Are the functions f(x) and g(x) inverses of each other? Use composition of functions to determine your answer.
f(x) = 7x-1
x+1
g(x)
O Yes
O No

3√4x/5

the / slash before the 5 is over so you put the 3√4x at the top of the fraction and the 5 at the bottom, so it would be 3√4x divide 5

The  expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign is A)  [tex]x^2+2x+1[/tex].

What is area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

Here the given square shaped traffic sign side length a = x+1

We know that, area of square = [tex]a^2[/tex] square unit.

Then, area of the square shaped traffic sign is

=> A = [tex](x+1)^2[/tex]

=> A = [tex]x^2+2x+1[/tex]

Hence the  expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign is A)  [tex]x^2+2x+1[/tex].

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Answer:

(- 8, 2 )

Step-by-step explanation:

y = [tex]\frac{1}{2}[/tex] x + 6 → (1)

y = - [tex]\frac{3}{4}[/tex] x - 4 → (2)

substitute y = [tex]\frac{1}{2}[/tex] x + 6 into (2)

[tex]\frac{1}{2}[/tex] x + 6 = - [tex]\frac{3}{4}[/tex]x - 4

multiply through by 4 ( the LCM of 2 and 4 ) to clear the fractions

2x + 24 = - 3x - 16 ( add 3x to both sides )

5x + 24 = - 16 ( subtract 24 from both sides )

5x = - 40 ( divide both sides by 5 )

x = - 8

substitute x = - 8 into either of the 2 equations and evaluate for y

substituting into (1)

y = [tex]\frac{1}{2}[/tex] (- 8) + 6 = - 4 + 6 = 2

solution is (- 8, 2 )

Answer:

Answer is B. 3x^2 +2x - 2.5

Step-by-step explanation:

Just factor out and simplify.

[tex]\frac{0.25x^2*(3x^2+2x-2.5)}{0.25x^2}[/tex]

x cannot be 0 or else the denominator is 0 making the function undefined.

Answer:

it is B

Step-by-step explanation:

The possible number of combinations are 9,720.

In mathematics, a combination is a way of selecting a subset of items from a larger set, where the order of selection does not matter. The number of combinations of size k that can be chosen from a set of n items is denoted by the symbol C(n,k) or sometimes by ⁿCk, and is given by the formula:

C(n,k) = n! / (k! ×(n - k)!)

A number is a mathematical concept used to represent quantity or value. It can be a whole number, such as 1, 2, 3, or a decimal, such as 1.5 or 3.14. Numbers are used in various mathematical operations, such as addition, subtraction, multiplication, and division. They are also used in everyday life for counting and measuring.

There are a total of 9,720 possible combinations for a 4-number computer cable lock where each space can be any number 0-9, except for the restriction that all four numbers cannot be the same. To arrive at this number, we can first calculate the total number of possible combinations without the restriction, which is 10⁴ = 10,000. Then we subtract the number of combinations where all four numbers are the same, which is simply 10 (i.e. 0000, 1111, 2222, etc.), to get 9,990. Finally, we subtract the number of combinations where all four numbers are the same and also subtract the number of combinations where three out of four numbers are the same (which is simply 10×4 = 40 since there are 10 possible values for the repeated number and 4 possible positions for it), which gives us a final count of 9,720.

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Answer: ∠HDG

Step-by-step explanation:

Starting Angle: ∠HDE

Possible Supplement: ∠HDG

The five-number summary for the given data set is 18, 22, 26, 30, 31.

The five-number summary is a set of descriptive statistics that provides information about a dataset by summarizing the data's five most important features. It includes the minimum data point, the first quartile, the median, the third quartile, and the maximum data point.

In order to calculate the five-number summary for the given data set (20, 26, 18, 31, 22, 28, 30), we first need to arrange the data in ascending order: 18, 20, 22, 26, 28, 30, 31.

