(Written assignment) A student was asked to simplify the following rational expression:
(x^2+3x+2)/(x^2+6x+8)
Here is the student’s work, in which the expression was simplified incorrectly:
Questions for thought:
1. Please explain the student’s mistake and why it is incorrect.
2.This type of mistake is common in Algebra, why do you think it is so common?
3.Have you ever made a mistake like this?
4. If you have made a mistake like the one shown above, what helped make you stop making this mistake?
5.What advice would you give future Algebra 2 students to help stop them from making mistakes like this?
You do not have to answer all the questions in your response. As long as your answer has AT LEAST FIVE (5) COMPLETE SENTENCES you will get brainliest

The values of h and k are h=7 and k=46. The equation in the form (x+h)^(2)=k is (x+7)^(2)=46.

To solve the equation x^(2)+14x+3=0 by completing the square method, we need to follow these steps:

1. Rearrange the equation so that the constant term is on the right side: x^(2)+14x=-3

2. Find the value of h by taking half of the coefficient of the x term: h=14/2=7

3. Add the square of h to both sides of the equation: x^(2)+14x+7^(2)=-3+7^(2)

4. Simplify the right side of the equation: x^(2)+14x+49=46

5. Write the left side of the equation in the form (x+h)^(2): (x+7)^(2)=46

Therefore, the values of h and k are h=7 and k=46. The equation in the form (x+h)^(2)=k is (x+7)^(2)=46.

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To set up the equation and solve for the 2 consecutive odd integers whose product is 195, we can follow these steps:

1. Let x be the first odd integer. 2.The next consecutive odd integer will be x+2. 3.The product of these two integers is 195, so we can set up the equation: x(x+2) = 195 4.Expand the equation: x^2 + 2x = 195

5.Rearrange the equation to get a quadratic equation: x^2 + 2x - 195 = 0 6. Use the quadratic formula to solve for x: x = (-2 ± √(2^2 - 4(1)(-195)))/(2(1)) 7. Simplify the equation: x = (-2 ± √784)/2 8. Solve for the two possible values of x: x = (-2 + 28)/2 or x = (-2 - 28)/2 9. Simplify the equations: x = 13 or x = -15 10. Since x is an odd integer, we can reject the solution x = -15. 11. The first odd integer is x = 13, and the next consecutive odd integer is x+2 = 15.

12. Therefore, the two consecutive odd integers whose product is 195 are 13 and 15.

The final answer is 13 and 15.

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Answer: 216

Step-by-step explanation:

Equation:

270 x 80% = large buttons

To multiply by a percent, move the decimal to the left two places:

270 x 0.80 = large buttons

Solve:

270 x 0.80 = 216

Janet got 216 large buttons

Hope this helps!

The values of x and y are 100 and 40, respectively

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

The circle

On the circle, we have the following congruent angles

ADC and ABC

Using the above as a guide, we have the following:

x = 100

The sum of angles in a triangle is 180

So, we have

y + y + x = 180

This gives

2y + 100 = 180

So, we have

y = 40

Hence, the value of y is 40

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Answer:

The answer for 17x10^8 is 1,700,000,000 and the answer for 4x10^8 is 400,000,000

subtract them.

Hope that helps you out!

Answer:

y = -3/2x + 6

Step-by-step explanation:

Slope m = (y2 - y1)/(x2 - x1)

m = (6 - 0)/(0 - 4) = 6/-4 = -3/2

Slope-intercept form is y = mx + b

Substitue m = -3/2, y = 0, x = 4

0 = -3/2(4) + b

b = 6

y = -3/2x + 6

[2x^(2) + 7x + 6 = 0] has C. two real solutions

The quadratic equation 2[tex]x^{(2)}[/tex] + 7x + 6 = 0 has two real solutions. To solve, use the Quadratic Formula:

x = [-b ± √([tex]b^{2}[/tex] - 4ac)]/2a  

Where a = 2, b = 7, and c = 6.

