g(h(10) = g(12) = \sqrt{12-4}\\\)

                         \(\sf = \sqrt{8}\\\\ = \sqrt{2*2*2}\\\\ = 2\sqrt{2}\)

The exterior angle of the triangle is 62°.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.

Let us take the triangle as ABC.

Here \(m\angle C\)= 180-(5x-3)° [Because straight line angle is 180°].

We know that sum of all angles in triangle is add upto 180° Then,

=> \(m\angle A+m\angle B+m\angle C\)=180

=> 43°+3x°+180-5x+3=180°

=> -2x=180-180-43-3

=> -2x=-46

=> x=13°

Now exterior angle ,

=> 5x-3

=> 5*13-3

=> 65-3

=> 62°

Hence the exterior angle of the triangle is  62°.

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The solution to the given algebraic expression 3(2-4x) = 5-8x is x = 1/4

3(2-4x) = 5-8x

open parenthesis

6 - 12x = 5 - 8x

combine like terms

6 - 5 = -8x + 12x

1 = 4x

divide both sides by 4

x = 1/4

Ultimately, x = 1/4 is the answer to the algebraic expression.

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Answer:A

Step-by-step explanation:

Answer: A

Step-by-step explanation: I took the test

Hey there! :)

Answer:

Has one solution.

(Graphed below)

Step-by-step explanation:

***The equations are graphed below, but this can also be solved algebraically.***

Set each equation equal to each other:

-6x + 6 = -3x - 3

Add 6x to both sides:

6 = 3x - 3

Add 3 to both sides:

9 = 3x

x = 3.

Plug in the value of x into an equation to solve for y:

y = -6(3) + 6

y = -18 + 6

y = -12.

The system of equations only has ONE solution at (3, -12).

On the graph, as well, the point of intersection is at (3, -12). This is the solution.

Answer:

x > -5, so the correct answer is C.

Answer:

\(120in^3\)

Step-by-step explanation:

Find the diagram attached.

The volume of a triangular prism = \(\frac{base\ area *height}{3}\)

Since the base is a triangle, Base area = 1/2 * base * height

given base of the triangular base = 8in

height of the triangle = 9in

Base area = 1/2 * 8 * 9

Base area = 4*9

Base area = 36in²

Height of the prism = 10in

Volume of the prism = \(\frac{36*10}{3}\)

Volume of the prism = \(12*10\)

Volume of the prism = \(120in^3\)

Answer: 360

Step-by-step explanation:

volume is base times height