1. Explain how the expression 8-6x+x^2 is in standard form.

2. Is the expression equivalent to (x-4)(x-2)? Explain.

In online and blended learning environments, discussion-based assessments are often used as a way for students to engage in collaborative and reflective learning.

These assessments require students to participate in online discussions, often in small groups or with the whole class, to share ideas, ask questions, and build upon each other's thinking.

There are several ways that discussion-based assessments can be used in online and blended learning environments:

As a form of formative assessment:

Discussion-based assessments can be used as a way for teachers to check for student understanding and to provide feedback in real-time.

This can help teachers adjust their instruction to better meet the needs of their students.

As a way to encourage student engagement: Discussion-based assessments can help students feel more connected to their peers and to the learning community.

By providing opportunities for students to interact with each other, teachers can help students feel more invested in their learning.

As a way to promote critical thinking:

Discussion-based assessments can help students develop critical thinking skills by providing opportunities for them to analyze, evaluate, and synthesize information.

Through online discussions, students can learn how to articulate their own ideas and respond to the ideas of others.

As a way to promote collaborative learning:

Discussion-based assessments can help students develop collaborative learning skills by providing opportunities for them to work together to solve problems, share information, and build on each other's ideas.

To effectively use discussion-based assessments, teachers need to design questions and prompts that are thought-provoking and require students to engage in higher-order thinking.

Teachers also need to establish clear expectations for participation and provide guidelines for respectful and constructive discourse.

Finally, teachers should be actively engaged in the discussion and provide feedback and guidance to help students develop their thinking and communication skills.

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Answer: The distance left after 25 days is 1280 miles

Step-by-step explanation:

To calculate the distance, we use the formula:

[tex]s=\dfrac{d}{t}[/tex]

where,

s = speed of the bicycle = 80 miles/day

t = time taken = 25 days

d = distance travelled = ? miles

Putting values in above equation, we get:

[tex]\text{d}=(80 \ \text{miles}/\text{day} \times 25 \ \text{days})=2000 \ \text{miles}[/tex]

Total distance to the destination = 3280 miles

Distance traveled in 25 days = 2000 miles

Distance left after 25 days = [3280 - 2000] = 1280 miles

Hence, the distance left after 25 days is 1280 miles

Answer: To estimate the mean length of the insects Kylie found, we can use the formula:

mean = (sum of (length * frequency)) / (sum of frequency)

We can calculate the sum of (length * frequency) by multiplying each length by its corresponding frequency and adding up the products. We can also calculate the sum of frequency by adding up all the frequencies. Using the table given, we have:

sum of (length * frequency) = (5 * 5) + (8 * 15) + (7 * 25) = 5 + 120 + 175 = 300

sum of frequency = 5 + 8 + 7 = 20

Substituting these values into the formula, we get:

mean = 300 / 20

= 15

Therefore, an estimate of the mean length of the insects Kylie found is 15 millimetres.

Step-by-step explanation:

(2, -6)

When a point (x,y) is rotated counterclockwise by 180° about the origin, the new point becomes (-x, -y) ie the new x coordinate becomes negative of the original x coordinate and the new y coordinate becomes the negative of the original y coordinate

So resulting point W' = (-(-2), -6) = (2, -6)

Answer:

(2, -6)

Step-by-step explanation:

When a point (x,y) is rotated counterclockwise by 180° about the origin, the new point becomes (-x, -y) ie the new x coordinate becomes negative of the original x coordinate and the new y coordinate becomes the negative of the original y coordinate

So resulting point W' = (-(-2), -6) = (2, -6)

The number of days in which Meena would be able to complete the work alone is 24 days.

In order to determine the number of days in which Meena would be able to complete the work alone, we would have to assign variables to the amount of time taken by Mala, Meena, and Vinay, and then translate the word problem into an algebraic equation as follows;

Note: Combined work rate = 1/x + 1/y + 1/z

Based on the information provided, we have the following equations that models the work rate by each person;

1/(x + y) = 10 ⇒ 1/10 = x + y    ........equation 1.

