find the sum of 8a+2b-4 and 3b-5. write. in expanded form and then standard form​

The 30th term a30 of the sequence is -1445

The definition of the function is given as

arithmetic sequence of 1,-4,-9,-14

The above definitions imply that we simply subtract 5 from the previous term to get the current term

Using the above as a guide,

so, we have the following representation

First term, a = 1

Common difference, d = 5

An arithmetic sequence is represented as

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

For the 30th term, we have

a(30) = a + 29d

So, we have

a(30) = 1 + 29 * -5

Evaluate

a(30) = -144

Hence, the value of a30 is -144

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The measure of the inscribed angle is equal to 90 degrees

The inscribed angle theorem mentions that the angle inscribed inside a circle is always half the measure of the central angle or the intercepted arc that shares the endpoints of the inscribed angle's sides. In a circle, the angle formed by two chords with the common endpoints of a circle is called an inscribed angle and the common endpoint is considered as the vertex of the angle.

In this problem, the side length of the square is 5 which forms 90 degrees to all the other sides.

The measure of the circumscribed angle is 90 degree

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Yes, it is possible to find a function \( f(t, x) = 1 \) that is continuous and has continuous partial derivatives, making \( x_1(t) = t \) and \( x_2(t) = \sin(t) \) solutions to \( x' = f(t, x) \) near \( t = 0 \).

Certainly! We can find a function \( f(t, x) = 1 \) that satisfies the given conditions. Let's consider the differential equation \( x' = f(t, x) \), where \( x' \) represents the derivative of \( x \) with respect to \( t \). For \( x_1(t) = t \) and \( x_2(t) = \sin(t) \) to be solutions near \( t = 0 \), we need \( x_1'(t) = 1 \) and \( x_2'(t) = \cos(t) \) respectively.

Since \( f(t, x) = 1 \), it matches the derivatives of both \( x_1(t) \) and \( x_2(t) \) with respect to \( t \). The function \( f(t, x) = 1 \) is continuous and has continuous partial derivatives, making it a valid choice. Thus, \( x_1(t) = t \) and \( x_2(t) = \sin(t) \) satisfy \( x' = f(t, x) \) near \( t = 0 \).

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Answer: 300 mi.

Step-by-step explanation:

Let t be the time taken to drive to the park (at 60 mph)

Let t + 1 be the time taken to drive home from the part (at 50 mph)

Distance to the park = 60t

Distance from the park = 50(t + 1)

Obviously the distances should be the same so equate them.

60t = 50(t + 1)

60t = 50t + 50

10t = 50

t = 50/10

t = 5 hours

Now figure the distance.  You can use either equation for the distance to or from the park:

60t = 60(5) = 300 miles

or

50(t+1) = 50(6) = 300 miles

The distance to or from the park will be 300 miles.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Let assume t be the time taken to drive to the park (at 60 mph).

Let assume t + 1 be the time taken to drive home from the part (at 50 mph)

The Distance to the park = 60t

The Distance from the park = 50(t + 1)

Obviously the distances should be the same, so equate them;

60t = 50(t + 1)

60t = 50t + 50

10t = 50

t = 50/10

t = 5 hours

Now figure the distance. We can use either equation for the distance to or from the park:

60t = 60(5) = 300 miles

50(t+1) = 50(6) = 300 miles

Therefore, the distance to or from the park will be 300 miles.

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Step-by-step explanation:

so, if car have 120km/hr it maximum speed will be 85-95km/hr so the car travel 300km in around 5 or 5 unhalf hour

The answer to the given question is the angular acceleration of the wheel is 0.7742 rad/s².

We can use the formula for rotational dynamics:

τ = Iα

where τ is the torque applied, I is the moment of inertia, and α is the angular acceleration.

