Help please
Determine the sum of the measures of the interior angles of a dodecagon (12-sided polygon).

540°

360°

1,800°

2,160°

Answer:

➜ ∠4 = ∠2

➜ ∠2 + ∠3 = 180°

➜ ∠1 = ∠3

Step-by-step explanation:

     We can use vertical angles to prove the first statement true, ∠4 = ∠2.

     Next, ∠2 and ∠3 are supplementary angles, so if you add them together you will get 180 degrees. This statement is also true.

       Then, ∠1 and ∠2 are not complimentary angles. This statement is false.

       Lastly, we can use the same reasoning of the first one to prove this statement true as well. They are vertical angles, ∠1 = ∠3.

You ran 1/8 of miles more today than yesterday.

Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.

Miles you ran yesterday is three fourths of a mile.

Let 1 mile be M.

Miles you ran yesterday = 3/4 M

Today you ran seven-eighths of a mile.

Miles you ran today = 7/8 M

Difference of miles = 7/8 M - 3/4 M

3/4 is same as 6/8.

Difference of miles = 7/8 M - 6/8M

                                = 1/8 M

Hence you ran 1/8 of miles more than yesterday.

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The circumference of the circle is 43.98 in.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more generally referred to as the perimeter.

Given:

Pia drew a circle with a circumference of C and a diameter of 14 in

We have to find the circumference of the circle.

Since,

Circumference = 2*π*r

Here

Diameter of circle = 14 in.

⇒ Radius of circle = 7 in.

⇒ Circumference = 2*π*7 = 43.98 in.

Hence, the circumference of the circle is 43.98 in.

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If a train travels 283. 8km in 4. 4 hours, the train travels 71km in 1 hour and the train travels 114.5km in 2.5 hours.

Based on the assumption that the train is traveling at a constant speed throughout its journey.

To find the speed the train travels , we divide the total distance by the total time:

speed = 283.8km/ 4.4 hours

speed = 64.5 km/h

To find the distance the train travels , we multiply the speed of the train by the total time:

Distance travelled in 1 hour = 64.5 km/ hour × 1 hour

Distance travelled in 1 hour = 64.5 km

Distance travelled in 2.5 hours = 64.5 km/hour x 2.5 hours

Distance travelled in 2.5 hours = 161.25km

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Answer:

k = 9

Step-by-step explanation:

According to the Factor theorem, if (x - a) is a factor of f(x) then f(a) = 0

given (x - 6) is a factor of f(x) then f(6) = 0 , that is

3(6)³ - 17(6)² - 6k + 18 = 0

3(216) - 17(36) - 6k + 18 = 0

648 - 612 - 6k + 18 = 0

36 - 6k + 18 = 0

54 - 6k = 0 ( subtract 54 from both sides )

- 6k = - 54 ( divide both sides by - 6 )

k = 9

Sara's mom average speed is 66mph. The next step is to divide the distance by the time: 33/0.5 = 66 mph.

You may estimate the average pace at which an object will go a distance by looking at its average speed. Average speed is calculated by dividing a quantity by the time required to obtain that quantity.

Finding the distance and the time is necessary to calculate speed.

In this situation, you must deduct mile marker 88 from 121 to determine the distance.

121 - 88 = 33mile

Even though the time is 30 minutes, you're probably interested in miles per hour. 30 minutes must be converted to 0.5 hours.

The next step is to divide the distance by the time: 33/0.5 = 66 mph.

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On solving the provided question, we can say that - the percentage of the data is 5% = 5/100 = 0.05

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.

According to the authors, "the bases will be virtually totally present in their most probable forms. If this is the case, then only adenine and thymine and guanine and cytosine are viable base pairs, and the requirements for creating hydrogen bonds are more stringent (lines 31-35).

Options C and D are erroneous because the table does not support the authors' postulated pairing of nitrogenous bases in DNA molecules.

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No, 12 16 20 is not a right triangle. In order to be a right triangle, one side must be the same as the square root of the sum of the squares of the other two sides. In this case, the hypotenuse (side 20) is not equal to the square root of 12^2 + 16^2 which is 20.

No, 12 16 20 is not a right triangle. To determine whether or not something is a right triangle, we need to use the Pythagorean Theorem. This theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is side 20, and the other two sides are 12 and 16. When we calculate the square root of 12^2 + 16^2, we get 20, which does not match the length of the hypotenuse. Therefore, 12 16 20 is not a right triangle.

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Answer:

y = 7/2x + 5

Step-by-step explanation:

The slope intercept form is: y = mx + b

Our equation is

7x -2y = -10

We subtract 7x both sides

-2y = -7x - 10

Divided by -2, both sides

y = 7/2x + 5

So, the answer is y = 7/2x + 5

Answer:

The equation you have provided is 8 + 9x = 7, where x is the unknown number.

