5. The numbers 3.111... and 3.222... are both rational numbers. What is an irrational number that is between these two rational numbers?​

The height c of the flagpole c is 5.5 metres.

The triangles formed by the two flags are similar.  

Two triangles are said to be similar when they have two corresponding angles congruent and the sides proportional.

The distance between flag a is 12 metres.

The distance form the flag c to s is 10 metres.

The height of the flagpole a  is 12.1 metres.

Therefore, let's find the height of the pole c.

Hence, using proportion,

12.1 / c = 22 / 10

cross multiply

121 = 22c

divide both sides by 22

c = 121 / 22

c = 5.5

Therefore,

height of the flagpole c = 5.5 metres

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Answer:

The mathematical symbols used to indicate that the endpoints of an interval are not included in the graph of an inequality are "<" and ">" signs with a small circle or parenthesis next to them.

The symbol "<" with a circle or parenthesis on the right side indicates that the endpoint is not included, while the symbol ">" with a circle or parenthesis on the left side indicates that the endpoint is not included.

For example, the inequality x > 3 indicates that the variable x is greater than 3, but does not include 3 in its solution set. Similarly, the inequality y < -2 with a circle or parenthesis on the left side indicates that the variable y is less than -2, but does not include -2 in its solution set.

Step-by-step explanation:

Answer:

The correct answer is A′(−3, −2), B′(5, −2), C′(1, 2). The coordinates of the original triangle ABC are (1, -2), (9, -2), and (5, 2). Therefore, the coordinates of the image are A′(−3, −2), B′(5, −2), C′(1, 2).

Coordinates are used to describe a point in space or on a map. They are usually written as two numbers, which represent the position of the point on an x-axis and a y-axis. Coordinates can be used in a variety of ways, such as to describe the location of a specific object or to identify the boundaries of an area.

Triangle ABC is an example of a transformation in which the shape is shifted without changing its size or orientation. When a shape is translated, it is moved from one place to another without changing its size or orientation. In this case, the triangle is being translated 4 units down.

To calculate the new coordinates of the triangle, we need to subtract 4 from the y-coordinate of each of the vertices. The original coordinates of the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 from each of the y-coordinates, the new coordinates of the triangle are (1, −6), (9, −6), and (5, −2). This means that the new coordinates of the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).

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The cοrrect answer is A′(−3, −2), B′(5, −2), C′(1, 2). The cοοrdinates οf the οriginal triangle ABC are (1, -2), (9, -2), and (5, 2). Therefοre, the cοοrdinates οf the image are A′(−3, −2), B′(5, −2), C′(1, 2).

Cοοrdinates are used tο describe a pοint in space οr οn a map. They are usually written as twο numbers, which represent the pοsitiοn οf the pοint οn an x-axis and a y-axis. Cοοrdinates can be used in a variety οf ways, such as tο describe the lοcatiοn οf a specific οbject οr tο identify the bοundaries οf an area.

Triangle ABC is an example οf a transfοrmatiοn in which the shape is shifted withοut changing its size οr οrientatiοn. When a shape is translated, it is mοved frοm οne place tο anοther withοut changing its size οr οrientatiοn. In this case, the triangle is being translated 4 units dοwn.

Tο calculate the new cοοrdinates οf the triangle, we need tο subtract 4 frοm the y-cοοrdinate οf each οf the vertices. The οriginal cοοrdinates οf the triangle are (1, −2), (9, −2), and (5, 2). After subtracting 4 frοm each οf the y-cοοrdinates, the new cοοrdinates οf the triangle are (1, −6), (9, −6), and (5, −2). This means that the new cοοrdinates οf the triangle are A′(−3, −2), B′(5, −2), and C′(1, 2).

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The limit of f(x) as x approaches -6 from the positive side is 6.

When x gets closer to 2 on the positive side, we can see that the function seems to be heading towards a value of -8. As a result, f(x) has a limit of -8 as x approaches 2 from the positive side.

The function seems to be heading towards a value of 6 when x approaches 2 from the negative side. Hence, when x gets closer to 2 from the negative side, the limit of f(x) is 6.

