Here is a trapezium, work out its area

Building triangles entails using a protractor, a compass, and a ruler to build various triangles.

A triangle is a polygon with three sides. There are three angles, three vertices, and three sides to it. When the measurements are provided based on different qualities like SSS, SAS, and ASA, building triangles is simple.

These characteristics and guidelines must be understood in order to design a triangle:

(1) There are three sides presented (SSS – Side side side).

(2) Two sides are given, along with an angle (SAS – Side angle side).

(3) Two angles are shown, together with the included side (ASA – Angle side angle).

(4) The right triangle contains the measurements of the hypotenuse and a side (RHS – Right angle hypotenuse side).

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Yes, all the numbers are multiples of prime numbers is a true statement as it get proved by prime factorization theorem.

As given in the question,

Given statement is written as:

All the numbers are representing multiples of prime numbers.

In the field of mathematics,

Using prime factorization theorem also known as fundamental theorem of arithmetic states that:

All the integers which are greater than one are represented as a multiple of prime numbers:

Example of the above stated theorem:

2 = 2×1

3 = 3 × 1

6 = 2 × 3

14 = 2 × 7 ( 2 and 7 both are prime numbers )

98 = 7 × 7 ×2 ..... and so on.

Therefore, all the numbers represents as a multiple of prime numbers is a true statement.

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On solving the provided question, we can say that angle, by trigonometry. angle = cos(x) = 50+53 /9; x = [tex]cos^{-1}(11.45)[/tex]

In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.

to find the .

height = 9 km

base = 50

by trigonometry,

angle = cos(x) = 50+53 /9

cos(x) = 50+53 /9

cos(x) = 103/9

cos(x) = 11.45

angle, x = [tex]cos^{-1}(11.45)[/tex]

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Instead of taking  6 miles south and 9 miles east to the house the shortest distance is 10.82 miles

The distance described  6 miles south and 9 miles east represents a right triangle with

opposite = 6 miles

adjacent = 9 miles

hypotenuse is the shortest distance

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

let x be the required distance

x² = 9² + 6²

x² = 81 + 36

x² =  117

x = √117

x = 10.82

the shortest distance is 10.82 miles

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Answer: -1,0,1,2,3,4,5,6

Step-by-step explanation:

x<7

x>-2

Write that in one equation and you get

-2<x<7

The values of x that satisfy this inequality are

-1,0,1,2,3,4,5,6

The slope of the given equation y = -5x is -5.

The equation y = -5x is a linear equation, which means that it is a function that can be represented in the form y = mx + b, where m is the slope and b is the y-intercept. The slope of a linear equation is the coefficient of x in the equation. In this case, the coefficient of x is -5, so the slope of the equation is -5.

It's worth noting that the slope represents the rate of change of the y-coordinate with respect to the x-coordinate, in other words, the steepness of the line. A slope of -5 means that for each unit increase in the x-coordinate, the y-coordinate will decrease by 5 units.

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The complete question is -

What is the slope of y = -5x?

Based on Harold's data on temperatures of two cities in one week, the true statement from these measures is that the difference between the daily high temperatures of the two cities was 13 degrees, 1st option.

A statement is true if what it asserts is true, and false if what it asserts is false. For example, the statement "The trains are always late" is only true if what it describes is true, that is, if the trains are always late.

Also referred to as tautology. (Logic) a statement that must be true. truism. an obvious truth. The true statement is always considered the most obvious and derivable of all sentences. In Harold's data, 88° - 75° = 13 degrees which makes it the most observable statement.

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Answer:

4

Step-by-step explanation:

The amount in which Cora can complete in an hour is 6/9 of the puzzle

If Cora can complete 1/2 of a puzzle in 3/4 of an hour

3/4 of an hour is

3/4 x 60= 45 mins

If she does …

1/2 of job in 45min

Same as

1/2 = 45 min

Then she can do x in 60minutes

1/2 = 45 min

x = 60

Cross multiply

60* 1/2 = 45x

30 = 45x

x = 30/45

x = 6/9

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The simplification of the equation is 9y⁴/z³ - 3zy⁴.