To solve for x, you can first subtract 8 from both sides of the equation to get

9x = -1

Then divide both sides by 9

x = -1/9

So the number x is -1/9, which means that the product of x and 9 is equal to -1.

Keep in mind that this is not a natural number and it is not possible to represent the solution as a whole number.

Step-by-step explanation:

The total number of rectangles you can draw using the grid lines exists 1296.

A quadrilateral is a shape with two opposed sides that are equal and parallel. It is a polygon with four sides and four 90-degree angles. The shape of a rectangle is two dimensional.

A square is a particular type of closed figure that has four straight sides, four right angles, and sides that are all the same length. As a result, we can say that: A square is a particular variety of rectangle. Rectangles are not always squares, but squares are always rectangles.

Number 2 × 2 squares have 4 black squares

all 3 × 3 squares have at least 4 black squares, as do all 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8 squares.

there are 6 × 6 = 36   3 × 3 squares

there are 5 × 5 = 25   4 × 4 squares

there are 4 × 4 = 16    5 × 5 squares

there are 3 × 3 = 9     6 × 6 squares

there are 2 × 2 = 4     7 × 7 squares

there is   1          8 × 8 square

Summing we get 91 squares

The total number of rectangles you can draw using the grid lines exists (92)(92) = 1296.

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The total number of rectangles you can draw using the grid lines exists 1296.

A shape with two opposing sides that are equal and parallel is called a quadrilateral. It has four sides, four 90-degree angles, and is a polygon. A rectangle is a two-dimensional form.

An example of a closed form with four straight sides, four right angles, and all sides being the same length is a square. Therefore, we can state that a square is a certain type of rectangle. Squares are not always rectangles, but rectangles are always squares.

Number 2 × 2 squares have 4 black squares

all 3 × 3 squares have at least 4 black squares, as do all 4 × 4, 5 × 5, 6 × 6, 7 × 7, and 8 × 8 squares.

there are 6 × 6 = 36   3 × 3 squares

there are 5 × 5 = 25   4 × 4 squares

there are 4 × 4 = 16    5 × 5 squares

there are 3 × 3 = 9     6 × 6 squares

there are 2 × 2 = 4     7 × 7 squares

there is   1          8 × 8 square

Summing we get 91 squares

The total number of rectangles you can draw using the grid lines exists (92)(92) = 1296.

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Answer: C

Step-by-step explanation:

The HL Theorem states that if the hypotenuse and leg of a right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.

In this case, 16 is the hypotenuse (the longest side of a right triangle) and 13 is the leg.

The volume of a cone is one-third of the product of the area of the base times the height, i.e. Now multiply that by the number of cones: 6 * 75.40 cm^3 = 452.40 cm^3.

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Answer:340 cm long

Step-by-step explanation: multiply 7 x 10 then 70 x 12

The answer to the given that is 7x 5 2x question is  70

Explanation: In this case the answer is calculated by performing the operations in the order they are written. First, we multiply 7 and 5, which gives us 35. Then, we multiply 2 and x, which gives us 2x. Finally, we add 35 and 2x, resulting in 70

Multiplication is an arithmetic operation that involves multiplying two numbers together to produce a third number. It is usually represented by the multiplication sign (×) and is one of the four basic operations in mathematics. Hence the correct answer is 70.

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The first three terms of the sequence are 2.25, 2.30, and 2.35.

It is a sequence where the difference between each consecutive term is the same.

Example:

2, 4, 6, 8, 10 is an arithmetic sequence.

We have,

a(1) = 2.25

a(n) = a(n - 1) + 0.5

Now,

The first term = 2.25

The second term.

a(2) = a(1) + 0.5

= 2.25 + 0.5

= 2.30

The third term.

a(3) = a(2) + 0.5

= 2.30 + 0.5

= 2.35

Thus,

The first three terms are 2.25, 2.30, and 2.35.

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If the sum of three numbers is 50, it forms a linear equation that is x + y + z = 50. By solving this equation we can get the value of x, y and z.

The Equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. There are different types of equations like linear, quadratic, cubic, etc. There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. The most basic and simple algebraic equations consist of one or more variables in math.

The sum of three number is 50 the first number is twice the second number the third number is half the first number.

x + y + z = 50

x = 2y

z = x / 2

Here we form a linear equation. A linear equation may have more than one variable. A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. By solving this linear equation we can get the value of x, y and z.

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Answer  

x=-1/2,=29/4

explanation

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values.

The term "inequality" refers to a relationship between two expressions or values that is not equal to one another. Inequality originates from an imbalance, thus.

In order to get the variable on its own, you can solve a lot of straightforward inequalities by adding, removing, multiplying, or dividing the two sides. But as a result of them, the direction of the inequality will change: Using a negative number to divide or multiply both sides. right and left sides are switched.

