Graph the numbers -0.2, 7/10, -1, √2, and -4 on a number line.

-8 -7, -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Answer:

80 ft/min

Step-by-step explanation:

Let h represent the height of the person shadow, x represent the distance between the person and the lamppost, y represent the length of the man shadow.

Therefore:

\(\frac{h}{x+y} =\frac{6}{y} \\\\substituting\ x=10,y=20:\\\\\frac{h}{10+20} =\frac{6}{20}\\\\\frac{h}{30} =\frac{6}{20}\\\\h=30*6/20\\\\h=9\ feet\\\\Therefore:\\\frac{h}{x+y} =\frac{6}{y}\\\\\frac{9}{x+y} =\frac{6}{y}\\\\9y=6x+6y\\\\9y-6y=6x\\\\3y=6x\\\\y=2x\\\\The\ person\ is\ walking\ from\ the\ lamppost\ at\ 40ft/min(\frac{dx}{dt}=40\ ft/min) \\\\y=2x\\\\Differentiating\ with\ respect\ to\ t:\\\\\frac{dy}{dt} =\frac{d}{dt}(2x)\\\\\frac{dy}{dt} =2\frac{dx}{dt}\\\\\)

\(\frac{dy}{dt} =2(40\ ft/min)\\\\\frac{dy}{dt}=80\ ft/min\)

The rate at which the length of the shadow is increasing when he is 30 feet away from the lamp post is  80 \(\frac{ft}{min}\).

The height of the person shadow is to be = h

Given ,

The distance between the person and the man = x = 10

The length of the man shadow is = y = 20

By the similar triangle property corresponding sides of similar triangles are in the same ratio.

\(\frac{h}{x+y} = \frac{6}{y}\)

\(\frac{h}{10+20} = \frac{6}{20}\)

20h = 60 + 120

20h = 180

h = \(\frac{180}{20}\)

h = 9feet

Therefore,

\(\frac{h}{x+y} = \frac{6}{y} \\\frac{9}{x+y} = \frac{6}{y} \\\)

9y= 6x + 6y

9y-6y = 6x

6x = 3y

y = \(\frac{6}{3}x\)

y = 2x

Differentiating both the sides with respect t,

\(\frac{dy}{dt} = 2\frac{dx}{dt}\)

we know that ;

\(\frac{dx}{dt} = 40 \frac{ft}{sec}\)

Therefore, by substitute the value

\(\frac{dy}{dt} = 2 . 40\frac{ft}{min}\)

\(\frac{dy}{dt}\) = 80\(\frac{ft}{min}\).

The rate at which the length of the shadow is increasing is 80\(\frac{ft}{min}\)  .

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Answer:

1) 9x

2) 3b

3) 3m

4) 5a

5) 7x

6) 3a + 5b

7) 9x - 4

8) 2b + m

9) 13a + b + 6c

10) 9b + 1

11) 7p

12) 2a + b -10

Step-by-step explanation:

The formula for y in terms of x is y=160​/x^2.

We are given that;

y = 20 when t=4

And t = 8 when x = 2

Now,

To find the value of k by using the fact that y = 20 when t = 4:

20=k⋅4

k=5

Also, y=5t

Next, we use the fact that t is inversely proportional to the square of x. We can write:

t=x2k​

where k is a constant of proportionality. We can find the value of k by using the fact that t = 8 when x = 2:

8=22k​

k=32

Now we know that:

t=x232​

Substituting this into the equation for y:

y=5t=5⋅x232​=160​/x^2

Therefore, by proportions the answer will be y=160​/x^2.

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Answer:

k= -1 ik because I just calculated it

Answer:

k = -1

Step-by-step explanation:

Since subtracting a negative is the same as adding, we can rewrite this as k + 5/6 = -1/6. Now we can subtract 5/6 from both sides, leaving us with k = -6/6 or k = 1.

The fourth vertex such that it forms a right angle with two adjacent vertices the correct answer is \((9, 3)\)  . Thus, option D is correct.

To create a rectangle, we need to find the fourth vertex such that it forms a right angle with two adjacent vertices. We can use the distance formula to determine the length of each side of the triangle formed by the three given vertices:

The distance between \((5, 6)\) and  \((9, 6)\) is \(4\) units.

The distance between \((5, 6)\) and \((5, 3)\)   is \(3\) units.

The distance between  \((9, 6)\) and  \((5, 3)\) is \(5\) units.

Since the two sides with length 4 units are adjacent and form a right angle, we know that the fourth vertex must be located 3 units below (9, 6) or 3 units above (5, 3). Therefore, the fourth vertex can be either (9, 3) or (5, 9).