The minimum data point is 18, the first quartile is 22, the median is 26, the third quartile is 30, and the maximum data point is 31.

So, the five-number summary for the given data set is 18, 22, 26, 30, 31.

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The simple interest owed for the use of the money is $56.25.

The following formula can be used to determine the simple interest due for the usage of the money:

Simple Interest = P x r x t ÷ 360

Where P is the principal amount borrowed, r is the annual interest rate as a decimal, and t is the time period in days.

In this case, the principal amount P is $3000, the interest rate r is 2.5% or 0.025 as a decimal, and the time period t is 9 months or 270 days (assuming 30 days per month).

Simple Interest (SI) = $3000 x 0.025 x 270 ÷ 360

SI = $56.25

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The probability that a bus chosen at random has a working radio given that it is ready for service is approximately 85.3%

How to find the probability of a bus having a working radio given that it is ready for service?

We can use Bayes' theorem to find the probability of a bus having a working radio given that it is ready for service,

P(radio | ready) = P(ready | radio) * P(radio) / P(ready)

where

P(radio | ready) is the probability that a bus has a working radio given that it is ready for service.

P(ready | radio) is the probability that a bus is ready for service given that it has a working radio.

P(radio) is the probability that a bus has a working radio.

P(ready) is the probability that a bus is ready for service.

From the given information, we know that:

P(ready) = 0.84

P(radio | ready) = 0.67

To find P(ready | radio), we can use the formula:

P(ready | radio) = P(ready and radio) / P(radio)

From the given information, we know that:

P(ready and radio) = P(radio | ready) × P(ready) = 0.67 × 0.84 = 0.5628

To find P(radio), we can use the law of total probability:

P(radio) = P(radio | ready) × P(ready) + P(radio | not ready) × P(not ready)

We can assume that if a bus is not ready for service, it doesn't matter if it has a working radio or not. So we can simplify the equation to:

P(radio) = P(radio | ready) × P(ready) + P(radio | not ready) × (1 - P(ready))

From the given information, we know that:

P(radio | ready) = 0.67

P(ready) = 0.84

We don't have information about P(radio | not ready), but we can assume that it is lower than P(radio | ready) since a bus that is not ready for service is more likely to have a broken radio. Let's assume P(radio | not ready) = 0.3.

Then, we can calculate,

P(radio) = 0.67 × 0.84 + 0.3 × (1 - 0.84) = 0.6596

Now, we want to find P(radio | ready),

P(radio | ready) = P(ready | radio) × P(radio) / P(ready)

P(ready | radio) = P(ready and radio) / P(radio) = 0.5628 / 0.6596 = 0.853

Therefore, the probability that a bus chosen at random has a working radio given that it is ready for service is approximately 85.3% (rounded to the nearest tenth of a percent).

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The probability that a bus chosen at random has a working radio given that it is ready for service is approximately 85.3%

How to find the probability of a bus having a working radio given that it is ready for service?

We can use Bayes' theorem to find the probability of a bus having a working radio given that it is ready for service,

P(radio | ready) = P(ready | radio) * P(radio) / P(ready)

where

P(radio | ready) is the probability that a bus has a working radio given that it is ready for service.

P(ready | radio) is the probability that a bus is ready for service given that it has a working radio.

P(radio) is the probability that a bus has a working radio.

P(ready) is the probability that a bus is ready for service.

From the given information, we know that:

P(ready) = 0.84

P(radio | ready) = 0.67

To find P(ready | radio), we can use the formula:

P(ready | radio) = P(ready and radio) / P(radio)

From the given information, we know that:

P(ready and radio) = P(radio | ready) × P(ready) = 0.67 × 0.84 = 0.5628

To find P(radio), we can use the law of total probability:

P(radio) = P(radio | ready) × P(ready) + P(radio | not ready) × P(not ready)

We can assume that if a bus is not ready for service, it doesn't matter if it has a working radio or not. So we can simplify the equation to:

P(radio) = P(radio | ready) × P(ready) + P(radio | not ready) × (1 - P(ready))

From the given information, we know that:

P(radio | ready) = 0.67

P(ready) = 0.84

We don't have information about P(radio | not ready), but we can assume that it is lower than P(radio | ready) since a bus that is not ready for service is more likely to have a broken radio. Let's assume P(radio | not ready) = 0.3.