Rearranging this equation, we get:

α = τ / I

Plugging in the given values, we have:

α = 48 Nm / 62 kg⋅m²

Simplifying, we get:

α = 0.7742 rad/s²

Rotational dynamics deals with the motion of objects that are rotating around an axis. The key concept in rotational dynamics is torque, which is a measure of how much a force can cause an object to rotate. The moment of inertia is another important quantity in rotational dynamics, and it describes an object's resistance to rotational motion. The moment of inertia depends on the distribution of mass around the axis of rotation. The angular acceleration of a rotating object is directly proportional to the torque applied and inversely proportional to the moment of inertia. Therefore, a greater torque or a smaller moment of inertia will result in a greater angular acceleration. These concepts are used in a variety of applications, from the motion of planets to the operation of engines and turbines.

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Answer: 56%

Step-by-step explanation:

Since Janice bought a bag of green and yellow marbles and she received 14 green marbles and 11 yellow marbles, the total number of marbles will be:

= 14 + 11 = 25 marbles

Number of Yellow marbles = 11

Number of Green marbles = 14

Total number of marbles = 25

The percentage of the marbles that were green will be:

= Number of Green marbles / Total marbles × 100

= 14/25 × 100

= 14 × 4

= 56%

Answer:

2.353

Step-by-step explanation:

use a calculator...

Answer:

2.353

Step-by-step explanation:

Answer:

  225 5/6 m/s ≈ 225.8 m/s ≈ 226 m/s

Step-by-step explanation:

Speed is the ratio of distance to time. Here, we also need to do a units conversion.

There are 1000 m in 1 km, so the distance is ...

  5420 km = 5420×(1000 m) = 5.42×10^6 m

There are 60 seconds in a minute, and 3600 seconds in an hour, so the time is ...

  (6 h)×(3600 s/h) +(40 min)(60 s/min) = 21600 +2400 s = 2.4×10^4 s

Then the speed in meters per second is found by dividing meters by seconds:

  speed = (5.42×10^6 m)/(2.4×10^4 s) = 2.25833...×10^2 m/2

The average speed of the plane is 225 5/6 meters per second.

Answer:

Step-by-step explanation:

You need to convert all into decimals or all into fractions to compare

4 1/6= 4.166666

4.73

41/10= 4.1

4.168

Order:

   41/10      4 1/6      4.168    4.73

Answer:

here's the list of numbers in order from least to greatest:

4 1/6, 4.160, 41/10, 4.73.

Answer:

  max: 72 at (4, 8)

  min: 8 at (2, 0)

Step-by-step explanation:

The attached graph shows the solution set as a white area. The shaded areas are excluded from the solution set. The dashed boundary lines indicate those lines are not excluded from the set. The vertices of the polygon are (0, 2), (2, 0) and (4, 8).

The line f(x,y) = 0 is shown for reference. The maximum value of f(x,y) will be found at the vertex of the solution set that is farthest from this line. The minimum will be found at the vertex of the solution set that is closest to this line.

The maximum value of f(x, y) is 72 at (x, y) = (4, 8).

The minimum value of f(x, y) is 8 at (x, y) = (2, 0).

Answer:

3 pi 9

Step-by-step explanation:

Answer:

To estimate the number of pentagons in the tub, we can use the proportion of pentagons in the sample of geometric shapes that Mrs. Chen selected and apply it to the total number of geometric shapes in the tub.

The proportion of pentagons in the sample is:

4 / (3 + 2 + 2 + 4 + 2) = 4 / 13 ≈ 0.31

We can assume that this proportion is representative of the entire tub of geometric shapes, and we can apply it to the total number of geometric shapes in the tub:

0.31 x 250 ≈ 77.5

Rounding to the nearest whole number, we can estimate that there are approximately 78 pentagons in the tub.

Therefore, the estimated number of pentagons in the tub is 78.

At the air-polystyrene boundary with an incidence angle of 50°, the reflection coefficient is -0.08, the transmission coefficient is 0.9936, the reflectivity is 0.0064, the transmissivity is 0.9874, and the power carried by the incident, reflected, and transmitted beams is 0.6 W, 0.0032 W, and 0.5968 W, respectively, for an illuminated area of 1 m².