1/(y + z) = 12 ⇒ 1/12 = y + z    ........equation 2.

1/(x + z) = 15 ⇒ 1/15 = x + z    ........equation 3.

x + y + y + z + x + z = 1/10 + 1/12 + 1/15

2(x + y + z) = 15/60

2(x + y + z) = 1/4

x + y + z = 1/8

From equation 2, we have:

x + (y + z) = 1/8

x + 1/12 = 1/8

x = 1/8 - 1/12

x = 1/24

x = 24 days.

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The answer to the simplified expression is option D. 15d^2 - 31d - 12

Expansion is the process of multiplying a given set of terms in a bracket with other terms in another bracket. It can be done using the grid method of expansion.

Considering the given question to fill the blanks, we have;

       3d     +        1

5d  15d^2         5d

-12  -36d          -12

Thus, adding the terms one to another gives;

15d^2 + 5d - 36d - 12

15d^2 -31d - 12

The correct answer after simplifying the expression is: 15d^2 -31d - 12. Thus option D.

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Answer:

1<4(3)+2

1<12+2

1<14

so therefore we say the answer is 1 is lesser than 14

Arithmetic operations helps us to determine the value of x for quotient of 20 divide 5 is subtracted from the difference of 16 and 6 is equals to the 6.

In arithmetic, a quotient can be defined as the result of the division of a number by any divisor. It is the number of times the divisor is contained in the dividend a quantity produced by the division of two numbers. The quotient can be determined by dividing the dividend with the divisor. Formula, Quotient = Dividend ÷ Divisor. We have to determine value of x which equals to quotient of 20 divide 5 is subtracted from the difference of 16 and 6. First we have to determine quotient 20 divides 5. Using quotient formula, quotient= 20 ÷ 5 = 4. So, Quotient is 4. Now, the difference of 16 and 6 that is equals to 16 minus 6 = 16 - 6 = 10. Thus, x = 16 - 6 - ( 20÷ 5)

=> x = 10 - 4

=> x = 6

Hence, required value of x is 6.

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Complete question :

The quotient of 20 divide 5 is subtracted from the difference of 16 and 6 equals to x. what is x?

Answer:

x=6

Step-by-step explanation:

20 ÷ 5 = 4. So, Quotient is 4. Now, the difference of 16 and 6 that is equals to 16 minus 6 = 16 - 6 = 10. Thus, x = 16 - 6 - ( 20÷ 5)

=> x = 10 - 4

=> x = 6

Hence, required value of x is 6.

Here is an organized list representing the sample space of drawing one letter tile and one number tile: {(A, 1), (A, 2), (A, 3), (B, 1), (B, 2), (B, 3), (C, 1), (C, 2), (C, 3)}

What is a sample space?

In probability theory, sample space refers to the set of all possible outcomes of a random experiment.

For example, if we toss a coin, the sample space would consist of two possible outcomes, heads or tails. Similarly, if we roll a die, the sample space would consist of six possible outcomes, the numbers 1 through 6.

The sample space is an important concept because it allows us to define the probabilities of events. In order to calculate the probability of an event, we divide the number of outcomes that are favorable to the event by the total number of possible outcomes in the sample space.

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John can run 4 miles in 40 minutes, so running 9 kilometers would take him approximately 56 minutes.

We're given that John can run 4 miles in 40 minutes. To find out how long it would take him to run 9 kilometers, we need to first convert 4 miles to kilometers.

One mile is equal to 1.60934 kilometers, so 4 miles is equal to 6.43736 kilometers (rounded to five decimal places).

Next, we can use the formula for speed:

Speed = Distance / Time

To solve for John's speed, we divide the distance he covered (6.43736 kilometers) by the time it took him to cover that distance (40 minutes):

Speed = 6.43736 km / 40 min ≈ 0.160935 km/min

Now we can use this speed to determine how long it would take John to run 9 kilometers. We can use the same formula as before, but this time we'll be solving for time:

Time = Distance / Speed

Substituting in the values we know:

Time = 9 km / 0.160935 km/min ≈ 55.8627 min

Rounding this answer to the nearest minute, we get:

Time ≈ 56 min

Therefore, it would take John approximately 56 minutes to run 9 kilometers.