The function seems to be getting closer to a value of 6 when x approaches -6 from the positive side. Hence, as x gets closer to -6 on the positive side, the limit of f(x) is equal to 6.

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The value of x in the diagram is 12.5

Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors. Equal scale factors mean that the lengths of their corresponding sides have a matching ratio.

The ratio of the corresponding sides of similar shapes are equal.

Therefore;

3x/60 = 5x/8x

3x/60 = 5/8

300 = 24x

divide both sides by 24

x = 300/24

x = 12.5

therefore the value of x is 12.5

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The vector V in linear form will be v = –11i + 6j i.e. A.

In mathematics, a vector is a mathematical object that has both magnitude and direction. It is typically represented as an arrow in space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

Now,

Vector RS can be represented as the difference between the coordinates of R and S:

RS = S - R

RS = (-36, 11) - (-25, 5)

RS = (-36 + 25, 11 - 5)

RS = (-11, 6)

To represent RS in linear form, we can use the components of the vector as coefficients of the basis vectors i and j:

RS = -11i + 6j

Therefore,

               the correct option is v = -11i + 6j.

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Answer:

A is right

Step-by-step explanation:

It is true that graphs exponential functions either increase or decrease for all x-values.

An exponential function is defined as follows:

y = ab^x.

In which:

An exponential function can either increase or decrease depending on the values of a and b, however the behavior is uniform, meaning that it is true that graphs exponential functions either increase or decrease for all x-values.

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9% percent of Team B’s mean absolute deviation is the difference in the mean of the individual times of members.

The result of dividing the sum of a set of values by the total number of values in the set is mean.

The average distance between each observation and the mean is shown via a measure of variability known as the mean absolute deviation (MAD).

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does.

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48

The line of best fit has the following equation

y = 3.2x + 25

Since the x-values are 20 and 35, we must enter these values into the equation and subtract them to determine the difference in the y-values:

y(20) - y(35) = (3.220 + 25) - (3.235 + 25)

y(20) - y(35) = (64 + 25) - (112 + 25)

y(20) - y(35) = 89 - 137

y(20) - y(35) = -48

For x-values of 20 and 35, 48 is the most logical prediction for the difference in y-values.

Thus, Option (A) 48 is the correct answer.

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The triangles are classified as:

4. Acute 5. Obtuse 6. Obtuse 7. Acute 8. Obtuse 9. Acute 10. Obtuse

To classify a triangle as right, obtuse, or acute, we need to apply the Pythagorean Theorem, which 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.

If the square of the hypotenuse is greater than the sum of the squares of the other two sides, then the triangle is obtuse. If the square of the hypotenuse is less than the sum of the squares of the other two sides, then the triangle is acute.

4. To check if this is a right triangle, we need to find if 9² is equal to 4² + 6², which is not true, so the triangle is acute.

5. To check if this is a right triangle, we need to find if 16² is equal to 10² + 12², which is not true, so the triangle is obtuse.

6. To check if this is a right triangle, we need to find if (8√6)² is equal to 8² + 16², which is not true, so the triangle is obtuse.

7. To check if this is a right triangle, we need to find if 29² is equal to 20² + 21², which is true, so the triangle is acute.

8. To check if this is a right triangle, we need to find if √73² is equal to 3² + 8², which is not true, so the triangle is obtuse.

9. To check if this is a right triangle, we need to find if 12² is equal to 8² + 10², which is true, so the triangle is acute.

10. To check if this is a right triangle, we need to find if (3√34)² is equal to 9² + 15², which is not true, so the triangle is obtuse.

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1. The loan term of the truck is 5 years.

2. The contractor has to pay R30,801.67 per month towards the truck, including the insurance cover amount.

3. In in June 2022, the contractor owed the financer R669,050.10, excluding the insurance amount.

1. The loan term of the truck in years is calculated as follows:

Number of years = Loan term in months / 12

Number of years = 60 months / 12

Number of years = 5 years

Therefore, the loan term of the truck is 5 years.

2. Monthly repayments = Monthly instalment of the truck + Insurance premium

Monthly repayments = R22,301.67 + R8,500

Monthly repayments = R30,801.67

Therefore, the contractor has to pay R30,801.67 per month towards the truck, including the insurance cover amount.