So, x = [-7 ± √([tex]7^{2}[/tex]- 4(2)(6))]/2(2)  

x = [-7 ± √(49 - 48)]/4  

x = [-7 ± 1]/4  

x = -3/2 and x = 1/2  


Therefore, the equation has two real solutions: x = -3/2 and x = 1/2.

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The length of the segment indicated is 10.6.

Pythagoras discovered that the square of the hypotenuse in a right-angled triangle with a 90° angle is equal to the sum of the squares of the other two sides.

The triangle has three sides: the hypotenuse, which is always the longest, the opposite, which doesn't touch the hypotenuse, and the adjacent (which is between the opposite and the hypotenuse).

By Pythagoras' theorem;

a² + b² = c²

a= 16.4

b= 12.5

c =?

16.4² +  12.5² = c²

c² =  268.96 - 156.25 = 112.4

c² = 112.4

c = √112.4

c= 10.6

Therefore, the length of the segment indicated is 10.6.

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The events in terms of whether they are complimentary or not are:

The probability that it will not rain tomorrow is 2 / 3.

In probability theory, complementary events are two events that together cover all possible outcomes, meaning that if one event occurs, the other cannot occur. For example, in part (a) of the question, the events of getting an even number and getting an odd number when rolling a die are mutually exclusive, meaning that they cannot happen at the same time.

In part (b), the events of getting a prime number and getting an even number when rolling a die are not complementary events because the number 2 is both prime and even.

In parts (c) through (g), the events listed are complementary events. For example, in part (c), the events of all students attending class and no students attending class cover all possible outcomes, and only one of them can happen at a time.

If the probability of rain tomorrow is 1/3, the probability of no rain tomorrow is:

P(not raining) = 1 - P(raining)

P(not raining) = 1 - 1/3

P(not raining) = 2/3

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Number of students that selected the elective subject of religion in 2014 is 1344

The problem tells us that in 2013, there were 1400 students who selected the elective subject of religion.

Then, in 2014, this figure decreased by 4%. This means that the new figure in 2014 will be 4 percentage less than the figure in 2013.

To calculate what 4% of 1400 is, we need to multiply 1400 by 4/100, which gives us 56. So, 56 students did not select the elective subject of religion in 2014 compared to 2013.

So, the number of students who selected the elective subject of religion in 2014 is

= 1400 - 56

= 1344

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They will be 72 km far apart after 2 hours. The solution has been obtained by using the concept of relative speed.

The speed of a moving body relative to another might be referred to as relative speed. The differential between two moving bodies is used to calculate their relative speed. Yet, the relative speed of two bodies travelling in opposition to one another is determined by summing their respective speeds.

We are given that the Serenity and the Mystic travels in the opposite direction at 16 mph and at 20 mph respectively.

So,

The relative speed = 16 + 20 = 36 mph

Now,

After 2 hours the distance between them will be as follows

36 × 2 = 72 mph

Hence, they will be 72 km far apart after 2 hours.

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Answer:

128688

Step-by-step explanation:

L x W x D cubic yards is the maximum amount of water the pool can contain.

Volume = Length x Width x Depth

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m3, cm3, in3, etc.

The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Many forms have various volumes. We have studied the several solids and forms that are specified in three dimensions, such as cubes, cuboids, cylinders, cones, etc., in 3D geometry. We will discover how to calculate the volume for each of these shapes.

from the question:

We need to know the pool's dimensions in order to calculate how much water it can store. Assume the pool has the following dimensions: L yards in length, W yards in breadth, and D yards in depth.

The following formula can be used to determine the pool's volume:

Volume = length, width, and depth

Volume = L, W, and D cubic yards.

The pool may therefore hold a maximum volume of water that is L x W x D cubic yards.

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The maximum amount of water that the pool can contain is the volume of the pool = L x W x D cubic yards.

The volume of a closed surface or object is a three-dimensional mathematical measurement. Cubic volume metrics include m3, cm3, in3, etc.