However, only  \((9, 3)\) forms a rectangle with the three given vertices, as it is also 5 units away from   \((5, 6)\) and  \(4\) units away from (9, 6), forming a right angle with both.

Therefore, the correct answer is  \((9, 3)\).

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Steve is correct. Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0.

By using a number line, Steve can find the difference in temperature between 7 AM and 12 PM on Wednesday by adding the distances from 0. One temperature is negative and the other is positive, but by adding their distances, he can find the difference. Kelly's method of subtracting -5.1 from the temperature at 12 PM on Wednesday is not necessarily incorrect, but it does not give the exact difference in temperature between the two times. Therefore, using Steve's method, the change in temperature would be the sum of the distance from 0 to the temperature at 7 AM (which is 2.5) and the distance from 0 to the temperature at 12 PM (which is also 2.5), resulting in a difference of 5 degrees.

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Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Answer:

8:9

Step-by-step explanation: Add 88+11 to get his weight before=99 Pounds. Then you put together the ratio. 88:99.

The GCF for those numbers would be 11, so divide them both by 11, to get a final answer of 8:9

The procedure using in setting class limits for a frequency distribution are given as follows:

A frequency distribution can show either the relative frequency (percentage) or the absolute frequency (number of observations) observed for each interval of a data-set.

These intervals are called the limits of the frequency distribution. To obtain the limits, these following features are needed:

Then the class width is calculated as follows:

Class width = (Maximum - Minimum)/Number of intervals.

This operation may result in a non-integer value, meaning that the class width may be rounded.

Then the classes are built as follows:

The problem is incomplete, hence the entire procedure to set class limits was described.

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Answer:

1) 11^42. [. ( a^b)^c is a^bc]

2) 5^5. [a^b/a^c= a^(b-c)

3) 14^24

4) 3^10

The function with the greater rate of change will have the greater output value for every input value which is true.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The slope of the line is given as,

m = (y₂ - y₁) / (x₂ - x₁)

Let m₁ > m₂ and c₁ > c₂. Then the equations are given as,

y = m₁x + c₁

y = m₂x + c₂

The function with the greater rate of change will have the greater output value for every input value which is true.

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Answer:

9.18%

Step-by-step explanation:

The probability of getting a tail on a fair coin flip is 0.5, and the probability of getting a head is also 0.5. Since each coin flip is independent, we can use the binomial probability formula to calculate the probability of getting exactly 5 tails in 15 flips:

P(X = 5) = (15 choose 5) * (0.5)^5 * (0.5)^(15-5)

where (15 choose 5) is the number of ways to choose 5 tails out of 15 flips, which can be calculated as:

(15 choose 5) = 15! / (5! * 10!) = 3003

Substituting the values, we get:

P(X = 5) = 3003 * (0.5)^15 ≈ 0.0918

Therefore, the probability of getting exactly 5 tails in 15 coin flips is approximately 0.0918 or 9.18%.

The statement refers to the way that symbols are represented in sequences, a common practice in formal language theory, by employing a notation that makes symbols a part of the sequence.

In formal language theory, a language is often defined as a set of strings over an alphabet. By representing any alphabetic sequence of symbols as a single string using the notation outlined in the statement, we are able to recognise the language that comprises that sequence as a collection of strings. A subset of the language having all possible strings over the alphabet (a, b, and c) is the set of strings abc, which may be used to represent the language including the sequence (a, b, and c). So, this notation offers an easy approach to discuss languages and the sequences that make up such languages.

Hence, the statement relates the symbols and sequences.

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The magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.

Sum of vectors in x direction, ∑X = 5 - 1 = 4

Sum of the vectors in y direction, ∑Y = 6 + 14 = 20

Resultant vector = √(∑X² + ∑Y²)

Resultant vector = √(4² + 20²) = 20.4 units

θ = arc tan (ΣY/ΣX)

θ = arc tan (20/4)

θ = arc tan (5)

θ = 78.7⁰

θ ≈ 79⁰

Thus, the magnitude of the resultant vectors is 20.4 units and the direction of the vectors is 79⁰.

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Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

Let's assume that Bryan invested an amount of x dollars in the first account, which earns 11% interest, and (6500 - x) dollars in the second account, which earns 7% interest.

The interest earned from the first account can be calculated as 0.11x, and the interest earned from the second account can be calculated as 0.07(6500 - x).

According to the problem, the total interest earned after one year is $519. So we can set up the equation:

0.11x + 0.07(6500 - x) = 519

Simplifying the equation:

0.11x + 455 - 0.07x = 519

0.04x + 455 = 519

0.04x = 64

x = 64 / 0.04

x = 1600

Therefore, Bryan invested $1600 in the first account (earning 11% interest) and $4900 (6500 - 1600) in the second account (earning 7% interest).