The reflection and transmission coefficients are given by the Fresnel equations:

\(r_{s} = \frac {n_{1}cos\theta_{i} - n_{2}cos\theta_{i}}{n_{1}cos\theta_{i} + n_{2}cos\theta_{i}}\)

\(t_{s}= \frac{2n_{1}cos\theta_{i}}{{n_{1}cos\theta_{i} + n_{2}cos\theta_{i}}}\)

where \(n_{1}\) and \(n_{2}\) are the refractive indices of air and polystyrene, respectively,  \(\theta_{i}\) and \(\theta_{t}\)are the angles of incidence and transmission, respectively.

For \(n_{1}\)=1 , \(n_{2}\)=2.6 , \(\theta_{i}\)=50∘ , we find that \(r_{s}\)=0.23 and \(t_{s}\)=0.77.

(b) The reflectivity and transmissivity are the squared magnitudes of the reflection and transmission coefficients, respectively. Therefore, reflectivity is \(R=\vert r_{s} \vert ^{2} = 0.053\) and the transmissivity is \(T=\vert t_{s} \vert ^{2} = 0.59\).

(c) The power carried by the incident beam is given by

\(pi = \frac{1}{2} \epsilon_{0} E_{0}^{2}c\)

Where \(E_{0}\) is the amplitude of the electric field and c is the speed of light. For \(E_{0}\) =20 V/m, we find that \(P_{i}\)=\(1.33*10^{-6}W.\)

The power carried by the reflected beam is given by

\(P_{r}=RP_{i} = 6.99 * 10^{-8} W\)

and the power carried by the transmitted beam is given by

\(P_{t}=TP_{i} = 7.86 * 10^{-7} W.\)

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The first 3 terms of the sequence using the expression are -5, -4 and -1

From the question, we have the following sequence that can be used in our computation:

n(n – 2) – 4

This means that

T(n) =  n(n – 2) – 4

Set n = 1, 2 and 3

So, we have

T(1) =  1 * (1 – 2) – 4 = -5

T(2) =  2 * (2 – 2) – 4 = -4

T(3) =  3 * (3 – 2) – 4 = -1

Hence, the first 3 terms of the sequence using the expression are -5, -4 and -1

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Answer:

9

Solving steps:

=> 6÷2(1+2)

divide 6 by 2

=> 3(1+2)

add values inside the bracket

=> 3(3)

multiply 3 by 3

=> 9

Answer:

9

Step-by-step explanation:

Use parenthesis, exponents, multiplication, division, addition, and subtraction, witch stands for PEMDAS.

1. 1+2 is the first step, since it is in the parenthesis. This gives you 3

2. You do 6÷2, since that is the next step. Since the operations are from left to right  , you move on the next step, witch is divison. This also gives you 3.

3. You do the final step, witch is to multiply, so you do 3 x 3 , witch gives you 9.

The relationship between the triangles is angle angle side.

We know that triangles could be related in certain ways. The way that a triangle is related to each other can be used to determine the relationship then the several ways that triangles could be related to eacjh other are;

Side angle side

Angle angle side

side side side.

We can see that the angles and the sides of this triangles are the same so the relationship between then can be said to be on the basis of angle side angle.

Looking at the images, it is clear that the triangles are congruent because there are two sides and an angle that are equal.

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Answer:

$43.64

Step-by-step explanation:

If the tax rate = 3.9% and the product u are buying is priced at $42

Then, the amount you will pay for the object will be,

$42 + 3.9/100 * 42

=> 42 + 0.039 * 42

=> 42 + 1.638

=> 43.638

43.638 when rounded to the nearest hundredth is,

43.64

Hope it helps :)

Answer:

5.09

Step-by-step explanation:

You eliminate the decimal by multiplying both sides by 10:

10(.25x+0.5)=10(0.61+0.14x)

Then you get your new equation and combine like terms:

25x+5=61+14x

-14x           -14x

11x+5=61

11x+5=61

    -5  -5

11x=61

Then finally you do 61/11 which gets you around 5.09 if you round to 2 decimal places.

Answer: m<XVY = 82°

Step-by-step explanation: The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs.

Since the measures of the intercepted arcs are 86° and 78°,

we can setup the equation m<XVY = 1/2(86 + 78).

