Part of a book fell out. The first page of this part has number 143. The last page has a number written with the same digits. How many pages are in the part of the book which has fallen out?

The least common denominator (LCD) of the rational expressions is (x+1)(x-1).

When adding or subtracting rational expressions, we need to find a common denominator. The least common denominator (LCD) is the smallest multiple of the denominators of the rational expressions.

To find the LCD, we follow these steps:

Let's consider an example to illustrate this process:

Example:

Find the LCD of the rational expressions:

x/(x+1) and 1/(x-1)

Step 1: Factor the denominators:

x+1 and x-1

Step 2: Identify the common factors:

There are no common factors in this case.

Step 3: Take the product of the highest powers of each common factor:

Since there are no common factors, we skip this step.

Step 4: Include any unique factors:

The unique factors are x+1 and x-1.

Step 5: Simplify the resulting expression:

The LCD is (x+1)(x-1).

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The least common denominator of the rational expressions in this problem is given as follows:

4x(x + 5).

The rational expressions for this problem are defined as follows:

9/(4x + 20), 10/(x² + 5x).

The denominators are given as follows:

The denominators can be simplified as follows:

The least common denominator is the multiplication of the unique factors, hence it is given as follows:

4x(x + 5).

The expression that completes this problem is given as follows:

9/(4x + 20), 10/(x² + 5x).

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The formula for the estimator of the slope in a simple linear regression model, when the intercept is known to be 0, can be derived as follows: β = Σ(xi * yi) / Σ(xi^2)

In a simple linear regression model, we aim to find the equation of a straight line that best fits the relationship between two variables: the independent variable (x) and the dependent variable (y). When the intercept is known to be 0, it means that the line passes through the origin (0, 0).

To estimate the slope (β) of this line using the Ordinary Least Squares (OLS) method, we need to minimize the sum of squared differences between the observed y-values and the predicted y-values on the line.

We start by calculating the sum of the product of each x-value (xi) and its corresponding y-value (yi). This is represented as Σ(xi * yi). Next, we calculate the sum of the squares of each x-value, represented as Σ(xi^2).

The estimator of the slope (β) is then derived by dividing the sum of the product Σ(xi * yi) by the sum of the squares Σ(xi^2):

β = Σ(xi * yi) / Σ(xi^2)

This formula provides an estimate of the slope in the simple linear regression model when the intercept is 0, allowing us to quantify the relationship between the independent and dependent variables.

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Answer:

(x,y)(3x,3y)

Step-by-step explanation:

Similar means same shape (the ratios of the lengths of their corresponding sides are equal).

So the 3rd option, everything is multiplied by 3, both x and y.

So pick (x,y)(3x,3y)

Answer:

2

Step-by-step explanation:

-2^2=4

4*1/2=2

Answer:

Step-by-step explanation

ayo so basically this is a pythagorus theorum question

the formula is

c²= a² + b²

where c is the hypotenuse (the longest line , opposite of the right angle aka here 13ft !!)

a and b ,  where a  is the down line as a (4ft ) and b the unknown one

(just remember and lookout for the hypotenuse!)

so now put the numbers in formula

(13)²= (4)² +(b)²

169= 16 +(b)²

169-16=(b)²

153= (b)²

(put b first )

(b)² = 153

√(b)²= √153

(the square gets cut with the square root)

b= 12.36931688

b+12.4

Step-by-step explanation:

here

27/-9

=-3

so X>-3

now you can calculate

Answer:

x > -3; x is any number more than -3.

Step-by-step explanation:

-9 x > 27

x > 27÷-9

x > -3

Answer:

Yes, according to the angles and sides of the hills

Answer:

Answers

1.  40o, obtuse

2.  90o, right

3.  scalene

4a.  equilateral

4b.  isosceles

4c.  scalene

5.  An acute triangle has 3 acute angles, not just 1.  The figure contains a right angle and is therefore a right triangle.

6.  obtuse

7.  58o, acute

8.  Yes, because the measures add up to 180o.

9.  C

10.  The triangle would be isosceles, because isosceles triangles have two sides the same length.

Step-by-step explanation:

Therefore, the solution to the equation 2/3x + 5 = 1/5 - 2x is x = -9/5.

Describe a formula. To create the expression known as an equation, two sides are connected by the equals symbol (=). The variables in the equation 2x+1 = 9 are 2x+1 on the left and 9 on the right (RHS).

To simplify the equation 2/3x + 5 = 1/5 - 2x, we can start by getting rid of the fractions. To do this, we can multiply every term in the equation by the least common multiple (LCM) of the denominators of the fractions, which is 15.