Any three-dimensional solid's volume is the area it takes up.

Forms come in a wide range of volumes. We have looked at a variety of three-dimensional solids and shapes, including cubes, cuboids, cylinders, cones, and more. In this lesson, we'll learn how to determine the volume of each of these forms.

Here we need to know the pool's dimensions in order to calculate how much water it can store.

Let the pool's length be L yards.

Let the pool's breadth be W yards.

Let the pool's depth be D yards.

The following formula can be used to determine the pool's volume:

Volume = length × width × depth

⇒ Volume = L × W × D cubic yards.

The pool may therefore hold a maximum volume of water that is:

L x W x D cubic yards.

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The values of the variables are x = 23, y = 41/3, and z = -22/3.

The matrix equation Ax = b for the given set of linear equations is:

```
| -3 0 -6 |   | x |   | 11 |
|  5 -2  3 | * | y | = | 17 |
|  2 -1 -7 |   | z |   | -3 |
```

Where A is the coefficient matrix, x is the column matrix of variables, and b is the column matrix of constants.

To find the inverse of matrix A, we perform row operations on the augmented matrix [A|I]:

```
| -3 0 -6 | 1 0 0 |
|  5 -2  3 | 0 1 0 |
|  2 -1 -7 | 0 0 1 |
```

First, we divide the first row by -3:

```
| 1 0 2 | -1/3 0 0 |
| 5 -2 3 |  0   1 0 |
| 2 -1 7 |  0   0 1 |
```

Then, we subtract 5 times the first row from the second row, and 2 times the first row from the third row:

```
| 1 0  2  | -1/3  0  0 |
| 0 -2 -7 |  5/3  1  0 |
| 0 -1 -3 |  2/3  0  1 |
```

Next, we divide the second row by -2:

```
| 1 0  2  | -1/3  0   0 |
| 0 1 7/2 | -5/6 -1/2 0 |
| 0 -1 -3 |  2/3  0   1 |
```

And then we add the second row to the third row:

```
| 1 0  2  | -1/3  0   0 |
| 0 1 7/2 | -5/6 -1/2 0 |
| 0 0  1/2|  1/6 -1/2 1 |
```

Finally, we divide the third row by 1/2, and subtract 2 times the third row from the first row, and 7/2 times the third row from the second row:

```
| 1 0 0 |  0   1  -2 |
| 0 1 0 | -4/3 2  -7/2|
| 0 0 1 |  1/3 -1  2 |
```

So, the inverse of matrix A is:

```
|  0   1  -2 |
| -4/3 2  -7/2|
|  1/3 -1  2 |
```