3. Number of instalments paid = Loan term in months / 2

Number of instalments paid = 60 months / 2

Number of instalments paid = 30 months

The total amount of money owed to the financer excluding the insurance in June 2022 would be:

Total amount owed = Remaining instalments x Monthly instalment of the truck

Total amount owed = (Loan term in months - Number of instalments paid) x Monthly instalment of the truck

Total amount owed = (60 months - 30 months) x R22,301.67

Total amount owed = 30 months x R22,301.67

Total amount owed = R669,050.10

Therefore, in June 2022, the contractor owed the financer R669,050.10, excluding the insurance amount.

The significance of including an insurance cover when a contractor purchases a water tanker is to protect the asset from unforeseen circumstances such as accidents, theft, or damage. If the contractor did not have insurance, they would have to pay for any repairs or replacements out of pocket, which could be expensive and financially devastating. Insurance also provides peace of mind and allows the contractor to focus on their business operations without worrying about potential risks to their asset.

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Answer: Three equivalent ratios of 8 : 5 are 16 : 10, 24 : 15 and 32 : 20.

Step-by-step explanation:

The triangles include:

4) To determine if a triangle is right, obtuse, or acute, we need to use the Pythagorean Theorem to determine if the square of the longest side equals the sum of the squares of the other two sides.

Here, the longest side is 9, and the other two sides are 6 and 7.

9² = 6² + 7²

81 = 36 + 49

81 = 85

Since 81 is not equal to 85, the triangle is not a right triangle. To determine if it's obtuse or acute, we need to check the cosine of the largest angle using the Law of Cosines.

cos A = (b² + c² - a²) / 2bc

Let's choose 9 as side a, since it's the largest side:

cos A = (6² + 7² - 9²) / (84)

cos A = 0.048

Since cos A is positive, angle A is acute. Therefore, the triangle is acute.

5) Using the same process as above:

16² = 10² + 12²

256 = 100 + 144

256 = 244 + 12

Since 256 is greater than 244, the triangle is obtuse.

6) Again, using the same process as above:

(8√6)² = 8² + 16²

192 = 64 + 256

192 = 320

Since 192 is less than 320, the triangle is obtuse.

7) 29² = 20² + 21²

841 = 400 + 441

841 = 841

Since 841 is equal to 841, the triangle is a right triangle.

8) √73 is greater than 8 and 3, so it must be the largest side.

(√73)² = 8² + 3²

73 = 64 + 9

73 = 73

Since 73 is equal to 73, the triangle is a right triangle.

9) 12² = 8² + 10²

144 = 64 + 100

144 = 164 - 20

Since 144 is less than 164, the triangle is obtuse.

10) 15² = 9² + (3√34)²

225 = 81 + 306

225 = 387 - 162

Since 225 is less than 387, the triangle is obtuse.

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Answer:

Step-by-step explanation:

We are given that T is the midpoint of LM, J is the midpoint of MO, and P is the midpoint of LO. This means that LT = TM, JO = OM, and LP = PO.

We can use this information to find the lengths of the sides of triangle LMO. Since T is the midpoint of LM, we have LT = TM = 9. Similarly, since J is the midpoint of MO, we have JO = OM = 12. Finally, since P is the midpoint of LO, we have LP = PO = (LO)/2 = 32/2 = 16.

Now, we can use the Pythagorean theorem to find the length of the third side, LM:

LM^2 = LT^2 + TM^2

LM^2 = 9^2 + 16^2

LM^2 = 337

LM = sqrt(337)

Therefore, the perimeter of triangle LMO is:

LM + MO + LO = sqrt(337) + 2(12) + 32

Perimeter = sqrt(337) + 56

To find the perimeter of triangle TJP, we need to find the lengths of the sides TJ, JP, and TP. Since T and J are midpoints of their respective sides, we know that TJ = 2(LT) = 18 and JP = 2(JO) = 24. To find TP, we can use the Pythagorean theorem:

TP^2 = TJ^2 + JP^2

TP^2 = 18^2 + 24^2

TP^2 = 900

TP = 30

Therefore, the perimeter of triangle TJP is:

TJ + JP + TP = 18 + 24 + 30

Perimeter = 72

Therefore, the perimeter of triangle TJP is 72.