So, we have:

15 * (2/3x + 5) = 15 * (1/5 - 2x)

Expanding the left-hand side, we get:

10x + 75 = 3 - 30x

Bringing all the x terms to one side and all the constant terms to the other, we get:

10x + 30x = 3 - 75

Combining like terms, we get:

40x = -72

Dividing both sides by 40, we get:

x = -72/40 = -9/5

Therefore, the solution to the equation 2/3x + 5 = 1/5 - 2x is x = -9/5.

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Camillo should buy 60 containers of the 40-oz size, and the total cost of those containers would be $744.00.

To calculate the size of the container Camillo should buy, we need to find a container size that can accommodate the required 2,400 oz of peanut butter.

By comparing the given container sizes, we can see that the 40-oz container is the largest one available. As Camillo needs 2,400 oz of peanut butter, he would need to purchase multiple containers.

To find out how many of those containers Camillo will need, we can divide the total amount of peanut butter needed (2,400 oz) by the size of each container (40 oz). This gives us:

Number of containers = Total amount needed / Size of each container

Number of containers = 2,400 oz / 40 oz

Number of containers = 60 containers

So Camillo would need to buy 60 of the 40-oz containers to meet his requirement.

To calculate the total cost of those containers, we need to multiply the number of containers (60) by the price of each container. The price for each 40-oz container is $12.40. Therefore:

Total cost = Number of containers * Price per container

Total cost = 60 containers * $12.40

Total cost = $744.00

Hence, the total cost of the 60 containers would be $744.00.

In summary, Camillo should buy 60 containers of the 40-oz size, and the total cost of those containers would be $744.00.

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Complete Question

Camillo needs 2,400 oz of peanut butter.

What size container should Camillo buy?

How many of those containers will he need?

What will be the total cost of those containers?

Container Size    Price          Unit Price

12-oz                   $2.52           $0.21/oz

16-oz                   $4.00           $0.25/oz

32-oz                  $5.12             $0.16/oz

40-oz                  $12.40           $0.31/oz

The solutions to the equation are x = -1, x = -8, and x = 1/2.

The equation 4x³ + 32x² + 42x - 16 = 0 can be divided throuh by 2 as follows:

2x³ + 16x² + 21x - 8 = 0

We can test each of these possible roots by substituting them into the equation and seeing if we get 0. When we substitute -1, we get 0, so -1 is a root of the equation. We can then factor out (x + 1) from the equation to get:

(x + 1)(2x² + 15x - 8) = 0

We can then factor the quadratic 2x² + 15x - 8 by grouping to get:

(x + 8)(2x - 1) = 0

This gives us two more roots, x = -8 and x = 1/2.

Therefore, the solutions to the equation are x = -1, x = -8, and x = 1/2.

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Answer: 99m

Step-by-step explanation:

To satisfy the given conditions, the projection of vector *w onto *u and *v must be equal to h1, 2, 0i.

Let *u = h1, 0, 0i and *v = h0, 1, 0i. These are two different nonzero vectors in R3. To find the third vector *w, we can consider a vector that has h1, 2, 0i as its projection onto *u and *v.
We can use the projection formula: proj*u(*w) = ((*w · *u) / (||*u||^2)) * *u and proj*v(*w) = ((*w · *v) / (||*v||^2)) * *v.
Since proj*w*u = proj*w*v = h1, 2, 0i, we can choose *w = h1, 2, k] with k being a nonzero value. Let k = 1.
Thus, the three different nonzero vectors in R3 that satisfy the given conditions are *u = h1, 0, 0i, *v = h0, 1, 0i, and *w = h1, 2, 1i.

Let the three vectors be *u, *v, and *w. We are given that proj*w*u = proj*w*v = h1,2,0i.proj*w*u = proj*w*v = h1,2,0i.Thus, *u and *v must have the same component in the direction of *w. Thus, *v must be a scalar multiple of *u.Now, let's assume *u = h1,0,0i and *w = h0,1,0i. We have proj*w*u = h0,0,0i and proj*w*v = h1,2,0i, so we need *v to be a scalar multiple of h1,0,0i that has a component in the direction of *w. The simplest vector that fits this description is h1,1,0i.Thus, we have *u = h1,0,0i, *v = h1,1,0i, and *w = h0,1,0i as three different nonzero vectors that satisfy the given condition.

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Answer:

4, 7, 8 and 9.

(4)(7)(8)(9)

= 4 × 7 × 8 × 9

= 2016

Verify it on a calculator for your satisfaction ☺

Hope that helps...

Answer:

B

Step-by-step explanation:

It has two or more terms.

Explanation:

The graph of the linear equation y = -1/3x, aka y = -x/3, goes through the points (0,0) and (3,-1). To generate any point, plug in a value for x to get its paired value of y.

Another way to graph this line is to start at (0,0). Then move down 1 and over to the right 3 units to arrive at (3,-1). Draw a straight line through those points.