Then, we can calculate,

P(radio) = 0.67 × 0.84 + 0.3 × (1 - 0.84) = 0.6596

Now, we want to find P(radio | ready),

P(radio | ready) = P(ready | radio) × P(radio) / P(ready)

P(ready | radio) = P(ready and radio) / P(radio) = 0.5628 / 0.6596 = 0.853

Therefore, the probability that a bus chosen at random has a working radio given that it is ready for service is approximately 85.3% (rounded to the nearest tenth of a percent).

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Its value is always one greater than the sample size.

In statistics, the degree of freedom represents the number of values in the final calculation of a statistic that is open to varying. In other terms, it is the number of distinct data points used to calculate a statistic.

The degree of freedom (df) for a sample data set is equal to the sample size minus one (df = n - 1), where 'n' represents the sample size. This means that the sample size is always one less than the degree of freedom.

The answer choices do not accurately depict the concept of the degree of freedom. The sum of all differences between the data values and the sample mean may not equal zero. The value of the degree of freedom does not always equal the sample size; rather, it is always one less than the sample size. Therefore, the correct statement is always that its value exceeds the sample size by one.

Although part of your question is missing, you might be referring to the full question:
Which of the following is true with regard to the degree of freedom?
The sum of all the differences between the data value and the sample mean can be any number
The sum of all the differences between the data value and the sample mean is always zero
Its value is always one more than the sample size
Its value is the same as the sample size

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Answer:

[tex]\frac{5}{12}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}[/tex] - [tex]\frac{1}{3}[/tex]

[tex]\frac{9}{12}[/tex] - [tex]\frac{4}{12}[/tex] = [tex]\frac{5}{12}[/tex]

Helping in the name of Jesus.

The height of the actual pyramid is 98 feet.

How to find the height of the actual pyramid?

To find the height of the actual pyramid, we need to use the two scales given to us and convert the height on the drawing to the height of the actual pyramid. Here are the steps to follow,

Use the scale for the drawing to the replica to convert the height on the drawing to the height of the replica,

[tex]3 \frac{1}{2} \: inches \: \times \frac{2 \: feet}{ 1 \: inch}= 7 \: feet[/tex]

Use the scale for the replica to the actual pyramid to convert the height of the replica to the height of the actual pyramid,

[tex]7 \: feet \times \frac{ 14 \: feet }{1 \: foot}= 98 \: feet[/tex]

Therefore, the height of the actual pyramid is 98 feet. The answer is A. 98 feet.

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We can compute the expected value using the given values in the problem such as we have the cost of drawing and submitting the model amounting of $11,000.

We also know that once the project is awarded to them, the anticipated profit is $180,000. Therefore, the expected value is just $180,000 minus $55,000 and the answer is $125,000.

We can compute the expected value using the given values in the problem such as we have the cost of drawing and submitting the model amounting of $11,000.

We also know that once the project is awarded to them, the anticipated profit is $180,000. Therefore, the expected value is just $180,000 minus $55,000 and the answer is $125,000.

Using percentage, the correct answer is "The value of P is $3,500 and it corresponds to 70% of her salary".

The denominator of a percentage, also known as a ratio or a fraction, is always 100. For instance, Sam would have received 30 points out of a possible 100 if he had received a 30% on his maths test. In ratio form, it is expressed as 30:100, and in fraction form, as 30/100. Here, "percent" or "percentage" is used to translate the percentage symbol "%." The percent symbol can always be changed to a fraction or decimal equivalent by using the phrase "divided by 100".

First, we need to calculate L.