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Answer:

see explanation

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(i)

y = 3x - 4

with slope m = 3 and y- intercept c = - 4

(ii)

y = - 3x + 7

with slope m = - 3 and y- intercept c = 7

Answer:

here we can see clearly,

The explicit form of the geometric sequence is an = 27 * (-2/3)^(n-1)

In a geometric sequence, each term is obtained by multiplying the previous term by a fixed number called the common ratio, denoted by r.

So, if we know the first term and the common ratio, we can find any term in the sequence, including the nth term, using the formula:

an = a1 * r^(n-1)

where a1 is the first term and an is the nth term.

To find the common ratio, we can divide any term by the previous term:

r = -18/27 = -2/3

Now we can use the formula to find the nth term.

an = 27 * (-2/3)^(n-1)

Therefore, the explicit form of the geometric sequence is an = 27 * (-2/3)^(n-1)

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As a result, Bank Padarn's AER is 2.0186%. This shows that Bank Padarn gives a greater interest rate when compared to the AER provided by Banc Teilo (1.9%).

A benchmark 30-year fixed mortgage's current average interest rate is 6.91% as of today, Tuesdays, March 21, 2023, a decrease of 3 basis points from seven days ago. If you're looking to refinance your mortgage, the current average 30-year fixed interest rate of 6.93%, which has been constant over the past week.

We must convert a nominal rate provided by Bank Padarn to the an AER in order to contrast the two rates.

AER is calculated as (1 + r/n)n - 1 where r is just the nominal rate of return & n is the annual frequency of interest payments.

r = 1.98% and n = 12 for Banc Padarn (since interest is paid monthly). The algorithm yields the following results when we enter these values: AER Equals (1 + 0.0198/12)12 - 1 ≈ 0.020186 = 2.0186%

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In a sample of 10,000 observations from a normal population, about 27 would be expected to lie beyond three standard deviations of the mean, therefore, the correct option is b.

For a normal distribution, about 99.7% of the data is expected to lie within three standard deviations of the mean. This is known as the empirical rule or the 68-95-99.7 rule.

Using this rule, we can estimate the number of observations beyond three standard deviations of the mean for a sample of 10,000. Since the distribution is normal, we know that the mean and standard deviation completely describe the distribution.

Assuming the sample is representative of the population, we can use the empirical rule to estimate the number of observations beyond three standard deviations of the mean. Since three standard deviations from the mean cover 99.7% of the data, the remaining 0.3% of the data would be expected to lie beyond three standard deviations.

Therefore, the correct answer is c. about 27, since 0.3% of 10,000 is approximately 27.

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A tie costs 12 euros and a shirt costs 25 euros.

Let's start by assigning variables to the unknown values. Let x be the price of a tie, and let y be the price of a shirt. We know that y = x + 13, since a shirt costs 13 euros more than a tie.

We also know that we bought three shirts and two ties, and paid a total of 99 euros. Using this information, we can set up an equation

3y + 2x = 99

Here we have to use to substitution method, substituting y = x + 13, we get

3(x + 13) + 2x = 99

Simplifying this equation, we get

5x + 39 = 99

Subtracting 39 from both sides, we get

5x = 60

Dividing both sides by 5, we get

x = 12 euros

Now that we know the price of a tie, we can use y = x + 13 to find the price of a shirt

y = x + 13

y = 12 + 13

y = 25 euros

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Answer:

5/8

Step-by-step explanation:

1/4*2 4/8

1/4*2 1/2

1/4*5/2

5/8

Answer:  k = 67 4/5

Step-by-step explanation:

101 3/5 =k+33 4/5

first isolate your variable by subtracting 33 4/5 from both sides

101 3/5 - 33 4/5 = k

now subtract

to subtract 4/5 from 3/5, you have to borrow 5/5 or 1 whole from 101 and add it to 3/5.  5/5 + 3/5 = 8/5.  101 - 1 = 100.

so now you have

100 8/5 - 33 4/5 = k

100 - 33 = 67

8/5 - 4/5 = 4/5

your answer is 67 4/5

Check your work.