The graph is shown in the diagram below. Points B, C, F, H, J are all below that red line.

Wouldnt the answer be anything above 12? Because if Y is unknown, and you're taking 2 away from it, and it still has to be greater than 10, then it should be anything above 12. Unless it's saying that the number is greater than 10, and you are just taking away 2 from a number and it doesn't have to be greater than 10.

Yes, we should conduct a Chi-Square test for independence on this data since the data is categorical on both variables.

The best thing to do with regards to Political Views would be to combine the "very liberal" with "liberal" and the "very conservative" with "conservative".

The best thing to do with regards to ThriftShop would be to combine the "regularly" with "sometimes" since they both represent some level of shopping at thrift stores.

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The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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Answer:

  D.  1/2

Step-by-step explanation:

Given the side adjacent to an angle is 25 and the tangent of the angle is 1/5, you want to know the tangent of an angle with the same opposite side, but an adjacent side of 10.

The tangent of an angle is the ratio of the opposite side to the adjacent side.

  Tan = Opposite/Adjacent

Then the Opposite side is ...

  Opposite = Adjacent · Tan(x) = 25·1/5 = 5

For angle y, the opposite side is the same, but the adjacent side is only 10:

  Tan(y) = Opposite/Adjacent = 5/10

  tan(y) = 1/2

Answers:

=====================================================

Explanation:

The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that \(-4 < x \le 3\). It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).

The interval \(-4 < x \le 3\) then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.

It says: x is between -4 and 3. It can't equal -4 but it can equal 3.

So the use of parenthesis versus square brackets tells the reader which endpoint is included or not.

--------------------------------------------------

The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.

The range as a compound inequality is \(-5 < y \le 5\). This condenses into the shorthand of (-5, 5] which is the range in interval notation.

Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.

Answer:

Hello,

Step-by-step explanation:

Domain(f)= ]-4;3]={x€R | -4<x≤3}

Rang(f)=]-5;5]={y€R | -5< y ≤5}

Answer:

X= 200 * 18 /120 = 30

Step-by-step explanation:

Please Brainlist

Step-by-step explanation:

refer the above attachment

thankyou

The teacher's goal in introducing students to a card game where they must find the missing addend could be to develop and enhance their algebraic reasoning skills.

By presenting the problem as a puzzle or game, the teacher aims to engage the students in a fun and interactive way while fostering their ability to think critically and solve mathematical problems. The game helps students practice identifying the missing addend and applying algebraic thinking to find the solution. Additionally, it promotes the development of problem-solving strategies, logical reasoning, and the ability to generalize mathematical patterns, which are foundational skills in algebraic reasoning.

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Answer:

Left box:  1/2n

Right box = 2n - 22

Step-by-step explanation:

Since we want one-half the number and n represents the unknown number, we have 1/2n on the left-hand side of the equation.

Thus, you want to put 1/2n in box on the left.

Twice the number and 22 less than this is given by:  y: 2n - 22 less than this means we subtract.  Thus, we have 2n - 22 as the numerator on the right hand side of the equation.

Thus, you want to put 2n - 22 in the box on the right.

Answer:

Each crust is 1.2 inches

Step-by-step explanation:

12/10 is 1.2

Answer:

Each crust is 1.2 inches.

Step-by-step explanation:

12 ÷ 10 = 1.2

Hope this Helped! HAVE A GOOD DAY!!!!!!!!!!

Answer:

We have the proportion: 8/10 = 100/y

We can solve for y by cross-multiplying.

That is, 8y = 100 * 10 Simplifying the right-hand side, 8y = 1000

Dividing both sides by 8 to solve for y, y = 125

Hence, the value of y is 125.

Finally, we have the expression: y = √80We can simplify this expression by factoring 80 into its prime factors:80 = 2 * 2 * 2 * 2 * 5

Taking the square root of 2 * 2 * 2 * 2, we have:√(2 * 2 * 2 * 2) = 2 * 2 = 4

Therefore, y = 4√5The value of y is 4√5.

Step-by-step explanation:

Hope this helps!! Have a good day/night!!

Answer:

0 + m = m

Step-by-step explanation:

If we add zero to any number, the number does not change.

From statement equation, the number of correct answers will result in a passing grade is 9.3

Given that each question on the quiz is worth 8 points.

Also given a score of 75 is a passing grade.

Let the number of correct answered questions be x

Thus the total score of the correct answers is 8x

The statement equation is -

⇒ 8x = 75

⇒ x = 75/8 = 9.3

∴  x ≈ 9

Therefore, from statement equation, the number of correct answers will result in a passing grade is 9.3

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Answer:

23

explain:

230/300 = 77%

^^

That is how much she predicted

We have to subtract 77% from 100% to find out how much she missed

100- 77 = 23