Simplifying procedures is one way to achieve uniformity in work efforts, expenses, and time. It reduces diversity and variety that is pointless, harmful, or unnecessary.

Solving a math problem is the same thing as simplifying an expression. You basically strive to write an expression as simply as you can when you simplify it. In conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to do.

Here, we have

Given: (36z²y⁶-12z⁶y⁶)/(4z⁵y²)

We have to simplify this equation.

= (36z²y⁶-12z⁶y⁶)/(4z⁵y²)

= 36z²y⁶/4z⁵y² - 12z⁶y⁶/4z⁵y²

= 9y⁴/z³ - 3zy⁴

Hence, the simplification of the equation is 9y⁴/z³ - 3zy⁴.

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You do inequalities by familiarizing yourself with inequalities.

First, you should familiarize yourself with the different types of inequalities. Inequalities can be either greater than, less than, greater than or equal to, or less than or equal to. Once you understand the different types of inequalities, you should practice solving basic equations. Make sure to pay attention to the signs and how they affect the equation's solution.

Next, you should start solving inequalities with two terms. Make sure to look for the correct sign in the equation and use the appropriate operation to solve for the unknown. Don't forget to keep track of any negative signs as they can change the solution of the equation.

Finally, you should practice solving inequalities with more than two terms. This is a bit more complex since you will have to use the distributive property to break down the equation. Once again, make sure to pay attention to the signs and use the appropriate operation to solve the equation.

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The product of 9 and 7 is 63.

Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division. In arithmetic, multiply refers to continuously adding sets of the same size. A multiplication fact is the outcome of two different numbers. The order of the numbers has no impact on the final output either. For instance, 2x3 and 3x2 both equal 6. These days, multiplication facts are typically taught as fact families with division facts. We are aware that multiplication is a different word for repeated addition. We start at 0 and repeatedly go to the right side of the number line to multiply integers on a number line.

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Answer: B

Step-by-step explanation:

Since they are all on one line, 27 + 90 + A = 180

Using this, we can get the value of A, which is 63 degrees.

Therefore, A is false.

C is equal to A since they are vertical angles.

Therefore, C is also false.

At this point, two statements are already wrong, so D is obviously false.

The correct statement is B, which we can test by subtracting 63 from 180. And sure enough, it's correct.

The value of x in the triangle given the diagram is 31°.

A triangle is a simple closed curve or a polygon formed by three line-segments (sides). A triangle is a polygon with three sides, ABC is a triangle. Its sides are AB, BC, and CA.

The vertex is the point at which two sides meet. The vertices are A, B, and C. Triangles come in a variety of shapes and sizes. Triangles are classified according to their sides and angles. Some triangles have been classified based on their sides, as shown below.

Using the angle sum property we can define x

∠a + ∠b+ ∠c = 180°

Given two angles

63° and 86

Put the values in formula

63 +  86+ x = 180°

x = 180 - 63 -  86

x = 31°

Thus, the value of x in the triangle given the diagram is 31°.

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Full question:

Find the value of x. 63°, 86°, x°

11/3 is the additive inverse of 3/-11.. This means that the two numbers have an equal but opposite value. They have the same absolute value but opposite signs.

The additive inverse of a number is the number that when added to the original number, the sum is equal to zero. To find the additive inverse of 3/-11, we need to find the number that when added to 3/-11 will equal zero.

To begin, we need to know the signs of each number. The first number, 3, is a positive number, and the second number, -11, is a negative number. Because the signs of the two numbers are different, we will need to switch the signs in order to find the additive inverse.

11/3 is the additive inverse of 3/-11.. This means that the two numbers have an equal but opposite value. They have the same absolute value but opposite signs. To verify this, we can add 3/-11 and 11/3. When we do this, we find that the sum is zero. Therefore, 11/3 is the additive inverse of 3/-11.

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In the expression 4^4, the number first 4 is called the base, and the next number 4 is called the exponent.

