If the sum of n term of an ap is sn = 3n^2+5n writ its common difference

Log₁₀ is an expression used to represent logarithmic functions with a base of 10. To write log₁₀ in Microsoft Word, you can use the “Insert Equation” feature.

To access this, select Insert on the top menu bar, followed by Equation. In the new window that appears, select the Greek and Math Symbols tab. In this tab you will find the log₁₀ symbol that looks like an upside-down “y”. You can then click on the symbol and it will be added to your document.

If you need to type out the equation, you can type “log₁₀” and it will automatically be converted to the log₁₀ symbol.  You can also use the shortcut CTRL+Alt+L to insert the log₁₀ symbol directly into your document.

If you are using a Mac, you can use the shortcut Command+Shift+L.  The log₁₀ symbol is commonly used in mathematics and science, particularly in algebra and calculus. It is used to represent the logarithm of a particular number to the base 10.

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On solving the question, sum of exterior angle is 360 degree. Hence, the value of x is 120°.

The exterior angle of a triangle is equal to the sum of its two opposite interior angles, according to the external angle theorem. Remember that the total external angle, measured from each vertex, is always 360°. Alternatively stated, d + e + f = 360°.The angle that is created between a triangle's extended side and one of its sides is known as the external angle. A triangle has a total of 360 degrees in its outside angles.

x + ( x+6) +114 = 360

2x = 240

x = 120

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Answer:

11.75

Step-by-step explanation:

The quilt consists of a square array of 8 x 8 = <<8*8=64>>64 square pieces of fabric.

Since the length of the total quilt is 7.52 feet, the side length of each square piece of fabric is 7.52 / 8 = <<752/8=0.94>>0.94 feet.

However, since you are asked to enter your answer in the box in feet, you should express 0.94 feet as a decimal to the nearest hundredth. The nearest hundredth of a foot to 0.94 feet is 0.95 feet. Therefore, the side length of each square piece of fabric is approximately 0.95 feet, or approximately 11.75 inches.

So the answer is 11.75 feet.

Answer:

  2m⁴ +0m³ -3m² +0m +7

Step-by-step explanation:

You want the index form of 2m⁴-3m²+7.

The index form of a polynomial has terms with all indices present in decreasing order, using 0 coefficients where necessary.

The given polynomial is missing indices 3 and 1, so we add those with coefficients of 0:

  2m⁴ +0m³ -3m² +0m +7

The lowest ratio for 54 m in 2.5 hours will be:

= 54 / 2.5 is 21.6 : 1.

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

This simply indicates that you're dividing the variable A by B. Let USA say for instance, the ratio will be 3/10 if A is 5

3 and B is 10.

In this case, the lowest ratio for 54 m in 2.5 hours will be:

= 54 / 2.5.

= 21.6 / 1

= 21.6:1

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Answer:

29000000000*140% = 40600000000

=40.6 billion

Step-by-step explanation:

right!!!

Sequence of transformation is first moving 5 unit in y axis than mirror image  with y axis.

A particular order of transformational events is referred to as a transformational sequence. This indicates that more than one transformation is handled by a series of transformations, and the order in which they happen is important.

The line of reflection must pass through the centre point for the figure to map onto itself. The sides of the figure are cut by two lines of reflection. The vertices of the figure are intersected by two lines of reflection. As a result, there are four potential lines of reflection that pass through the center.

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Answer:

No triangle

Step-by-step explanation:

Since [tex]4+4=8[/tex], the side lengths fail to satisfy the triangle inequality theorem. Thus, no such triangle exists.

Total = 240+240 = 480 potential combinations with a red shirt, green pants, and a green hat, or a green shirt, red pants, and a red hat, respectively.

The total number of possible outcomes for all four of these scenarios is 208, which is equivalent to 64 + 64 plus 16 plus 64. Consequently, we have a total of 120 different costumes to choose from (8 + 5 + 3).              8 × 5 × 3 = 120 . Given that you have 4 options for shirts, 3 options for shorts, and 2 options for shoes, the formula should be formatted as         4 × 3 ×2. You now have 24 wardrobe choices.

A "set" is made up of one top and one bottom. Since every bottom can be worn with every top, multiplying the tops by the bottoms gives us the total number of possible outfit combinations. Since dresses often aren't worn with tops or bottoms, they are introduced after the multiplication has occurred.