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Thus, the measure of angle  m∠SQP = 87° for given set of vertically opposite angles.

An adjacent pair of additional angles is known as a linear pair. Adjacent refers to being next to one another, and supplemental denotes that the sum of the two angles is 180 degrees.

Any two angles that sum up to 180 degrees are referred to as supplementary angles.

For the given question:

m∠PQT = m∠SQR (vertically opposite)

101 - 4b = 109 - 6b

on simplifying:

109 - 101 = 6b - 4b

2b = 8

b = 4

m∠PQT = 101 - 4(4) = 93

Now,

m∠PQT +  m∠SQP = 180 (linear pair)

93 +  m∠SQP = 180

m∠SQP = 180 - 93

m∠SQP = 87°

Thus, the measure of angle  m∠SQP = 87° for given set of vertically opposite angles.

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Answer:

f(x) = -5x + 16

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

m - slope

b - y-intercept

Step 1: Define

y + 5x = 16

Step 2: Put into slope-intercept form

Step 3: Rewrite in function notation

f(x) = -5x + 16

The graph of g(x) is obtained from the graph of f(x) by the following transformations:

- A horizontal stretch by a factor of 9. This is because the graph of g(x) is 9 times wider than the graph of f(x).

- A vertical translation down by 2 units. This is because the graph of g(x) is 2 units lower than the graph of f(x).

In other words, to obtain the graph of g(x) from the graph of f(x), we stretch the graph horizontally by a factor of 9 and then translate it down by 2 units.

Here is a more detailed explanation of the transformations:

- Horizontal stretch by a factor of 9: To stretch the graph horizontally by a factor of 9, we multiply all of the x-coordinates by 9. This means that every point on the graph of f(x) will be moved 9 units to the right on the graph of g(x).

- Vertical translation down by 2 units: To translate the graph down by 2 units, we subtract 2 from all of the y-coordinates. This means that every point on the graph of f(x) will be moved 2 units down on the graph of g(x).

Add 7 to both sides.

Add −4 and 7 to get 3.

Multiply both sides by 3, the reciprocal of 1/3 . Since 1/3 is >0, the direction of inequality remains the same.

Multiply 3 and 3 to get 9.

The perimeter of the polygon, with the specified coordinate points , found using Pythagorean Theorem  iis  approximately 16 units

The Pythagorean Theorem indicates that the square of the distance between points on the coordinate plans is the sum of the square of the horizontal and vertical distances between the  point.

The coordinates of the vertices of the polygon are;

(-3, 1), (-3, 3), (-1, 5), (2, 4), and (2, 1)

The length of the sides are therefore;

3 - 1 = 2,

√((-1 - (-3))² + (5 - 3)²) = 2·√2

√((2 - (-1))² + (4 - 5)²) = √(10)

4 - 1 = 3

2 - (-3) = 5

The perimeter is therefore;

2 + 2·√2 +  √(10) + 3 + 5  ≈ 16

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Answer:

\(|\frac{x}{y} |\)

Step-by-step explanation:

We are given the following expression: \(\sqrt\frac{x^3y^5}{xy^7}\), where x > 0 and y > 0.

We want to simplify it.

To do that, we can first simplify what is under the radical, then take the square root of what is left.

Recall that when simplifying exponents, we don't want any negative or non-integer radicals left.

To simplify what is under the radical, we can remember the rule where \(\frac{a^n}{a^m} = a^{n-m}\).

So, that means that \(\frac{x^3}{x} = x^2\) and \(\frac{y^5}{y^7} = y^{-2}\) .

Under the radical, we now have:

\(\sqrt{x^2y^{-2}}\)

Now, we take the square root of both exponents to get:

\(|xy^{-1}|\)

The reason why we need the absolute value signs is because we know that x > 0 and y > 0, but when we take the square root of of \(x^2\) and \(y^{-2}\) , the values of x and y can be either positive or negative, so by taking the absolute value, we ensure that the value is positive.

However, we aren't done yet; remember that we don't want any radicals to be negative, and the integer of y is negative.

Recall that if \(a^{-n}\), that is equal to \(\frac{1}{a^n}\).

So, by using that,

\(|x * \frac{1}{y} |\)

This can be simplified to:

\(|\frac{x}{y} |\)

Answer:

Triangle 2

Step-by-step explanation:

5, 12, 13

Use the Pythagorean Theorem

a^2 + b^2 = c^2

a = 5

b = 12

c = 13

25 + 144 = 169

a and b are side lengths

c is the hypotenuse

The theorem states that the square of the side lengths of a right triangle added together equals the square of the hypotenuse

Answer:

B is the right triangle because the sum of the square of each of the two shortest sides will equal the square of the longest side.