Now, we can perform matrix multiplication A^-1b to get the values of the variables:

```
|  0   1  -2 |   | 11 |   | x |
| -4/3 2  -7/2| * | 17 | = | y |
|  1/3 -1  2 |   | -3 |   | z |
```

```
| x |   | 1(17) + (-2)(-3) |   | 23 |
| y | = | (-4/3)(11) + 2(17) + (-7/2)(-3) | = | 41/3 |
| z |   | (1/3)(11) + (-1)(17) + 2(-3) | = | -22/3 |
``

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Answer:

3.5 * 10²

Step-by-step explanation:

In standard form, the number before the point has to be less than ten so

0.035 = 3.5 *10²

Kiara's rate is 4 miles per hour. Take note that this simply asks for her current rate, not an average rate.

To find Kiara's rate at the 9-hour mark, we can subtract the distance she has traveled so far (26 miles) from the total distance (38 miles) to get the distance she traveled in the last 3 hours, which is 12 miles.

Then, we can divide the distance she traveled in the last 3 hours by the time taken (9 - 6) to get her rate:

Therefore, Kiara's current rate is 4 miles per hour.

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The x and y-intercept of the given point (1,1), (-5,7) is 2 and 2.

The equation of a line can be represented in slope intercept form can be represented as follows:

y = mx + b

where

Therefore, let's find the slope.

(1,1), (-5,7)

m = 7 - 1 / -5 - 1

m = 6 / -6

m = - 1

Let's find the x and y-intercept using (1, 1)

y = -x + b

1 = -1 + b

b = 1 + 1

b = 2

Therefore,

y = - x + 2

Let's find x and y-intercept

y = -(0) + 2

y = 2

- x = y + 2

-x = 0 + 2

x = 2

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Answer: y=mx+b

Step-by-step explanation:

The function that describes the profit earned from the sales of the bikes over a period of x years is: [tex]P(x) = 100x^3 + 6x^2 + 9x[/tex]. The Option A is correct.

The profit earned from the sales of the bikes can be calculated by subtracting the cost of manufacturing from the revenue earned. Therefore, the function that describes the profit earned can be represented as:

[tex]P(x) = S(x) - C(x)[/tex]

Substituting the given functions for S(x) and C(x), we get:

[tex]P(x) = (100x^3 + 6x^2 + 97x + 215) - (88x + 215)[/tex]

Simplifying this expression, we get:

[tex]P(x) = 100x^3 + 6x^2 + 9x.[/tex]

Full question "A company sells bikes that are light and fast. The revenue earned over a period of x years can be represented by the function, S(x) = 100x3 + 6x2 + 97x + 215. The cost of manufacturing the bikes can be represented by the function, C(x) = 88x + 215. Which function, P(x), describes the profit earned from the sales of the bikes over a period of x years?"

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Answer:

3 pages per minuet 90pages/30min=3 pages per min

Step-by-step explanation:

Answer:

3 pages

Step-by-step explanation:

Create a ratio:

30 minutes is equal to 1 hour

90 pages/30 minutes

Divide 90/30

90/30=3

Alya reads 3 pages per minutes

Hope this helped you!

Stay safe and have a good day/night! :)

The lateral surface and the total surface areas of the prism are 96 in² and 2304 in² respectively.

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

Given is prism, we need to find the lateral surface and the total surface areas,

Lateral surface area = (perimeter of base) × length

Perimeter of base = 3 × 4 = 12 in

length = 8 in

The lateral surface area = 12 × 8 = 96 in²

Total surface area = (perimeter of base) × length × 2(base area)

= 96 × 2(3×4)

= 96 × 24

= 2304 in²

Hence, the lateral surface and the total surface areas of the prism are 96 in² and 2304 in² respectively.

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The length of the dog run is 18.5 feet and the width is 14 feet. Micah can use his 65 feet of fencing to make a dog run with these dimensions.

To find the length of the dog run, we need to solve the equation for L. Here are the steps:

1. Start with the given equation: 2L + 2(L - 4.5) = 65
2. Distribute the 2 on the right side of the equation: 2L + 2L - 9 = 65
3. Combine like terms: 4L - 9 = 65
4. Add 9 to both sides of the equation: 4L = 74
5. Divide both sides of the equation by 4: L = 18.5

So, the length of the dog run is 18.5 feet. Since the length is 4.5 feet more than the width, we can find the width by subtracting 4.5 from the length:

W = L - 4.5
W = 18.5 - 4.5
W = 14

Therefore, the width of the dog run is 14 feet.

In conclusion, the length of the dog run is 18.5 feet and the width is 14 feet. Micah can use his 65 feet of fencing to make a dog run with these dimensions.