1/3 or 33.33% of L spend on gift.

2/5 or 40% of L spent on savings.

This would leave her with $200 for miscellaneous expenses:

= 100% - (33.33% + 40%)

= 100% - 73.33%

= 26.67%

So, 26.67% = $200 for miscellaneous expenses

Rule of three, to calculate L.

26.67% is $200.

100% will be:

= (100 X 200) ÷ 26.67

= 20000 ÷ 26.67

= $750

L= $750

Now we going to calculate K.

"K is twice the amount of L".

K = L X 2

K = 750 X 2

K= $1,500

Finally, we going to calculate P.

P = J - K

J = $5,000

K = $1,500

P =$5,000 - $1500

= $3,500

Rule of three

5000 is 100%

3500 will be:

= 3500 x 100 ÷ 5000

= 350000 ÷ 5000

P = 70%

The value of P is $3,500 and it corresponds to 70% of her salary.

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The difference is accounted for by d. all of these

The percentage of the nation is 46.8 percent

The economic condition most likely to be caused by a war affecting oil production in the Mid East would be cost-push inflation

The accurate response is (d) all of these. An overflow in population can influence Gross Domestic Product (GDP) by enlarging the labor force, potentially promoting productivity and efficiency as well as heightening output through more accessible assets and advanced technology. Inflation might also affect GDP by escalating prices and reducing buying capability.

Therefore, the precise answer is (d) 46.8 percent. The Lorenz Curve is a pictorial rendering of income inequality and the Gini coefficient estimates the severity of disparity. According to fresh records, the most affluent 20 percent of households in the United States keep virtually 46.8 percent of the national income.

The economic state maybe instigated by a conflict impacting oil production in the Middle East would be (b) cost-push inflation. A disruption in the offering of petroleum may consequence in elevated construction costs for businesses, which could then pass on such augmented charges to customers via higher rates. This manner of inflation is referred to as cost-push inflation.

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The leading coefficient of a third-degree function that has the output of -110 x=3 and has zeros of 14, I, -I is 10

If a third-degree function has zeros 14, I, and -I, it can be factored as: f(x) = a(x - 14)(x - I)(x + I)

'a' denotes the leading coefficient.

We may use the knowledge that the function's output is -110 when x = 3 to calculate the value of 'a'.

Substituting x = 3 into the function's factored form yields:

f(3) = a(3 - 14)(3 - I)(3 + I) = -110

When we simplify this equation, we get:

a(-11)(3 - I)(3 + I) = -110

a(-11)(9 - I^2) = -110

a(-11)(9 + 1) = -110 (since I2 = -1)

a(-11)(10) = -110

-110a = -1100

a = 10

Hence , the third-degree function's leading coefficient is 10.

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The standard form equation of the ellipse as described in the task content is;

It is evident from the task content that the standard form equation of the ellipse is to be determined.

Recall, the equation of an ellipse takes the form;

(x - h)²/a² + (y - k)²/b² = 1

where (h, k) is the center and a represents the distance of the center to each vertex on the x-axis and b represents the distance from the center to each vertex on the y-axis.

Therefore, for the given scenario where center is at the origin; the equation of the ellipse is;

x²/2² + y²/5² = 1

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Answer:

We can use the continuous compounding formula to solve this problem:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

In this problem, we know the final amount (A = $1255.66), the interest rate (r = 4% = 0.04), and the time (t = 4 years). We want to find the initial amount (P).

Substituting the known values into the formula, we get:

1255.66 = Pe^(0.04*4)

Simplifying the exponent:

1255.66 = Pe^0.16

Dividing both sides by e^0.16:

1255.66 / e^0.16 = P

Using a calculator to evaluate e^0.16, we get:

1255.66 / 1.17351087099 = P

Simplifying:

P = $1069.44

Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).

