Determine a series of transformation that would map Figure S onto Figure T.

\(b=\frac{3A}{2m}\).

\(A = \frac{2}{3} mb\)

\(\frac{3}{2} A = \frac{2}{3} mb*\frac{3}{2}\\ \\\frac{3}{2} A =mb\)

\(\frac{\frac{3}{2} A}{m} =\frac{mb}{m} \\ \\\frac{\frac{3}{2} A}{m} = b\\ \\\frac{3}{2}*\frac{A}{m} =b\\ \\\frac{3A}{2m}=b\\\\ b=\frac{3A}{2m}\)

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Step-by-step explanation:

(((x3) - 2x2) - 4x) - 2 = 0

STEP

2

:

Checking for a perfect cube

2.1 x3-2x2-4x-2 is not a perfect cube

Trying to factor by pulling out :

2.2 Factoring: x3-2x2-4x-2

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -4x-2

Group 2: -2x2+x3

Pull out from each group separately :

Group 1: (2x+1) • (-2)

Group 2: (x-2) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

2.3 Find roots (zeroes) of : F(x) = x3-2x2-4x-2

Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers

Answer:

x- intercept = - 8 , y- intercept = 4

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

x - 2(0) = - 8

x - 0 = - 8

x = - 8 ← y- intercept

to find the y- intercept let x = 0 in the equation and solve for y

0 - 2y = - 8

- 2y = - 8 ( divide both sides by - 2 )

y = 4 ← y- intercept

Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

The calculated volume of the prism is 702 cubic cm

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

The trapezoidal prism (see attachment)

The formula of the volume of a trapezoidal prism is

Volume = Base area * Height

Where we have

Base area = 1/2 * (8 + 10) * 6

Evaluate the sum of 8 and 10

Base area = 1/2 * 18 * 6

Evaluate the products of 1/2, 18 and 6

Base area = 54

Also, we have

Height = 13

So, the volume is calculated as

volume = 13 * 54

Evaluate

volume = 702

Hence, the volume of the prism is 702 cubic cm

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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:

First one 28

Second one 53

Step-by-step explanation:

Using pythagoras theorem

Sqrt(24^2+7^2)=28

sqrt(45^2+28^2)=53

Answer:

a) (1, 2) not on the graph.

b) (1, -1) is on the graph.

Step-by-step explanation:

Given the equation of the line as:

\(2x - y - 3 = 0\)

The points given are

a) (1, 2)

To determine whether it is on the graph of the line or not.

To do so, we can do 2 things:

1. Draw the graph and plot the point on the graph to check whether it is on the graph or not.

2. To put the point in the given equation of the line, whether the equation is satisfied or not.

For method 1: Kindly refer to the attached image of the line and point plotted.

Method 2:

Let us put \(x=1, y=2\) in the Left Hand Side (LHS) of equation.

\(2\times 1 - 2 - 3\\\Rightarrow -3 \neq 0 , RHS\)

(1, 2) Not on the graph.

(b) (1, -1)

For method 1: Kindly refer to the attached image of the line and point plotted.

Method 2:

Let us put \(x=1, y=-1\) in the Left Hand Side (LHS) of equation.

\(2\times 1 - (-1) - 3\\\Rightarrow 3-3 = 0 = RHS\)

(1, -1) is on the graph.

Answer:

It is not equivalent

Step-by-step explanation:

Because the first expression simplified is 3x with the power of 9, and the first expression simplifies to x with a power of 9.

Answer:

No, they are not equivalent.

Step-by-step explanation:

In the case of the first expression: x³ * x³ * x³, you will solve the power first, before multiplying the whole numbers.

However, in terms of the second one, you are multiplying the powers first, and then solving for the power.

Take for example, x = 2. Plug in 2 for x in the expressions given:

x³ * x³ * x³ = 2³ * 2³ * 2³ = 8 * 8 * 8 = 64 * 6 = 512

However,

2^(3 * 3 * 3) = 2^(27) = 134,217,728

~

The probability is closer to one than zero.

Probability theory is used to analyze and predict the likelihood of events happening in various fields such as statistics, gambling, physics, finance, and more. It allows us to make informed decisions based on the likelihood of different outcomes. In probability theory, the total number of possible outcomes is important to determine the probability of a single event occurring. By comparing the favorable outcomes to the total outcomes, we can calculate the probability of an event happening.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. Probability for Class 10 is an important topic for the students which explains all the basic concepts of this topic. The probability of all the events in a sample space adds up to 1.For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But when two coins are tossed then there will be four possible outcomes,  i.e {(H, H), (H, T), (T, H), (T, T)}.