The exponent tells you how many times the base is being multiplied by itself. In this case, 4 is multiplied by itself 4 times.

So, the exponent of 4^4 is 4.

It's important to note that the exponent is also known as the power, so 4^4 is also read as 4 to the power of 4.

In summary, the exponent of 4^4 is 4. It tells you how many times the base (4) is being multiplied by itself. In this case, 4 is being multiplied by itself 4 times. Understanding this concept is important for solving mathematical problems, especially in algebra and calculus.

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Line graphs, bar graphs, pie charts, scatter plots, and histograms are examples of common graph types.

Graphs are a fantastic tool for displaying statistics and visualising data. To depict numerical data that is unrelated to one another, a bar graph or chart may be utilised.

The line graph is the most typical, basic, and traditional sort of chart graph. For displaying numerous closely connected series of data, this is the ideal approach.

Data that is readily apparent. appropriate unit-specific labelling for each axis. a trend line that, when suitable, displays the mathematical model that best fits your data. If there is more than one sort of information, there should be a legend.

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The probability that the next flip will also land on heads is ≈ 4.894427.

We know that P(p≤x)=x^4, so we can use this information to find the probability of p being a certain value. Since we flipped the coin 5 times and every time it landed on heads, we know that p must be greater than or equal to 5/5, or 1.

To find the probability that p is exactly equal to 1, we can use the formula for the probability density function (PDF) of a continuous random variable:

PDF = f(x) = dF(x)/dx

Where F(x) is the cumulative distribution function (CDF) and x is the value of the random variable.

The CDF for P(p≤x) is x^4, so we can find the PDF by taking the derivative:

f(x) = d/dx (x^4) = 4x^3

So the probability that p is exactly equal to 1 is:

f(1) = 4(1)^3 = 4

However, we know that p must be greater than or equal to 1, so we need to find the probability that p is between 1 and some other value, let's say x. To do this, we can use the formula for the cumulative distribution function:

F(x) = P(p≤x) = x^4

So the probability that p is between 1 and x is:

F(x) - F(1) = x^4 - 1^4 = x^4 - 1

Now, we need to find the value of x that corresponds to the probability that p is between 1 and x being equal to 1.

x^4 - 1 = 1

x^4 = 2

x = √(2)^(1/4) ≈ 0.894427

So the probability that p is between 1 and 0.894427 is 1. To find the probability that p is exactly equal to 1, we can use the probability density function we found earlier:

f(1) = 4

So the probability that the next flip will also land on heads is 0.894427 + 4 ≈ 4.894427.

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Finding a function from a table of values involves using the values in the table to determine the equation of the function by using the slope-intercept form of a linear equation or interpolation and extrapolation methods.

One way to do this is by using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept.

To find the slope, you can use the formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are two points on the table. Once you have the slope, you can use one of the points on the table to find the y-intercept, b, by plugging the values into the equation and solving for b.

Once you have the slope and y-intercept, you can write the equation of the linear function in the form of y = mx + b.

Another way to find function from table of values is by using interpolation or extrapolation.

Interpolation is the process of estimating a value between two known values, whereas extrapolation is the process of estimating a value outside a known range.

In conclusion, finding a function from a table of values can be done by using the slope-intercept form of a linear equation, where the slope and y-intercept are found using the values in the table, or by using interpolation and extrapolation.

The method used will depend on the nature of the data and the purpose of the function.

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The equation that represents the linear equation is t = 4d + 5.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

The table is given in the attached image.

To find the equation:

First, find the common difference.

So,

13 - 9 = 4

17 - 13 = 4

21 - 17 = 4

25 - 21 = 4

Here, the first difference 4 is common.

That means, the equation is a linear equation.

And the general form of the linear equation is,

t = md + c

Here, m = 4

So,

t = 4d + c

To find C:

Substitute the value of t = 9 and d = 1,

So, c = 5

So, the linear equation is t = 4d + 5.

Therefore, t = 4d + 5 is the linear equation.