Step-by-step explanation:

compounded continuously, given that there is $1255.66 in the account after four years, we can use the formula:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

Substituting the known values into the formula, we get:

1255.66 = Pe^(0.04*4)

Simplifying the exponent:

1255.66 = Pe^0.16

Dividing both sides by e^0.16:

P = 1255.66 / e^0.16

Using a calculator to evaluate e^0.16, we get:

P = 1069.44

Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).

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Answer:

We can use the continuous compounding formula to solve this problem:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

In this problem, we know the final amount (A = $1255.66), the interest rate (r = 4% = 0.04), and the time (t = 4 years). We want to find the initial amount (P).

Substituting the known values into the formula, we get:

1255.66 = Pe^(0.04*4)

Simplifying the exponent:

1255.66 = Pe^0.16

Dividing both sides by e^0.16:

1255.66 / e^0.16 = P

Using a calculator to evaluate e^0.16, we get:

1255.66 / 1.17351087099 = P

Simplifying:

P = $1069.44

Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).

Step-by-step explanation:

compounded continuously, given that there is $1255.66 in the account after four years, we can use the formula:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the time in years.

Substituting the known values into the formula, we get:

1255.66 = Pe^(0.04*4)

Simplifying the exponent:

1255.66 = Pe^0.16

Dividing both sides by e^0.16:

P = 1255.66 / e^0.16

Using a calculator to evaluate e^0.16, we get:

P = 1069.44

Therefore, the initial amount placed in the account was $1069.44 (rounded to the nearest cent).

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The coordinates of P when written as a fraction and as a decimal, is:

Point P has the coordinates of ( 3/4 , 5/6 ) which means that it is already in fraction form as it has both a numerator and a denominator for the x and ya values.

We can then convert these fractions to decimal form as shown :

x - value : 3 ÷ 4 = 0.75

y - value : 5 ÷ 6 = 0.83

In decimals, it is:

(0.75, 0.83)

In conclusion, as a fraction, point P is ( 3 / 4, 5 / 6 ), and as a decimal, point P is ( 0.75, 0.83 ).

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Given that lines a and b are parallel, lines e and f are parallel and the angles formed by their intersection is x at the intersection of lines b and e. The value of x is 82 degrees. So, the correct answer is B).

We are given that Lines a and b are parallel and Lines e and f are parallel. Horizontal lines e and f are intersected by lines a and b.

At the intersection of lines a and e, the upper left angle is 82 degrees, and the bottom left angle is 98 degrees.

We need to find the value of x, which is the bottom right angle at the intersection of lines b and e. Here are the steps to solve the problem:

Since lines a and b are parallel, the angle at the top left of the intersection between b and f is also 98 degrees. This is because alternate interior angles are congruent.

We know that the angle at the top left of the intersection between a and e is 82 degrees.

Therefore, the angle at the bottom left of the intersection between f and b is

angle at the bottom left of the intersection between f and b = 180 - (82 + 98) = 0

This means that line f and line b are collinear, and therefore, they do not intersect.

Since line e intersects both lines a and b, the angle at the bottom right of the intersection between b and e is 180 degrees (a straight line).

Therefore, x = 180 - the angle at the bottom left of the intersection between b and e, which is 98 degrees.

x= 180 - 98 = 82

Hence, x = 82 degrees.

So, the correct option is B).

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--The given question is incomplete, the complete question is given

" Lines a and b are parallel and lines e and f are parallel.

Horizontal lines e and f are intersected by lines a and b. At the intersection of lines a and e, the uppercase left angle is 82 degrees, and the bottom left angle is 98 degrees. At the intersection of lines b and e, the bottom right angle is x degrees.

What is the value of x?

8

82

98

172 "--

The answer to each statement are:

a. ST is tangent to circle R at point T - True

b. m<RST ≅ m<SRT - False

c. m<STR ≅ m<QPR - True

A tangent is a straight line drawn in such a way that it intersects externally a point on the circumference of a circle. Thus it touches a circle externally at a point on its boundary.