So we get m<XVY = 1/2(164) or m<XVY = 82°

Answer:

b

Step-by-step explanation:

The statement describes the slope of the line of best fit for the data is the temperature decreases by about 1.2 degrees Fahrenheit for each

1-degree increase north in latitude.

A line of best fit is a straight line that is used to model the relationship between two variables in a set of data.

The line is drawn so that it comes as close as possible to all the data points in the set, and is also known as the trend line or regression line.

We have,

To determine the slope of the line of best fit for the given data, we need to calculate the correlation coefficient between the latitude and the high temperature.

If the correlation coefficient is negative, it means that the temperature decreases as latitude increases, and the slope will also be negative.

If the correlation coefficient is positive, it means that the temperature increases as latitude increases, and the slope will also be positive.

Using a spreadsheet or calculator, we can find that the correlation coefficient between latitude and high temperature is approximately -0.89, which indicates a strong negative correlation.

Therefore, the temperature decreases as latitude increases.

To find the slope of the line of best fit, we can use the formula:

slope = correlation coefficient * (standard deviation of y / standard deviation of x)

where x represents latitude and y represents high temperature.

Using the given data, we can calculate the standard deviation of latitude as approximately 5.22 degrees and the standard deviation of high temperature as approximately 7.05 degrees Fahrenheit.

Substituting these values into the formula, we get:

slope = -0.89 x (7.05 / 5.22) = -1.2

Therefore,

The temperature decreases by about 1.2 degrees Fahrenheit for each

1-degree increase north in latitude.

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Answer:

B:10.5

Step-by-step explanation:

half of 21 is 10.5

Answer:

The answer is A. y=2x+4

Step-by-step explanation:

The y-intercept is on positive 4, so the equation will end with +4. the rise over the run is 2/1, which is simplified to 2. So 2x. So the answer is y=2x+4.

Hope this helped.

Answer:

$2.25

Step-by-step explanation:

You have to set up a proportion to show how much the cost of milk is when discounted per gallon. 0% off, the milk would be $3.75. 40% off, the milk would be x. Now I flipped the percents because that is how much you are actually paying.

Proportion would look something like this:

3.75/100 = x/60

solve for x:

225 = 100x

x= 2.25

Answer:

GCF

Step-by-step explanation:

Each row will have the same number of plants.  So we want to know what's the biggest number we can divide 45, 81, and 63 by.  That means we need to find the greatest common factor.  In this case, it's 9.  Each row can have at most 9 seeds.

A car manufacturer wants to lean about the brand preferences, then the company should survey a sample of all electric car owners.

A survey is a set of questions used in human subject research with the goal of gathering specific information from a particular population. Surveys can be carried out via the phone, by mail, online, at street corners, and even in shopping centers. Surveys are employed to collect data or learn more in areas like demography and social research.

Survey research is frequently used to evaluate ideas, beliefs, and emotions. Surveys may have narrow, specialized objectives, or they may have more general, extensive objectives.

As the manufacturer wants to learn about the brand preferences of electric car owners that what type of things people like nowadays, or what kind of improvement he can do in his model or design or other things, he should prefer a sample of all electric car owners.

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If we define our population as all the households in the city of Chicago and use the Chicago telephone directory to draw our sample units, we would likely have a survey with sample frame error. Correct option is A.

Sample frame error occurs when the sampling frame, in this case, the Chicago telephone directory, does not accurately represent the population of interest.

In this case, the telephone directory would exclude households without a landline phone or those who choose not to have their phone number listed. This means that the sample would not include all households in the population, leading to biased results.

A representative survey (option B) would be one in which the sample accurately represents the population in terms of relevant characteristics such as age, gender, income, education, and other important demographic factors.

In contrast, a survey containing error (option C) is a general term that includes both sampling error and non-sampling error, such as measurement error or response bias.

Finally, a census (option D) is a study in which data is collected from all individuals or units in a population, not just a sample. Therefore, using a telephone directory to draw a sample from the population does not constitute a census.

In conclusion, using the Chicago telephone directory to draw a sample of households would likely result in a survey with sample frame error, which can lead to biased results and limit the generalizability of the findings to the entire population.

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