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Answer:

18

Step-by-step explanation:

18

The result of the given polynomial division (2x^(3)+4x^(2)+7x+5 divided by x+1) using long division method is 2x^(2) + 2x + 5.

To find the result of the given polynomial division using long division method, we need to follow the steps below:

Step 1: Write the dividend and the divisor in long division form.

        ______________________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5

Step 2: Divide the first term of the dividend by the first term of the divisor. In this case, 2x^(3)/x = 2x^(2). Write the result above the dividend.

        2x^(2)  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5

Step 3: Multiply the result by the divisor and write the product under the dividend.

        2x^(2)  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5
        - (2x^(3) + 2x^(2))
        ---------------------

Step 4: Subtract the product from the dividend and bring down the next term.

        2x^(2)  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5
        - (2x^(3) + 2x^(2))
        ---------------------
                2x^(2) + 7x + 5

Step 5: Repeat the process until the degree of the remainder is less than the degree of the divisor.

        2x^(2) + 2x + 5  _______________
x + 1  |  2x^(3) + 4x^(2) + 7x + 5
        - (2x^(3) + 2x^(2))
        ---------------------
                2x^(2) + 7x + 5
        - (2x^(2) + 2x)
        ---------------------
                   5x + 5
        - (5x + 5)
        ---------------------
                   0

Step 6: Write the final result as the quotient plus the remainder over the divisor.

[tex](2x^{3} + 4x^{2} + 7x + 5)/(x + 1) = 2x^{2} + 2x + 5[/tex]

Therefore, the answer is 2x^(2) + 2x + 5

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Answer: 64.24 cm square

Step-by-step explanation:

length x width

11 x 7 = 77cm square

The radius of the circle is 2cm

The area of the circle = 

 r^2 = 2^2 12.57

Hence the area of the shaded region=

Area of rectangle – area of circle= 77 – 12.57= 64.43 cm2

This size sample of this binomial distribution have:

P = 0.24
Mean = 50.4
Standard Deviation = 6.19

About 24% of a population are of a particular ethnic group. 210 people are randomly selected from this population.

First, we need to convert the percentage to a decimal by dividing by 100:

P = 24% / 100 = 0.24

Next, we can compute the mean and standard deviation of the binomial distribution for a sample size of 210 and probability of success of 0.24:

Mean = np = 210 * 0.24 = 50.4

Standard Deviation = √(np(1-p)) = √(50.4 * (1-0.24)) = √(38.304) = 6.19

So, the mean of this binomial distribution is 50.4 and the standard deviation is 6.19.

Therefore,
P = 0.24
Mean = 50.4
Standard Deviation = 6.19

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Answer:

B

Step-by-step explanation:

I think so because the rise is going downward, which means it’s a negative number. Therefore m= -1/4

After solving the length of BM is 4 cm.

As we know from the question;

AB = 8cm

DL ⊥ AB

BM ⊥ AD

DL = 5cm

AD = 10cm

Think about the parallelogram ABCD now.

Here, let AB be the parallelogram's base and DL be its altitude (height).

The parallelogram's area is determined by: Base × Height

Area of ‖gm ABCD = AB × DL

Area of ‖gm ABCD = 8 × 5

Area of ‖gm ABCD = 40cm²

Now,

Think of AD as the parallelogram's base, and BM as its altitude (height).

area of ‖gm ABCD = AD × BM

10 × BM = 40cm²

Divide by 10 on both side,

BM = 40/10

BM = 4cm

length of BM = 4cm.

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The complete question is:

In ‖gm ABCD, it is given that AB = 8cm, DL ⊥ AB and BM ⊥ AD such that DL = 5cm and AD = 10cm. Then, BM = ?

The factored form of the given polynomial is [tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}[/tex]

To factor the given polynomial completely, we need to find the greatest common factor (GCF) of all the terms. The GCF of 60a^(3)b^(2), 10a^(2), and -50a^(4)b^(2) is 10a^(2).

So, we can factor out 10a^(2) from each term to get:

[tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}[/tex]

Now, we can check our answer by multiplying the factors back together:

[tex]10a^{(2)}(6ab^{(2)}+1-5a^{(2)}b^{(2))}=60a^{(3)}b^{(2)}+10a^{(2)}-50a^{(4)}b^{(2)}[/tex]

Therefore, the factored form of the given polynomial is [tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}.[/tex]

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Answer:30

Step-by-step explanation: