Adding and subtracting rational expressions, What is the difference? 2x+5/x^2-3x - 3x+5/x^3-9x - x+1/x^2-9?

Answer:B

Step-by-step explanation:

R^2=Q^2-P^2

R^2=2025

R=45

Answer:

b) 45cm

Step-by-step explanation:

by pythagoras theorem:

R² = P² - Q²

R² = 53² - 28² = 2809 - 784

R² = 2025

R = √2025

R = 45cm

Hope this helps!

Answer:

∠ B = 121°

Step-by-step explanation:

ABCD is a cyclic quadrilateral

• opposite angles sum to 180°

∠ B and ∠ D are opposite angles , then

∠ B + 59° = 180° ( subtract 59° from both sides )

∠ B = 121°

The sum of the 10th terms of the geometric progression is 1023

The sum of the terms of a geometric progression (GP) is a formula used to find the total of a series of numbers that are increasing or decreasing by a common ratio. A geometric progression is a sequence of numbers such that the ratio of any two consecutive terms is constant.

The formula for the sum of the n terms of a geometric progression with first term a and common ratio r is given by:

Sₙ = a(rⁿ - 1) / r - 1

where:

a is the first term of the progression

r is the common ratio

n is the number of terms in the progression

In the problem given;

a = 1, n = 10, r = 2

Using the formula above;

Sₙ = a(rⁿ - 1) / r - 1

Substituting the values into the formula

S₁₀ = 1(2¹⁰ - 1) / 2 - 1

S₁₀ = 1023

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there are 10 short answer questions on the test, we get this answer after solving.

Let's assume that the number of multiple choice questions on the test is "m", and the number of short answer questions is "s".

From the given information, we can set up a system of equations:

m + s = 30 (The total number of questions on the test is 30)

1m + 3s = 50 (The total number of points on the test is 50)

To solve for "s", we can use the first equation to find "m" in terms of "s":

m = 30 - s

Then we can substitute this expression for "m" into the second equation:

1(30 - s) + 3s = 50

Simplifying and solving for "s", we get:

30 - s + 3s = 50

2s = 20

s = 10

Therefore, there are 10 short answer questions on the test.

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Complete Question

Diego’s history teacher writes a test for the class with 30 question. The test is worth 50 points and has two types of questions: multiple choice worth 1 points each, and short answer problems worth 3 points each. How many short answer questions are in the test? Explain or show you reasoning.

How to construct the right-angled triangle with a base of 6 cm and a hypotenuse of 11 cm.

Given:

To find:

Construct a right-angle triangle DEF

The constructed right-angle triangle DEF is given below:

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Answer:

348.75

Step-by-step explanation:

The number of students attended the play are 400 in number.

Two or more expressions with an Equal sign is called as Equation.

At a local play, student tickets cost $5 each and adult tickets cost $10 each. If ticket sales were $3,000

5x+10y=3000

The total number of tickets are 500

x+y=500

y=500-x

Now plug this in above equation

5x+10(500-x)=3000

5x+5000-10x=3000

5000-5x=3000

Add 5x on both sides

5000-3000=5x

2000=5x

Divide both sides by 5

400=x

Hence, the number of students attended the play are 400 in number.

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The boat will coast approximately 16752.9 feet (or about 3.17 miles) in the first 2 minutes after its motor quits.

From the problem statement, we know that the velocity of the boat, v, changes from 83 ft/s to 23 ft/s over a period of 1 second. Therefore, we can write:

[tex]dv/dt = -k v^2[/tex]

Separating variables and integrating from v = 83 at t = 0 to v = 23 at t = 1, we get:

[tex]∫83^23 dv / v^2 = ∫0^1 -k dt[/tex]

=> [1/83 - 1/23] = k

So the equation for the velocity of the boat as it coasts is:

[tex]dv/dt = -[(1/83 - 1/23)] v^2[/tex]

The differential equation is separable:

[tex]dv/v^2 = -[(1/83 - 1/23)] dt[/tex]

Integrating both sides, we get:

-1/v = [(1/83 - 1/23)] t + C

where C is an integration constant. Using the initial condition v(0) = 83, we get:

C = -1/83

Substituting this back, we have:

-1/v = [(1/83 - 1/23)] t - 1/83

Solving for v, we have:

v(t) = 83 / [1 + (83/23 - 1) t]

To find the distance traveled, we integrate v(t) from t = 0 to t = 120:

s =[tex]∫0^120 v(t) dt[/tex]

Substituting v(t) and simplifying, we have:

s = 23 ln(1 + 3.6087t) + 60.391t + C

where C is another integration constant. Using the initial condition s(0) = 0, we get:

C = 0

Therefore, the distance traveled by the boat in the first 2 minutes after its motor quits is:

s = 23 ln(1 + 3.6087t) + 60.391t

Evaluating this expression at t = 120 seconds, we get:

s = 23 ln(433.044) + 7246.92 ≈ 16752.9 ft

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The expression that represents all the possible widths of the rectangle is given as follows:

0 < x < 5.

The area of a rectangle of length l and width w is given by the multiplication of these dimensions, as follows:

A = lw.

For this problem, the length is 5 meters more than five times the width, hence:

l = 5 + 5w.

Hence the area is given as follows:

A = w(5 + 5w)

A = 5w² + 5w.

The area is less than 100m², hence the inequality is given as follows:

5w² + 5w < 100

5w² + 5w - 100 < 0.

w² + w - 20 < 0.

(w + 5)(w - 4) < 0.

Hence the solutions are:

The width cannot be negative, hence the interval is:

0 < x < 5.

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To determine how many dollars a restaurant makes per day, the restaurateur would need to measure the "revenue" metric.

Revenue is the total amount of money a business earns from its sales or services provided over a specific period of time, in this case, daily. It includes all income generated by the restaurant from selling food and drinks to customers.

Measuring revenue is essential for any business as it helps the owner understand the financial health of their enterprise. By tracking revenue over time, the restaurateur can identify patterns and trends and make informed decisions to increase profits and improve the business's overall performance.

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The statement is True ' The height of a supply curve at a quantity of 100 represents the minimum price required to induce a producer to supply the hundredth unit"

A supply curve: what is it?

The relationship between the quantity of a good that a producer is willing to sell and the price of the good is graphically represented by the supply curve in economics.

The maximum price a producer will accept to sell a given quantity of the good is represented by the height of the supply curve at that quantity.

As a result, the minimum price necessary to persuade a producer to supply the 100th unit of the good is represented by the height of the supply curve at a quantity of 100.

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In a density curve, the proportion of data is represented by the option B) area under the curve and correct classification of shapes of density curves is option E)

A density curve is a curve on a graph that represents the distribution of values in a dataset.

A density curve, also called a density function, is a graphical representation of the relative frequency distribution of a continuous random variable. The type of distribution most commonly represented by a density curve is the normal distribution, but any distribution of a continuous variable may be represented by a density curve.

Normal distribution curve is a bell shaped curve obtained for the distribution having maximum frequency near the central value of distribution and the frequency gradually tapering off symmetrically on both side.so, All → Symmetric → Bell → Normal

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The coordinates of the other endpoint are (17, 3).

In order to determine the midpoint of a line segment with two (2) endpoints, we would add each point together and then divide by two (2):

Midpoint R = [(x₁ + x₂)/2, (y₁ + y₂)/2]

Next, we would determine the coordinate of MP with midpoint M at (7, 3) as follows;

12 = (7 + x₂)/2

24 = 7 + x₂

x₂ = 24 - 7

x₂ = 17.

For the other co-ordinate of P on line segment MP, we have:

3 = (3 + y₂)/2

6 = 3 + y₂

y₂ = 6 - 3

y₂= 3.

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The two plans cost the same for 60 minutes of calls. And  the two plans cost the same for 60 minutes of calls.

We can set the cost of the two plans equal to each other and solve for the number of minutes:

Plan A: $15 + $0.12x (where x is the number of minutes)

Plan B: $8 + $0.17x

$15 + $0.12x = $8 + $0.17x

Subtracting $8 from both sides:

$7 + $0.12x = $0.17x

Subtracting $0.12x from both sides:

$7 = -0.05x + $0.17x

Adding 0.05x to both sides:

$7 + 0.05x = $0.17x

Dividing both sides by 0.12:

x = (7 / 0.12) / (1 - 0.17/0.12) = 60 minutes

So the two plans cost the same for 60 minutes of calls. To find the cost, we can plug x = 60 into either equation:

Plan A: $15 + $0.12 x 60 = $15 + $7.20 = $22.20

Plan B: $8 + $0.17 x 60 = $8 + $10.20 = $18.20

So the two plans cost the same when there are 60 minutes of calls, and they both cost $18.20

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Complete Question

A telephone company offers two monthly plans. The a plan costs $15 plus $0. 12 additional for each minute of calls. Plan b costs $8 plus an additional 0.17 for each minute of calls For how many minutes of calls do the two plans cost the same? What is the cost at which two plans cost the same?

The expected number of rolls is 12.The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2.

The probability of rolling an even number on a fair, 6-sided die is 3/6, or 1/2. Therefore, the expected number of rolls can be calculated by multiplying the probability of rolling an even number (1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 12.

The expected number of rolls to get a specific result on a fair die can be calculated by multiplying the probability of achieving that result by the number of sides on the die. For example, if you wanted to know the expected number of rolls to get an odd number on a fair, 6-sided die, you would multiply the probability of rolling an odd number (3/6, or 1/2) by the number of sides on the die (6). In this case, 1/2 x 6 = 3. The same calculation could be applied to determine the expected number of rolls to get a specific number (e.g. a 4) on a fair, 6-sided die. The probability of rolling a 4 would be 1/6, and the expected number of rolls to get a 4 would be 1/6 x 6 = 6.

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The probability that an incoming call is for firefighting equipment (or any other reason besides medical assistance) is 0.33 or 33%.

The statement "the probability that an incoming call is for medical assistance is 0.67" can be expressed as:

P(Medical Assistance) = 0.67

This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.67 or 67%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:

P(Not Medical Assistance) = 1 - P(Medical Assistance) = 1 - 0.67 = 0.33

In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability

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The value of m for which the parallelogram WXYZ will be a square is (a) 2 .

For the parallelogram WXYZ to be a square ,

We know that , if parallelogram WXYZ is a square all, then all the sides are equal ;

So , we write WX = XY = YZ = ZW ;

To find the value of "m" , we use WX = ZW ;

substituting the values of sides of square from the figure ,

we get ;

⇒ 2m + 4 = m + 6 ;

⇒ 2m - m = 6 - 4 ;

⇒ m = 2 ;

Therefore , the value of "m" for the square WXYZ is 2 .

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The given question is incomplete , the complete question is

What value of m would make parallelogram WXYZ a square ?

(a) 2

(b) 3

(c) 4

(d) 5

Beth's rate of travel is 2.2 meters per second and Amy's line is steeper

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

The table of values

See attachment for the graph

From the graph, we have

Beth's rate of travel = 2.2 meters per second

This is so because from the graph:

As x increases by 1. y increases by 2/2

Here, we have

Amy's rate of travel = 75/30 meters per second

Evaluate

Amy's rate of travel = 2.5 meters per second

The higher the rate, the steeper the line

This means that Amy's line is steeper

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We can rewrite ln(27000) in terms of ln(5) and ln(6) as ln(27000) = 3ln(5) + 3ln(6) by using logarithmic property.

Due of their connection to exponential functions, logarithmic functions are crucial. Logarithms can be used to examine exponential equations and the properties of exponential functions.

We can use the logarithmic property that says:

log_a(xⁿ) = n×log_a(x)

to break down 27000 into factors that involve 5 and 6.

First, we can write:

27000 = 5³× 6³

When we take the natural logarithm of both sides, we obtain:

ln(27000) = ln(5³ × 6³)

Using the property above, we can simplify this expression as:

ln(27000) = ln(5³) + ln(6³)

Using another logarithmic property that says:

log_a(bⁿ) = c×log_a(b)

we can further simplify the expression:

ln(27000) = 3ln(5) + 3ln(6)

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Solving the equation: x - 1/x = 15/13

We will see that the value of x is 28/13

For a number x, we define the reciprocal number as 1/x.

We know that the difference between theses two is 15/13, then we can write:

x - 1/x = 15/13

(x² - x)/x = 15/13

(x² - x) = (15/13)*x

x² - x - (15/13)*x = 0

x² - (1 + 15/13)*x = 0

x² - (28/13)*x = 0

x*(x - 28/13) = 0

x = 0 is not a solution, because 1/x exists, then the solution is x = 28/13.

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The solution that will satisfy the linear inequality y ≥ x + 4 include the following:

2. (-1, 4).

4. (0, 4).

In order to determine which ordered pairs are valid and true solutions based on the given linear inequality, we would have to test the given ordered pairs by substituting their values into the linear inequality as follows;

For ordered pair (0, 0), we have:

y ≥ x + 4

0 ≥ 0 + 4

0 ≥ 4 (False).

For ordered pair (-1, 4), we have:

y ≥ x + 4

4 ≥ -1 + 4

4 ≥ 3 (True).

For ordered pair (2, 3), we have:

y ≥ x + 4

3 ≥ 2 + 4

3 ≥ 6 (False).

For ordered pair (0, 4), we have:

y ≥ x + 4

4 ≥ 0 + 4

4 ≥ 4 (True).

For ordered pair (-1, 4), we have:

y ≥ x + 4

0 ≥ -1 + 4

0 ≥ 3 (False).

In this exercise, we would use an online graphing calculator to plot the given system of inequalities 2x + y < 1 and 4x - 3y ≥ 12 as shown on the number line attached below.

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the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).

Assuming that the state narcotics bureau has more than 5 agents from which to choose, the number of different possible teams that can be formed is equal to the number of combinations of 5 agents out of the total number of agents the bureau has. This can be calculated using the formula nCr (n choose r), where n is the total number of agents and r is the number of agents in each team, which in this case is 5.

Therefore, the number of different possible teams that can be formed is equal to nCr, or n!/(r!(n-r)!).

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Answer:

Step-by-step explanation:

the probability of drawing a face card=12/52

drawing the king of diamonds=1/52

Answer:

Probability of face is 12/52

The value of the variable T is 60

These are described as expressions that are composed of coefficients, factors, constants, variables and terms.

These algebraic expressions are also identified by mathematical or arithmetic operations, such as;

We have;

T= 3db

Substitute the values

T = 3(4)(5)

expand

T = 60

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All the numbers less than -10 and upto negative infinity will make the mentioned statement true.

Let us assume the number to be x. So, twice the number will be 2x. Then, nine more will be represented as: 2x + 9. Now, the total is less than -11, so representing the information in expression along with sign.

2x + 9 < - 11

Rewriting the expression according to 2x

2x < - 11 - 9

Performing subtraction on Right Hand Side of the equation

2x < - 20

x < - 20/2

Performing division on Right Hand Side of the equation

x < - 10

So, the numbers below -10 will make the statement true.

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The two correct statements are a. The rate of change is 3 over the interval 1 ≤ x ≤ 2 & The rate of change is 3 over the interval 1 ≤ x ≤ 3. And as well as The rate of change is 5 over the interval 2 ≤ x ≤ 3 is also correct statement.

Divide the change in y-values by its change in x-values to determine the average rate of change. Identifying changes in measurable parameters as average speed or mean velocity calls for the knowledge of the average rate of change.

The average rate is the concentration change over a selected time period. It matters when you take the measurements. The solution is to find the slopes of the line to the concentrations time versus curve at that location.

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The perimeter of the rectangle is 2ab² ( 5ab² + 3)

The area of the rectangle is 15a³b^6

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let l=5a²b^4  ,   w= 3ab²

Perimeter = 2(l+w)

                 = 2(5a²b^4 + 3ab² )

                 =2 [ ab² ( 5ab² + 3)]

                 = 2ab² ( 5ab² + 3)

Area = l*w

        =  5a²b^4 *3ab²

        = 15a³b^6

The perimeter of the rectangle is 2ab² ( 5ab² + 3)

The area of the rectangle is 15a³b^6

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Answer:

17 people surveyed own a cat.

Step-by-step explanation:

Let d stand for dog, c stand for cat, and b stand for both. In total, d + c + b = 100 people. The number of people who own a dog is four times the number of people who own a cat, so d = 4c. In the problem, it's given that 15 people own both a dog and a cat. So, b can be replaced with 15. Now, d + c + 15 = 100. This system of equations can be solved by substitution.

d = 4c

d + c + 15 = 100

4c + c + 15 = 100

5c + 15 = 100

5c = 85

c = 17

Check:

The number of dog owners is 4 * 17, or 68.

68 + 17 + 15 = 100

The letter grades (A, B, C, D, F) for business analysis students are categories that represent different levels of achievement, so the variable's classification is (b) Categorical Data.

The Categorical data are defined as the variables that represent characteristics or attributes, and they are often expressed as labels or categories.

The Quantitative data, on the other hand, are  the numerical values which  represent measurements or quantities.

Since the letter grades are not numerical values and do not represent a measurement or quantity, they cannot be classified as quantitative data.

Therefore , the letter grades represents a Categorical Variables .

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The given question is incomplete , the complete question is

The letter grades (A, B, C, D, F) of business analysis students are recorded by a professor. this variable's classification .

(a) is time series data

(b) is categorical data

(c) is quantitative data

(d) cannot be determined