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Answer: 70-20x = 60-15x, where x is the number of pizzas purchased.

Step-by-step explanation:

(TLDR, the solution to the given equation is that the cards will have the same amount of money left on them if both jim and clara buy two pizzas each. feel free read my explanation on how to write equations like this in the future, should you need it.)

so, we know that since jim and clara received $70 and $60 gift cards (respectively), these numbers are called constants, because their original values do not depend on anything (they are given). while these numbers may decrease with the amount of pizzas bought, their original values are fixed.

now, the price for one pizza at jim's pizza restaurant is $20, right? so if you buy 2 pizzas, it'll be $40, 3 pizzas are $60, and so on. but we can actually represent the price of the pizzas as 20x (where x is the number of purchased pizzas, and 20 is the price of one pizza), and this expression works for any number of pizzas you buy. you can also apply this to clara's restaurant, as the total price of the number of pizzas she buys is represented by 15x.

the words charges and left in this problem tells you that you're going to need to subtract from the total amount of money on the gift cards. using the expressions above, the amount of money jim has left on his card can be expressed as 70 (amount of money on the card) MINUS 20x (number of money spent on however many pizzas were bought (x)). likewise, the amount of money left on clara's card after she buys however many pizzas can be represented as 60-15x. you can then set the equations equal to each other and solve for x, which tells you how many pizzas they each need to buy to have the same number of $$ left on their cards.

70-20x = 60-15x

10=5x

2=x. hope this helped :3

The correct option is option (c)-"The distribution is skewed right."

The distribution of the ages of the Best Actor Oscar winners is slightly skewed to the right.

A histogram of the ages of the Best Actor Oscar winners shows that the majority of the ages are centered around the mean age, with a few ages on the higher end that extend the right tail of the distribution. This creates a small skewness to the right.

The distribution seems to be centered at around 42-43.

The age distribution ranges from about 30 to about 75, without taking into account an outlier.

It's worth noting that the distribution is not extremely skewed, and the majority of the ages are still grouped around the center of the distribution.

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By using the fact that the interior angles should add up to 360°, we will see that:

C = 142°

We know that for any polygon of N sides, the sum of the interior angles is equal to:

S = (N - 2)*180°

In this case, the polygon has 4 sides, then:

S = (4 -2)*180° = 360°

Then we can write the equation:

A + B + C + D = 360°

Replacing the known angles we get:

68° + 43° + C + 107° = 360°

And now we can solve this for C.

C = 360° - 107° - 43° - 68°

C = 142°

That is the measure of the angle BCD.

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Answer:

1. g=-3

2. a=-2

3. s=19

4. f=-12

5.d=8

6.a=-28

7.w=12

Step-by-step explanation:

1)  take 4-7 to get -3

2)  take 10 divided by -5 to get -2

3) take 10+9 to get 19

4) take 3-15 to get -12

5) take -64 divided by -8 to get 8

6) take -4 times 7 to get -28

7)take 7 plus 5 to get 12

The expression x3 3x2 12x 19 is a polynomial expression in standard form.

To add 24 to this expression, we need to add 24 to each of the terms. This means that the answer is x3 + 3x2 + 12x + 43. To check our work, we can use theFOIL  method to expand the expression and make sure that the coefficients of each of the terms are correct. The FOIL method stands for First, Outer, Inner, Last. The first and last terms are the x3 and 43, the outer terms are 3x2 and 12x, and the inner terms are 3x2 and 12x. When we multiply these terms, we get x3 + 3x2 + 12x + 43, which is our final answer.

Calculation

x3 + 3x2 + 12x + (19 + 24)

= x3 + 3x2 + 12x + 43

The expression x3 3x2 12x 19 is a polynomial expression in standard form.

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Answer:

(4,14) (8,28))

Step-by-step explanation:

3.5(4) = 14

3.5(8) = 28

The coordinates that can be applied to the equation y > 2 + 9x is the cartesian coordinate system

A system that identifies your precise location on a graph is the Cartesian coordinate system.  

This system can be used to graph a collection of points that will give your equations' solutions, which makes it handy. Each axis will have its own variable in the equations that are employed with this system.

The x-axis, a horizontal axis, and the y-axis, a vertical axis, are the two axes that make up the Cartesian coordinate system.

The variables x and y will be present in equations for lines in this system.

Hence the cartesian coordinate system is applicable for the equation given as y > 2 + 9x

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A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.

Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.

given

A binomial is a difference of squares if both terms are perfect squares. Remember that we might first need to filter out a common element.

If a binomial is found to be a difference of squares, it is factored into two binomials. the first being the first term's square root less the second term's square root.

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The greatest number of classrooms is 4, Joanne can distribute materials

5 flyers and 4 buttons.

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor or GCF.

Given:

Joanne is campaigning for class president and plans to distribute some campaign materials.

20 flyers and 16 buttons.

She wants each classroom to receive an identical set of campaign materials, without having any materials left over.

In order to find the greatest number of classrooms, Joanne can distribute materials:

We have,

the number of flyers = 20.

Number of buttons = 16

We need to find the GCF.

GCF of 16 - 1,2,4,8,16

GCF of 20-1,2,4,5,10,20

Clearly, 4 is the GCF.

Therefore, total number of classrooms = 4

Number of flyers distributed to each classroom

= Total number of flyers / Total number of classroom

= 20/4

= 5

Number of buttons distributed to each classroom

= Total number of buttons/ Total number of classrooms

= 16/4

= 4

Therefore, the Joanne can distribute 5 flyers and 4 buttons to each classroom.

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30° =  angle DAE

Step-by-step explanation:                      

We have ACD with angle ACD = 150°, and because CD = CA, angle CAD and ADC are equal, so angle CAD = [180 -150] / 2 = 30/2 = 15°.

 if we draw AE in ABE using the same process, angle EAB = 15°,
so CAB = 60° = angle =CAD + angle DAE + angle EAB

60   =  15  + angle DAE + 15

60  = 30 + angle DAE
30° =  angle DAE  

Triangle with an equilateral shape. An equilateral triangle is a triangle with all of its sides being the same length. An equilateral triangle, for example, has three sides equal to 5cm. Because the three sides are equal, the three angles opposite the equal sides are equal in size.  

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Volume of prism is given by V= base area × height cubic unit. The expression 48 × 3  unit³ can be used to represent the volume of the prism.

Prism is a three-dimensional geometrical figure having identical two ends. A prism has flat faces, similar bases and equal cross sections. A prism is normally bounded by plane faces.

Volume of prism is calculated by the product of base area and height of the prism. At first, we need to calculate the base area and then height is multiplied with it.

Prisms are different types such as triangular prism, rectangular prism, pentagonal prism and hexagonal prism so depending on the figure area for the base is different. As a result, different shaped prism has different formula for volume calculation.

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In the given the diagram of a circle, the measure of angle MON is 60°.

A circle is a two-dimensional shape created by a collection of points that are spaced uniformly or uniformly apart from a fixed point (centre) on the plane. The radius of a circle is the fixed distance between each point and the fixed point, which together make up the circle's origin or centre.

All angles add upto 360°

100 + 140 + ∠MOP =  360

∠MOP = 120°

Draw an imaginary straight line extending MO, making MOM'

∠QOM' = 180 - 140

            = 40 = ∠MOQ'  (vertically opposite)

Draw an imaginary straight line extending NO, making NON'

Draw an imaginary straight line extending PO, making POP'

P'OQ = 180 - 100

         = 80 = ∠Q'OP   (vertically opposite)

Draw an imaginary straight line extending QO, making QOQ'

P'OM = 60° = M'OP  (vertically opposite)

Now, ∠N'OQ = 180 - 60 - 2(40)

                     = 20°

Then, ∠P'ON' = 80 - 20

                     = 60

And ∠MON = 40 + 20

                    = 60°

Hence, In the given the diagram of a circle, the measure of angle MON is 60°.

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Teo can fill 28 glasses in  4 2/3 pitches of juice.

Teo  has 4 2/3 pitches of juice.

First we write the improper fraction (mixed fraction) as a proper fraction.

4 2/3

= [(4 × 3) + 2] / 3

= (12 + 2) / 3

= 14/3

One glass holds 1/6 of a pitcher.

Let m number of glasses hold 14/3 pitches of juice.

By unitary method,

m × (1/6) =  14/3

To find the value of m we need to divide fractions.

m = (14/3) / (1/6)

m = (14/3) × (6/1)

m = 14 × 2

m = 28

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If Hermione paid 98 coins and Luna paid 28 coins, Hermione paid for 672 Chocolate Frogs.