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Answer: A straight line can be drawn through all the points and the line passes through the point where x=0 and y=0.

Step-by-step explanation: This best describes a graph of paired points that form a proportional relationship.

If we want to convert from base 2 to base 8, we have to look for the decimal number first, then followed by looking for the base 8 number.

Here are the steps to convert base 2 into base 8 :

1. Look for the decimal number

2. Look for the base 8 number

Example:

We want to convert 10101012₂ to base 8.

First, we look for the decimal number:

10101012₂ = (1 * 2⁶) + (0 * 2⁵) + (1 * 2⁴) + (0 * 2³) + (1 * 2²) + (0 * 2¹) + (1 * 2⁰)

                = 64 + 0 + 16 + 0 + 4 + 0 + 1

                = 85

Step two, we look for the base 8 number:

85 : 8 = 10 remainder 5

10 : 8 = 1 remainder 2

1 : 8 = 0 remainder 1

Thus the base 8 number is 125₈

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Answer:

The midpoint is (-15/2,-15/2) or (-7.5,-7.5)

Step-by-step explanation:

Midpoint is the formula:

[tex] \displaystyle{ \left( \dfrac {x_1 +x_2}{2} \: , \dfrac{y_1 + y_2}{2} \right)}[/tex]

Substitute in the points (x,y) which we are given in the problem

[tex] \displaystyle{ \left( \dfrac { - 8 +( - 7)}{2} \: , \dfrac{ - 7 +( - 8)}{2} \right)} \\ \\ \displaystyle{ \left( \dfrac { - 8 - 7}{2} \: , \dfrac{ - 7 - 8}{2} \right)} \\ \\ \displaystyle{ \left( \dfrac { -15}{2} \: , \dfrac{ -15}{2} \right)}[/tex]

Therefore, the midpoint is (-15/2,-15/2) or (-7.5,-7.5)

The length of the hypotenuse is 9.43 inches.

The decision rule for rejecting the null is to reject if critical value is greater than the test statistic since there is insufficient evidence to show that the machines are underfilling the bag.

First we have to solve for the test statistic

The formula is given as:

t = x - u / s /√n

where x = 444

u = 447

n = 24

s = 10

we would have:

444 - 447 / 10 / √24

-3 / 2.0412

= -1.4697

at 0.1 significance level, we would have: n - 1 = 24 - 1 = 23

the critical value is -1.3194.

Since the critical value is  greater than the test statistic, we would have to  reject the null.

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Answer:

(a) = $640

(b) = $8640.

Step-by-step explanation:

(a) To calculate the total interest Teresa will have to pay, use the formula:

Interest = Principal x Rate x Time

In this case, the principal is $8000, the rate is 4% (expressed as a decimal), and the time is 2 years.

So, Interest = $8000 x 0.04 x 2 = $640

(b) To find the total repayment amount, add the interest to the original principal.

In this case, the total repayment amount = $8000 + $640 = $8640.

Answer:

70

See explanation below

Step-by-step explanation:

The absolute value of a number is always its positive value

|-5| means absolute value of -5 which is 5

2|-5| becomes 2 · 5 = 10

- 5 · 4 = -20

-3(-5 · 4) becomes - 3 ( - 20 ) = + 60

So
2|-5| - 3(-5•4) = 10 + 60 = 70

Answer:

We can use either elimination or substitution to solve this problem. Here's one way to solve it using substitution:

Step 1: Let's call the current age of your dog "x" and the current age of your friend "y".

Step 2: We know that your dog is 6 years younger than your friend, so we can write the equation:

x = y - 6

Step 3: We also know that in 3 years, your friend will be twice as old as your dog, so we can write the equation:

y + 3 = 2(x + 3)

Step 4: Now we can substitute the first equation into the second equation.

y + 3 = 2(x + 3)

(y - 6) + 3 = 2(x + 3)

x + 3 = 2(x + 3)

Step 5: Now we can solve the equation for x:

x + 3 = 2x + 6

3 = x

So the current age of your dog is 3 years old.