An inequality results from the comparison of two or more algebraic expressions using the symbols, >, or. They are the mathematical expressions with unequal sides.

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Answer:

probably 21

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

csc x = 1/sinx    

so    sinx ( 1 + cscx )

     = sinx ( 1 + 1/sinx)

      = sinx + sinx /sinx

      = sin x + 1              Done .

Polya's 4 step method is a process designed to help problem solvers become better at tackling difficult problems.

It was developed by the mathematician George Polya in 1945 and consists of four basic steps:

1. Understand the problem: The first step is to read and understand the problem. This means understanding the problem and identifying what information is given and what is required.

2. Devise a plan: The second step is to identify a strategy or plan of attack. This involves breaking the problem down into smaller parts, identifying the key elements, and using logical reasoning to identify a solution.

3. Carry out the plan: The third step is to execute the plan. This involves following the steps of the plan in order to solve the problem.

4. Look back: The fourth and final step is to take a look back at the solution and evaluate it. This involves checking to make sure the solution is correct and making any necessary adjustments.

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Answer:

16p^12 q^4

Step-by-step explanation:

Open up the parenthesis and simplify.

2^4 is 16

p^3 times ^4 is p^12

q times ^4 is q^4

So your answer is 16p^12 q^4

Answer:

16p^12 q^4

Step-by-step explanation:

This is because the power 4 will multiple with all the variables inside

hence, p^3 will become p^12

and q^1 will become q^4

the power 4 will also change 2 into 2^4 which is 16

The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logb(x)

The domain of the logarithmic function [tex]f(x) = log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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The domain of the given function would be x > 0.

What is a function?

In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The given function is f(x) = logb(x)

The domain of the logarithmic function [tex]f(x)=log_b(x)[/tex] is the set of all positive real numbers x such that x > 0. This is because the logarithm of a non-positive number is undefined.

Hence, the domain of the given function would be x > 0.

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Answer:

Step-by-step explanation:

This is pretty simple. To find the area of anything in square centimeters, you multiply the length by the height. You already have both of those number, so you just have to do 4.2 x 4.2 (or 4.2 to the second power). The answer is  21.84 square centimeters.

Answer: 21.84 square centimeters

Slope Sales will be $-159.474 at 0 degrees Celsius, which is nonsensical to understand.

A line's steepness is determined by its slope. The "gradient overflow" is a mathematical expression for the gradient (the change in y divided by the change in x). The ratio of the vertical change (rise) between two points to the horizontal change (run) between the same two places is referred to as the slope. The slope-intercept form of an equation is used to represent each time a straight line's equation is stated as y = mx + b. The line's slope is m. b is b at the point where the y-intercept is, and (0, b). As an illustration, the equation y = 3x - 7 has a slope of 3, and its y-intercept is (0, 7).

given information,

Temperature=20 egression equation,

[tex]sales= 442.284\\ Slope=$ 30.0879[/tex]

temperature increases by 1 degree

$30.0879, on average.

[tex]y-intercept= -159.474[/tex]

At 0 degree celsius of temperature, Sales will be [tex]$-159.474[/tex]which is meaningless to interpret.

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Therefore , the solution of the given triangle comes out to be  AC = 10 units and PD = 6 units.

Triangles, which have three sides and three angles, can be made by joining any three points in a plane. They are among the earliest geometric shapes to be studied. Triangles are especially important since they may be divided into each polygon, whether it has four, five, six, or n sides.

Here,

Let AD and DC are 2x and x respectively.

We have, BC = 10 units

=> 2x =10

=> x = 10/2

=> x= 5

Now ,

=> AP + PF = 8 + y

=> 8 + y = 12

=> y =4

Therefore , the solution of the given triangle comes out to be  AC = 10 units and PD = 6 units.

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Roberto paid 16.7% of the bill as a tip.

To find the percent of the bill Roberto paid as a tip, you can use the formula: (tip / total bill) x 100 = tip percentage

In this case, the tip was $7.15 and the total bill was $35.75 + $7.15 = $42.90. We know the formula to calculate percentage share of an item to total items.

Plugging these values into the formula:

(7.15 / 42.90) x 100 = 16.7 %

Roberto paid 16.7% of the bill as a tip, rounded to the nearest percent.

Thus, we know Roberto paid 16.7% of the bill as a tip.

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The number of points is simply 5 times this random variable, and E(C*Y) = C*E(Y), where C is a constant and Y is a random variable, according to expected value principles. As a result, E(X) = 5*2 = 10.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

The number of dice that are showing an even number is a binomial random variable with n = 4, and p = 1/2 (because half the faces on the die are even and half are odd).

The expected value of this random variable is n*p = 4*1/2 = 2.

The number of points is simply 5 times this random variable, and by the rules of expected value, E(C*Y) = C*E(Y), where C is a constant and Y is a random variable. Thus E(X) = 5*2 = 10.

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