Using the graphs, Olivia is correct if she used one of those two approaches. Michael and Angelica both use the wrong strategies.

An organised-representation of the data is all that the graph is. It facilitates our understanding of the facts. Data is the term used to describe the numerical information obtained through observation.

The development of a research question is followed by the ongoing observational collection of data. The data is then organised, distilled, categorises, and visually represented.

Information and data have different purposes: Data is an unadorned truth; information is the meaning that can be inferred from data.

Challenge 1

Olivia may have, for example, translated 10 units to the right after reflecting over the x axis.

Let's use point C to apply this series of steps.

C = (-2,-4) (-2,-4)

After reversing the x axis, C' becomes (-2,4); the y coordinate changes sign, and C" becomes (8,4) after moving to the right by 10 units. The x coordinate is then increased by 10.

The graphic shows that point C (-2, -4) shifts to C"(8,4). The other four points I'll let you investigate.

Olivia may have also tried shifting 10 units to the right before reflecting across the x axis. The sequence here is irrelevant. Order does important, though, for several other combinations of transformations.

Challenge 2

The point (x,y) will become after reflection across the y axis (-x,y). Here, the sign is reversed, and only the x coordinate changes. The y coordinate remains constant.

With the y axis reflection, a point like C (-2, -4) becomes C'(2, -4). By moving up 8 units, we get at C"(2,4) by adding 8 to the y coordinate, but this is not what the graphic displays. Thus, Angelica's approach is flawed.

The last four points should also contain other contradictions, as well.

Challenge 3

Even Michael's approach is flawed. Instead of using an x axis reflection, he completely relies on translations to change ABCDE into A"B"C"D"E".

Quick inspection suggests that Michael might be right. Yet, if you examine much more closely, you'll notice that things aren't exactly in line.

This time, we'll choose point D rather than point C.

D can be found at (-6, -2). To reach D' if we move up 8 units, we must add 8 to the y coordinate (-6,6). Then, to move 10 units to the right, add 10 to the x coordinate. And brings us to D" (4,6).

The diagram, however, reveals that D" is actually at (4,2)

Let you examine the other points, please. The only points that should go to the right places are C and E; the remaining points should not. Once more, Michael's failure to apply an x axis reflection is to blame. His A"B"C"D"E" figure is reversed from how it should have been.

To sum up, the strategies mentioned in problem 1 are the proper ones to use in order to make ABCDE go to A"B"C"D"E. Olivia is correct if she used one of those two approaches. Michael and Angelica both use the wrong strategies.

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The third side of the triangle is 8  

Pythagoras' theorem is a fundamental principle in geometry that describes the relationship between the sides of a right triangle.

It states that: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Here we have

A right-angled triangle

From the figure

The sides of the triangle are 7 and √15  

As we know from Pythagoras' theorem

=> Hypotenuse² = side² + side²    

Substitute the above values in the condition

=> Hypotenuse² = (7)² + (√15)²    

=> Hypotenuse² = 49 + 15

=> Hypotenuse² = 64

=> Hypotenuse = 8  

Therefore,

The third side of the triangle is 8  

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Complete Question is given picture

i. The down payment is $11,000    

ii. The mortgage (loan) was for $99,000.      

iii. The current monthly payment is $471.15.  

iv. Total interest is $169,334.00.

The down payment is the initial payment made when purchasing a home, typically expressed as a percentage of the total purchase price.

In the given problem, the mortgage (loan) is the amount of money borrowed to purchase the home, which is equal to the purchase price of the home minus the down payment.

Here we have

Problem 1:

10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.  

The down payment was 10% of the purchase price of the home

=> Down payment = 10% of $110,000

= [10/100] × $110,000 = $11,000

∴ You will be paid $11,000 as your down payment.

Amount borrowed = the purchase price of the home - Down payment

=> Amount borrowed = $110,000 - $11,000 = $99,000

∴ Your mortgage (loan) was for $99,000.    