Considering the diagram and information given in the question, given a circle with center R and tangents PQ, ST. It can be deduce that the statements that are true or false are:

i. ST is tangent to circle R at point T - True

ii. m<RST ≅ m<SRT - False

ii. m<STR ≅ m<QPR - True

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The mean of the new data set is 15.12. and the median of the new data set is 14.4.

To increase each data value by 20%, we can multiply each value by 1.20. So the new data set becomes:

12 x 1.20 = 14.4

9 x 1.20 = 10.8

17 x 1.20 = 20.4

15 x 1.20 = 18

10 x 1.20 = 12

New data set: 14.4, 10.8, 20.4, 18, 12

To find the mean, we add up all the values and divide by the total number of values:

Mean = (14.4 + 10.8 + 20.4 + 18 + 12) / 5 = 15.12

Therefore, the mean of the new data set is 15.12.

To find the median, we first need to order the data set from smallest to largest:

10.8, 12, 14.4, 18, 20.4

The median is the middle value in the ordered set, which is 14.4.

Therefore, the median of the new data set is 14.4.

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statement B and D  are true. to determine which of the statements is true, we need to perform the indicated operations and simplify the expressions for the volumes of the boxes.

what is expressions ?

In computer programming, an expression is a combination of values, variables, and operators that produces a result or value. Expressions can be simple or complex, and they can be used in a variety of contexts, such as assigning values to variables, performing calculations, and making logical decisions.

In the given question,

To determine which of the statements is true, we need to perform the indicated operations and simplify the expressions for the volumes of the boxes.

The volume of the oak box is 2x³ + 5x² - 3xc*m³.

The volume of the maple box is 2x³ + 9x² - 2x - 24c*m³.

A. The oak box has a volume 4x² + x 24c*m³ greater than the maple box.

To compare the volumes, we need to subtract the volume of the maple box from the volume of the oak box:

(2x³ + 5x² - 3xcm³) - (2x³ + 9x² - 2x - 24cm³)

= 2x³ - 4x² + 2x + 24c*m³

Therefore, statement A is not true.

B. The maple box has a volume 4x² + x - 24c*m³ greater than the oak box.

To compare the volumes, we need to subtract the volume of the oak box from the volume of the maple box:

(2x³ + 9x² - 2x - 24cm³) - (2x³ + 5x² - 3xcm³)

= 4x² + x - 24c*m³

Therefore, statement B is true.

C. The total volume of 1 oak box and 1 maple box is 4x³ + 14x² + 5x + 24c*m³.

To find the total volume, we need to add the volumes of the oak and maple boxes:

(2x³ + 5x² - 3xcm³) + (2x³ + 9x² - 2x - 24cm³)

= 4x³ + 14x² - x - 27c*m³

Therefore, statement C is not true.

D. The total volume of 2 maple boxes is 4x³ + 18x² + 4x + 48c*m³.

To find the total volume of 2 maple boxes, we need to multiply the volume of 1 maple box by 2:

2(2x³ + 9x² - 2x - 24cm³) = 4x³ + 18x² - 4x - 48cm³

Therefore, statement D is true.

In summary, the correct statements are:

B. The maple box has a volume 4x² + x - 24c*m³ greater than the oak box.

D. The total volume of 2 maple boxes is 4x³ + 18x² + 4x + 48c*m³.

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The nearest kilometers to 999.09344471 km is 1000 km.

Given value is 999.09344471 Km.

We have to calculate the round off value to the nearest kilometers. we know that after the decimal if the value of tenth place is 5 or bigger than 5 then we add 1 to the tens place digit, this is the fundamental rule of rounding off.

Now on following this rule from the very right hand side up to the tenth place digit we come to the conclusion that only  the value after the decimal (934) is to be rounded off which is (900).

So 999.09344471 km is finally becomes 999.900 km after rounding of to nearest hundredth value.

Again rounding off 999.900 km to nearest km so it becomes 1000 km.