We can start the problem by using algebra. Let x be the number of Chocolate Frogs that Hermione paid for. Then we know that:

x + (2016 - x) = 2016 (the total number of Chocolate Frogs)

Also, we know that the cost of the Chocolate Frogs Hermione paid is 98 coins, and the cost of the Chocolate Frogs Luna paid is 28 coins. Let's assume the cost of each Chocolate Frog is y. Then we can write:

x * y = 98 and (2016 - x) * y = 28

Now we have a system of two equations with two variables (x and y). To find the value of x, we can use any method to solve the system of equations, such as substitution or elimination.

Using substitution, we can solve for y in the second equation and substitute it into the first equation:

(2016 - x) * y = 28

y = 28 / (2016 - x)

x * (28 / (2016 - x)) = 98

x * (28 / (2016 - x)) = 98

x = 98 * (2016 - x) / 28

Solving for x, we get:

x = 2016/3

So Hermione paid for 2016/3 = 672 Chocolate Frogs.

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Answer:

Hermione paid for 1,568 frogs.

Step-by-step explanation:

First, do 98 + 28. That will give you 126. Then do 2,016 / 126. That gives you 16. 16 x 98 = 1568 frogs.

Let's do Luna's to check our work.

28 x 16 = 448 frogs. 448 + 1568 = 2,016. So, Hermione paid for 1,568 frogs.

Amount of pineapple juice is more in Jo's drink and amount of Orange juice is less in Jo's drink as compare than the tropical punch recipe because these are not in that ratio as in the tropical punch recipe.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another. In a ratio, two quantities are compared using division. Here the dividend is called the 'antecedent' and the divisor is called the 'consequent'.

The Number of cups of pineapple juice = 222 liters

The Number of cups of orange juice = 333 liters

Thus ,

Total number of cub of juice = 222+333

                                               = 555 cups

In Jo's drink

The Number of cups of pineapple juice = 333 liters

The Number of cups of orange juice = 444 liters

Thus Total number of cub of juice = 333+444

                                                        = 777 cups.

The ratio of amount of pineapple juice and amount of Orange juice is 2:3 in the tropical punch recipe

Whereas the ratio of amount of pineapple juice and amount of Orange juice is 3:4 in Jo's drink

Thus we can see that Amount of pineapple juice is more in Jo's drink And Amount of Orange juice is less in Jo's drink.

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1000 yards in kilometers will be 0.9 km.

The yard is a United States customary measurement. In this form of measurement, we have yards, feet, and inches.

1 Yard = 3 feet.

1 foot = 12 inches.

Here we are given 1000 yards,

1000 yards = 3 X 1000 feet

= 3000 feet

= 36000 inches.

Now, converting this to the metric measures we know that

1 inch = 2.5 cm

Hence, 36000 inches = 90000 cm.

1 cm = 1/100 m

Hence, 90000 cm = 90000/100 m

= 900 m

1 m = 1/1000 km

Hence, 900 m = 900/1000 km

= 0.9 km

Hence, 1000 yeard = 0.9 km.

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For a roll of paper with dimensions 3 feet cut to any desire length,

a) The value of perimeter when cut to 2.5 feet is 11 feet.

b) The complete table with filled perimeter column is present above . The function notation for perimeter is , P =2(L+ W)

c) P(11) , represents the length of paper cut to 11 feet in this situation. It's value i.e., P(11) = 28 feet .

Perimeter is defined as the sum of all boundary length of any geometry. We have a roll of paper with dimensions 3 feet ( i.e, width) is cut to any length. From, it we conclude that that paper is like quadrilateral shape but not square.

a) when the paper cut in a length of 2.5 feet , so, length (L) = 2.5 feet

The perimeter of quadilateral ( rectangle in this case ) is 2(L+W) so, perimeter

= 2( 2.5 + 3)

= 11.0 feet

b) Now, we have to complete "perimeter coulmn ," in the table and side lengths are provided.

Width (w) = 3 feet

length (l) = 1 feet

perimeter = 2(4) = 8

similarly, side lengths (ft.) perimeter ( ft.)

2.5 11

1 8

2 10

11 28

L 2( L + W)

The functional notation for perimeter is

P = 2(L+W) .

c) P(11) represents the length of paper in feet when the paper is cut at a length of 11 feet . It's value is 28 feet . So, the value of P(11) is 28 feet.