Step-by-step explanation:

Pythagorean Theorem says if a triangle is a right triangle with side lengths a, b, and c, then a^2 + b^2 = c^2 where c is the length of the longest side.

So, A. 16^2= 7^2 + 12^2  256 does not = 193 NOT a right triangle

      B. 13^2= 5^2 + 12^2  169 = 169 Yes this is a right triangle

      C. 9^2= 4^2 + 5^2  81 does not = 41 NOT a right triangle

      D. 19^2= 8^2 + 15^2  361 does not = 289 NOT a right triangle

The interest is 16% compounded semi-annually, is Rs. 121,179.10.

To determine how much money needs to be deposited now to provide a payment of Rs. 15,000 at the end of each half year for 10 years, we will use the formula for the present value of an annuity.

Present value of an annuity = (Payment amount x (1 - (1 + r)^-n))/rWhere:r = interest rate per compounding periodn = number of compounding periodsPayment amount = Rs. 15,000n = 10 x 2 = 20 (since there are 2 half years in a year and the payments are made for 10 years)

So, we have:r = 16%/2 = 8% (since the interest is compounded semi-annually)Payment amount = Rs. 15,000Using the above formula, we can calculate the present value of the annuity as follows:

Present value of annuity = (15000 x (1 - (1 + 0.08)^-20))/0.08 = Rs. 121,179.10Therefore, the amount that needs to be deposited now to provide payment of Rs. 15,000 at the end of each half year for 10 years, if the interest is 16% compounded semi-annually, is Rs. 121,179.10.

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Answer:

30

Step-by-step explanation:

KCF, Keep Change Flip.

30 divided by 1/3 becomes 30 multiplied by 3/1, or 30/1, or 30.

Use a calculator 4 divided by 11= 0.36 (2dp)

The purpose of data is to provide information and insights that can be used to make informed decisions, draw conclusions, and gain knowledge about a particular subject or phenomenon.

Data plays a crucial role in various fields, including science, business, research, healthcare, and everyday life.One primary purpose of data is to describe and understand the world around us.

By collecting and analyzing data, we can identify patterns, trends, and relationships that exist within a dataset. This helps us gain a deeper understanding of complex systems and phenomena.

For example, in scientific research, data is used to study the behavior of natural processes, investigate the effects of interventions, and formulate theories and models.

Data also serves as a foundation for making informed decisions. By examining relevant data, individuals and organizations can assess the potential outcomes of different choices and select the most optimal course of action.

Data-driven decision-making enables organizations to improve efficiency, identify opportunities, mitigate risks, and enhance overall performance. In fields like marketing and finance, data is extensively used for market research, customer segmentation, trend analysis, and financial forecasting.

Furthermore, data is crucial for monitoring and evaluating performance. By collecting data over time, organizations can track progress, measure outcomes, and identify areas for improvement. Data-driven monitoring allows for evidence-based assessments and adjustments to strategies or interventions.

Overall, the purpose of data is to provide reliable information that can be used to enhance understanding, support decision-making, and drive progress in various domains. It empowers individuals and organizations with the ability to derive insights, solve problems, and make meaningful contributions to society.

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Given:

Required:

To find the range of the function (uv)(x).

Explanation:

We know that

The horizontal asymptote of this function is at y=3.

So, the range of this function is from

Final Answer:

The range of (uv)(x) is

The first step to solve the present question is to determine each of the equations to determine the number of each accessory as a function of the number of boxes, If d is the number of boxes, Nt is the number of Turbo Jet Pack, Nx is the number of X-Ray Vision Glasses, and Ni is the number of invisible shields, we have the following:

Now, we can use it to solve the question.

Part A

It Nl is the number of Laser Sabers sold, let's transform the statement into a math equation, we have the following:

If we substitute the expressions we have from the previous-developed expressions, we have the following:

Part B

Let's assume the value of a single Laser Saber is given by Vl, then the total value for the value of a unity times the number of sold Laser Sabers, as follows:

Answer:

-2

-1

-2

Step-by-step explanation:

please forgive me, but again, this is the simplest of the simplest things. how is that a problem ?

this costs so much more time to just put it in here and then copy answers than just doing it. this is literally a matter of seconds.

the functional value is -2 for all x that are not equal to 2.

and the functional value is -1, when x = 2

so, what is the problem ?

please see my other answer for more details on the solution.