The nearest kilometers to 999.09344471 km is 1000 km.

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Answer:

12 units.

Step-by-step explanation:

Convert the expression to vertex form:

d(t)=3t^2-12t+0

= 3(t^2 - 4t)

= 3[(t - 2)^2 - 4]

= 3(t-2)^2 - 12.

Minimum value = 12.

Answer:

16

Step-by-step explanation:

starting from month 2, how many more months will A be as tall as B?

A grows at 1.75 in per month

B grows at 1.5in per month

so 7.5+1.75x = 11+1.5x

solve for x

x=14

so from month 2, need to go for another 14 mos.

so at month 16, they'll be same height

The rate of change of the function given by the table is 1.

The rate of change represents the ratio of one quantity compared to another.

The rate of change is also known as the slope (the Rise/the Run), the gradient, unit rate, or constant rate of proportionality.

The rate of change is computed as the quotient between the Change in the Rise and the Change in the Run.

x     y   Rate of Change

5    3  

6    4  1 (1/1)

7    5  1 (1/1)

8    6 1 (1/1)

Thus, for the function represented by the table, the rate of change or unit rate is 1.

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Answer: Yes

Step-by-step explanation:

For questions like this, youve been given a value for x, and a value for y.

Plug in and see if it works out!

[tex]3x^2- 6x - 9 = y[/tex]

[tex]3(1)^2- 6(1) - 9 = -12[/tex]      ----- Plugging in for x and y

[tex]3 - 6 - 9 = -12[/tex]

[tex]-12 = -12[/tex]

Since -12 is indeed equal to -12, we conclude the statement is true;

In terms of the graph, this translates to, "Yes, the point (1, -12) is on the graph of [tex]y = 3x^2- 6x - 9[/tex]

So your answer is Yes

Therefore, the equation of the circle in standard form is: (x - 2)² + (y - 3)² = 40.

(xh)2+(yk)2=r2 is the equation of a circle in standard form. The radius is r units, and the centre is at (h,k). Mark points r units up, down, left, and right from the centre of the circle to graph it. Through these four points, draw a circle.

We must first determine the circle's centre and radius before we can determine its equation.

The circle's centre is defined as the point on a line segment that connects the diameter's two endpoints. Taking the average of the x-coordinates and the average of the y-coordinates will get the midpoint:

Midpoint: ((-3+7)/2, (-1+7)/2) = (2, 3)

The distance formula can be used to determine that the circle's radius is equal to half of its diameter:

diameter = √((7-(-3))²+ (7-(-1))²) = √(160) = 4√(10)

radius = (1/2)diameter = 2sqrt(10)

So the center of the circle is (2, 3) and the radius is 2sqrt(10).

Consequently, the circle's standard form equation is as follows:

(x - 2)²+ (y-3)²= (2√(10))²

Simplifying:

(x - 2)²+(y-3)²=40

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Option B is correct because the tangent of angle a is greater than 1 when a is between 0 and pi/4. Option G is correct because the tangent of angle a is also greater than 1 when a is between 3pi/4 and pi.

When tan(a) > 1, this means that the tangent of angle a is greater than the length of the adjacent side divided by the length of the opposite side in a right triangle. Since the adjacent and opposite sides of a unit circle have a length of 1, this means that the opposite side of angle a is less than 1.

To determine where angle a could be on the unit circle, we need to find the angles whose tangent is greater than 1. Since tangent is positive in the first and third quadrants, the angles we need to consider are in the first and third quadrants.

In the first quadrant, the angle whose tangent is 1 is pi/4, and the tangent increases as the angle increases. Therefore, angle a could be between 0 and pi/4 (option B).

In the third quadrant, the angle whose tangent is 1 is 5pi/4, and the tangent decreases as the angle increases. Therefore, angle a could also be between 3pi/4 and pi (option G).

Therefore, options B and G are correct, and angles a could be located in the regions described by these options on the unit circle.

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