To calculate the current monthly payment, use the formula for the monthly payment of a fixed-rate mortgage:

P = (A / D) x (r / 12)

Where:

A = amount borrowed

D = discount factor, i.e calculated as (1 - (1 + r / 12)⁻ⁿ)  

r = monthly interest rate,      

n = total number of payments,  

=> P = ($99,000 /124.4) x 0.0075 = $471.15  

∴ The current monthly payment is $471.15.  

The formula for total interest = (P x n) - A  

=> Total interest = ($471.15 x 360) - $99,000 = $169,334.00              

∴ You will pay a total of $169,334.00 in interest over the life of the loan.    

Therefore,

i. The down payment is $11,000    

ii. The mortgage (loan) was for $99,000.      

iii. The current monthly payment is $471.15.  

iv. Total interest is $169,334.00.      

Problem 2

This year, you check your loan balance. You see that you still have $88,536 left to pay on your loan. Your house is now valued at $150,000.

i. Amount paid off = Original loan amount - Current loan balance

Original loan amount = $99,000

Current loan balance = $88,536

Amount paid off = $99,000 - $88,536

Amount paid off = $10,464

∴ you have paid off $10,464 of the loan.

ii. Total paid = Monthly payment x Number of payments

P = ($99,000 / 207.483) x 0.0075

P ≈ $471.15

The number of payments is the number of months since you took out the loan. Since the loan was taken out 10 years ago, or 120 months ago, the number of payments is 120.

Total paid = $471.15 x 120

Total paid = $56,538

∴ you have paid $56,538 to the loan company so far.

iii. To determine how much interest you have paid so far, we need to subtract the amount paid off from the total amount paid:

Interest paid = Total paid - Amount paid off

Interest paid = $56,538 - $10,464

Interest paid = $46,074

∴ you have paid $46,074 in interest so far.

iv. Equity = Current value of the home - Current loan balance

Equity = $150,000 - $88,536

Equity = $61,464

∴ you have $61,464 of equity in your home.

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Answer:

Step-by-step explanation:

To relate the angular motion of the hour hand (h) and the angular motion of the second hand (s), we can use the following formula:

h = (s/360) * 30

The second hand makes a full rotation of 360 degrees in one minute, so in 60 minutes (or one hour), it rotates 21,600 degrees. We know that during this time, the hour hand moves 30 degrees.

Therefore, the equation relating h and s is h = (s/360) * 30.

Answer:

Yes

Step-by-step explanation:

We just need to (0,6) in the equation to see if it gives a true answer or not!

y = -x + 6

6 = 0 + 6

6 = 6

So, (0,6) is a solution to the equation y = -x + 6

The exponential growth equation is P ( t ) = 332 ( 1.0059 )^t , where t is the number of years and P ( t ) is the population after 2020

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial population be represented as x₀

Now , the value of x₀ = 332 million

And , the exponential growth rate r = 0.59 %

where the population of the U.S. at time/ years after 2020 is of the form equation P( t ) = aekt

On simplifying , we get

The population of the U.S. at a time P ( t ) = 332 ( 1 + 0.59% )^t

Now , the value of P ( t ) is

The population of the U.S. at a time P ( t ) = 332 ( 1 + 0.0059 )^t

The population of the U.S. at a time P ( t ) = 332 ( 1.0059 )^t

where the growth factor k = 1.0059

Hence , the exponential growth equation is P ( t ) = 332 ( 1.0059 )^t

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Answer:

See below

Step-by-step explanation:

[tex]7(6+ x)[/tex] = [tex](7)(6) + (7)(x)[/tex]
            = [tex]42 + 6x[/tex]

Answer:

c

Step-by-step explanation:

60>30 since pi is 180 ........

The expression that represents the area of the given door is (3w+8)w.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression.

A mathematical expression is made up of a statement, at least two integers or variables, and one or more arithmetic operations.

This mathematical operation enables the multiplication, division, addition, or subtraction of numbers. The following is the structure of an expression: Expression: (Number/Variable, Math Operator, Math Operator)

So, we know that:
width = w

And we also know that:

length = 3w + 8

Now, the area formula is:
l*w

Insert values as follows:

l*w

(3w + 8)w

Therefore, the expression that represents the area of the given door is (3w+8)w.

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Answer:

Step-by-step explanation 0.4 0.8 5 7 10, 10