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The representations of the inequality is  an open circle is at 1 and a bold line starts at 1 and is pointing to the right.

An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g. 5 < 6, x ≥ 2, etc.

Since our answer is x > 1.  An open circle will be at 1 and a bold line starts at 1 and is pointing to the right (>). Check the attached image.

Note: You only shade up if you have ≤ (less than or equal) or ≥ (greater than or equal).

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Answer:

21

Step-by-step explanation:

Answer:

1.67

Step-by-step explanation:

25/15 = 1.67

The mean is estimated by dividing the total of the values by the range of values.

Answer:

This is correct explanation

Step-by-step explanation:

A dividend is a number we want to divide by another number. It's supposed to be greater than 1000.

Quotient - the integer result of division. Remainder - well, what remains.

9/4 = 2, with remainder 1.

You want to find a number greater than 1000, which, when divided by another number, results in 37, with a remainder of 4.

I would multiply 37 by an increasing number until we get a product greater than 1000. This number is the one you are dividing by. Now add 4 to the product, so that when the sum is divided by the number you found we'll get a remainder of 4.

Answer:

194.4

Step-by-step explanation:

V=l*w*h

V=12*4.5*3.6

V=194.4

Mean = 24.47

Variance = 108.31

Standard deviation = 10.41

The probability distribution table has been attached to this response.

(1) To calculate the mean (m)

(a) First multiply each of the values of x by their corresponding probability values.

This is shown in the third column of the table.

(b) The sum of the results in the third column gives the mean of the distribution. i.e

m = ∑xP(x) = 11.52 + 9.36 + 3.15 + 0.44

m = 24.47

(2) To calculate the variance (σ²).

(a) First find the square of the difference between the values of x and the mean (m) calculated in (1b) above. i.e

(x - m)²

The result is shown in the fourth column of the table.

(b) Next, multiply each of the results in the fourth column (x - m)², by their corresponding probability values P(X = x). i.e

(x - m)²(P(X = x))

The result is shown in the fifth column of the table.

(c) Now find the variance (σ²) which is the sum of the results in the fifth column. i.e

σ² = ∑(x - m)²(P(X = x)) = 42.5411 + 0.8427 + 18.8330 + 46.0923

σ² = 108.3091

σ² = 108.31      [to 2 decimal places]

(3) To calculate the standard deviation (σ)

The standard deviation is the square root of the variance of the distribution. Calculate this by finding the square root of the result in (2c) above.

σ = √σ²

σ = \(\sqrt{108.31}\)

σ = 10.4072

σ = 10.41        [to 2 decimal places]

The slope field for the differential equation would be D . Graph D .

A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .

The length of line segments represents the magnitude, while the direction indicates the sign of the slope.

The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.

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The average number of hours that adults spend working each day is 8 hours and Ryan is correct because he got the average of 8 right.

We know that,

The sample mean is a statistic that is computed by taking the arithmetic mean of the values of a variable in a sample. If the sample is taken from probability distributions with a shared expected value, the sample mean is an estimator of that value.

The mean is gotten from the formula;

x' = ∑x/n

Number of hours of work per day are; 6, 7, 8, 9 and 10

Thus; sum up all of it

∑x = 6 + 7 + 8 + 9 + 10

∑x = 40

Mean is; x' = 40/5

x' = 8

Since Ryan concluded that the average is 8 hours,

Therefore,

We can say that Ryan is correct.

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To determine when the total cost of each health club will be the same, we can set up an equation and solve for the number of months.

Let's assume the number of months is represented by 'x'.

For Club A, the total cost is given by:

Total cost of Club A = $13 (one-time fee) + $28x (monthly fee)

For Club B, the total cost is given by:

Total cost of Club B = $19 (one-time fee) + $27x (monthly fee)

To find the number of months when the total cost is the same, we set the two equations equal to each other:

$13 + $28x = $19 + $27x

Simplifying the equation, we get:

$28x - $27x = $19 - $13

$x = 6

Therefore, after 6 months, the total cost of each health club will be the same.

To find the total cost for each club after 6 months, we substitute the value of 'x' back into the equations:

Total cost of Club A after 6 months = $13 + $28(6) = $13 + $168 = $181

Total cost of Club B after 6 months = $19 + $27(6) = $19 + $162 = $181

So, the total cost for both Club A and Club B will be $181 after 6 months.

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Answer:

B) Statistic

Step-by-step explanation:

The mean age of U.S. first ladies when they married would be a Statistic. This is because the mean age would be a specifically targeted value of the population that is being analyzed. In this scenario, the population would be all of the First Ladies, while the Sample would be the data gathered from the population under certain parameters. Statistics can be a variety of different values that revolve around the samples gathered such as average age, average height, max number of blue-eyed First Ladies, etc.

The instantaneous rate of change of y = √x at x = 2 is √2 / 2.

To find the instantaneous rate of change of y = √x at x = 2, we need to calculate the derivative of the function with respect to x and evaluate it at x = 2.

Taking the derivative of y = √x using the power rule for differentiation, we have:

dy/dx = (1/2) × x^(-1/2)

Now, substituting x = 2 into the derivative expression:

dy/dx = (1/2) × 2^(-1/2)

= (1/2) × √2

= √2 / 2

Therefore, the instantaneous rate of change of y = √x at x = 2 is √2 / 2.

None of the provided options (-1/2, -1/4, -1) are the correct instantaneous rate of change at x = 2.

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Answer:

1st option

Step-by-step explanation:

4 \(\frac{1}{3} \) ÷ 2 \(\frac{3}{5} \) ( change mixed numbers into improper fractions )

= \(\frac{13}{3} \) ÷ \(\frac{13}{5} \)

To perform the division

leave 1st fraction, change ÷ to × , turn 2nd fraction ' upside down'

= \(\frac{13}{3} \) × \(\frac{5}{13} \)

Answer:

the answer is A

\(4 \times \frac{1}{3} \div 2 \times \frac{3}{5} \\ = \frac{13}{3 } \div \frac{13}{5} \\ = \frac{13}{3} \times \frac{5}{13} \\ = \frac{5}{3} \)

Answer: he did his job fast but also very efficiently.

Step-by-step explanation:

its easy look at the word and then stop and think for a second and say hmmm in your head is it gonna be fast and then see it fast makes a good one and then the other one to just do the same thing and also i learend this in LA

The surface area of the rectangular prism is 396 square inches

He will need 504 tlles

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

7 in by 12 in by 6 in

The surface area of the rectangular prism is calculated as

Area = 2 * (7 * 12 + 7 * 6 + 12 * 6)

Evaluate

Area = 396

Hence, the area is 396 square inches

The number of tiles is 7 * 12 * 6 = 504

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Question

wants to tile the surface of a rectangular storage case that is 7 inches​ long, 12 inches​ wide, and 6 inches tall. If he uses all green​ tiles, how many tiles will he​ need?

-17/8

Step-by-step explanation:

10( x + 1) = 2 x-7

10x + 10 = 2x - 7

10 + 7 = 2x - 10x

17 = - 8x

x = -17 /8

Answer:

Hiya There....!!!

______________________

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

Decimal Form:

x  =  − 2.125

Mixed Number Form:

x  =  − 2/ 1 8

_______________________

“To forgive is wisdom, to forget is genius. And easier. Because it's true. It's a new world every heart beat.”

― Joyce Cary, The Horse's Mouth

__________________________

Think of life as a mytery because well it sort of is! You don't know what may happen may be good or bad but be a little curious and get ready for whatever comes your way!! ~Ashlynn

Answer:

$30,000 (at 3%) and $27,000 (at 2 7/8%)

Explanation:

The investor invested a total of 57000

• Let the amount invested at 3% simple interest = x

• Then, the amount invested at 2 7/8% simple interest = 57000-x

Recall the formula for simple interest:

Interest at 3%

Interest at 2 7/8%

Total Interest

The investor earned a total of $1676.25 in annual interest. Therefore:

Thus, the amount invested at 3% simple interest = $30,000

The amount invested at 2 7/8% simple interest = 57,000-30,000 = $27,000

a. The graph represents a proportional relationship.

b. The graph does not represent a proportional relationship.

c. The graph does not represent a proportional relationship.

d. The graph represents a proportional relationship.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable exists.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero presented as follows:

y = kx.

Hence graphs a and d represent proportional relationship, as they have intercepts at the origin.

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