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Complete question:

A roll of paper that is 3 feet wide can be cut to any length.

a. If we cut a length of 2.5 feet, what is the perimeter of the paper?

b. Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is L, use a function notation.

c) what does P(11) represent in this situation? What is its value?

Answer:

Step-by-step explanation: first we have to solve the bracket both side of equal to.

1/6(3x-6)=1/8(4x+)

x/2-1 = x/2+1

-2

The y intercept of the graph of the function f(d) indicates f(d) = 11 and the average rate of change of the function f(d) from d = 2 to d = 7 is 0.114, making 6.97 a reasonable domain to depict the growth function.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal.

An equation is a mathematical expression with two equal sides and an equal sign in between. An equation is a mathematical statement proving the equality of two numbers or values.

Equations can be categorized as either identities or conditional equations. For each value of the variables, an identity holds true. Only specific values of the variables make a conditional equation true. An equals symbol ("="), separating two expressions, is used to represent an equation.

Part A:

11.79 = 11(1.01[tex])^d[/tex]

substitute the values in the above equation, we get

[tex]$$& (1.01)^d[/tex] = 11.79 / 11

simplifying the equation, we get

[tex]$$& (1.01)^d[/tex] = 1.071818

d = log 1.071818 / log 1.01

The value of d = 6.97

Part B:

y-intercept is obtained when domain = 0

[tex]$& d=0 \Rightarrow f(0)=11(1.01)^0=11 \times 1=11 \\[/tex]

f(d) = 11

Part C:

Average rate of change,

[tex]$\Delta \mathrm{f} / \Delta \mathrm{d} & =(\mathrm{f}(7)-\mathrm{f}(2)) /(7-2) \\[/tex]

[tex]$& =\left(11(1.01)^7-11(1.01)^2\right) / 5 \\[/tex]

= 0.57 / 5 = 0.114

The y intercept of the graph of the function f(d) indicates f(d)=11 and the average rate of change of the function f(d) from d=2 to d=7 is 0.114, making 6.97 a reasonable domain to depict the growth function.

The complete question is:

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

f(d) = 11(1.01)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)

Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent?

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6.97 is an appropriate domain in which to represent the growth function because the y intercept of the graph of the function f(d) suggests that f(d) = 11 and the average rate of change of the function f(d) from d = 2 to d = 7 is 0.114 as studied by biologist.

A mathematical statement that establishes the equality of two mathematical expressions is the definition of an equation in algebra.

A mathematical expression with two equal sides and an equal sign in the middle is called an equation. A mathematical statement establishing the equality of two numbers or values is called an equation.

Either identities or conditional equations are categories for equations. Each value of the variables corresponds to a specific identity. A conditional equation can only be true for a certain range of variable values. An equation is represented by two expressions being separated by the equals sign ("=").

Part A:

11.79 = 11(1.01

substitute the values in the above equation, we get

[tex](1.01)^{d}[/tex] = 11.79 / 11

simplifying the equation, we get

  (1.01)^{0} = 1.071818

d = log 1.071818 / log 1.01

The value of d = 6.97

Part B:

y-intercept is obtained when domain = 0

d = 0

f(0) = 11[tex](1.01^{0} )[/tex] = 11 * 1 = 11

f(d) = 11

Part C:

Average rate of change,

Δf / Δd  = (f(7) - f(2)) / 7-2

= 0.57 / 5 = 0.114

The y intercept of the graph of the function f(d) indicates f(d)=11 and the average rate of change of the function f(d) from d=2 to d=7 is 0.114, making 6.97 a reasonable domain to depict the growth function.

The complete question is:

A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:

f(d) = 11(1.01)d

Part A: When the biologist concluded her study, the radius of the algae was approximately 11.79 mm. What is a reasonable domain to plot the growth function? (4 points)

Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)

Part C: What is the average rate of change of the function f(d) from d = 2 to d = 7, and what does it represent?

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Answer:

In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line.

Step-by-step explanation:

In order to determine whether a graph represents a linear function, we need to check if the graph is a straight line. A linear function is defined as a function of the form y = mx + b, where m and b are constants. The graph of a linear function is a straight line with a constant slope, and so any graph that is not a straight line is not a linear function.

Without the actual graph it's hard to say for sure, but based on the provided information, "The graph does not contain the point (20, –8)" indicates that the graph does not pass through this point (20, -8), and it could be indicating that it's not a straight line, So, The graph does not represent a linear function.