67 4/5 + 33 4/5 = 100 8/5 simplified to 101 3/5, our starting number.

solution is true so problem solved!

Answer:

the best move is king because it did not have a king

the answer is (C) $0 is incorrect, and (B) $5,000.00 and (D) $45.00 are also incorrect. The correct answer is (A) $450.00.

what is insurance ?

Insurance is a contract between an individual or an entity (the insured) and an insurance company (the insurer), in which the insurer agrees to compensate the insured for financial losses or damages that occur due to unexpected events, in exchange for the payment of premiums by the insured.

Based on the information provided, the employee with a family plan is on the "Individual+Spouse" premium plan, which has a monthly premium of $450.00. This means that regardless of whether or not the employee visits a doctor or hospital, they are required to pay this amount every month to maintain their insurance coverage.

Therefore, the answer is (C) $0 is incorrect, and (B) $5,000.00 and (D) $45.00 are also incorrect. The correct answer is (A) $450.00.

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Shannon broke down 1536 into three numbers: 256, 72, and 56, and then added the products of these three numbers to get her final answer of 256.

what is products and addition ?

The product is the result of multiplying two or more numbers together. For example, the product of 2 and 3 is 6, denoted as 2 x 3 = 6.Addition is another arithmetic operation that involves combining two or more numbers to find a total or a sum.

In the given question,

To solve 1536 ÷ 6, Shannon broke down the number 1536 into three numbers that are divisible by 6.

Let's start by finding the factors of 6: 1, 2, 3, and 6.

We need to find three numbers whose sum is equal to 1536 and each of which is divisible by 6.

We can start with the largest factor of 6, which is 6 itself. We can divide 1536 by 6 to get 256.

Now we need to find two more numbers whose sum is 128 and are also divisible by 6.

One such pair of numbers is 72 and 56.

We can verify that the sum of these three numbers is indeed 1536:

256 + 72 + 56 = 384 + 56 = 440 + 256 = 696 + 840 = 1536.

So, Shannon broke down 1536 into three numbers: 256, 72, and 56, and then added the products of these three numbers to get her final answer of 256.

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Answer:

I can see the pattern. There will be 30 toothpicks to make 10 squares accordingto your pattern. The pattern with an expression is +3.

Step-by-step explanation:

If you list the 4,7,10 and see the pattern between these numbers. You are adding 3 to the 4 to the 7 and 7 to the 10. Then, follow the pattern until you get 10 squares.

The second table is the one which represents a linear function.

In mathematics, the terms "linear function" refer to two distinct but connected concepts: In calculus and related subjects, a polynomial function of degree zero or one with a graph that is a straight line is referred to as a linear function.

⇒ The first table does not represent a linear function because for two different values of x, there is same value for y.

⇒ The second table represents the linear function as it forms a straight line on the graph.

⇒ The third table does not represent a linear function because it does not have a constant slope.

⇒ The last table does not represent a linear function because it does not have a constant slope.

Hence, the second table represents a linear function.

As x is constant as 1, then all the y inputs will be in a straight vertical line

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Question: Which of the following tables represents a linear function?

A. x | −4   −1    0    1    2

   y | −4    2   −4   0    2

B. x |   1      1     1    1   1

   y | −3   −2   −1   0   1

C. x |  −6       −1      0       2        3

    y |  −7     [tex]\frac{-16}{3}[/tex]    −5     [tex]\frac{-13}{3}[/tex]     −4

D. x | −2       −1      0    2    4

    y | −4      [tex]\frac{-2}{3}[/tex]     −1     [tex]\frac{2}{3}[/tex]     1

Answer:

$35.35

Step-by-step explanation:

First, let's add all these prices together:

$8.95 + $11.49 + $12.75 = $33.19

Then, let's find how much will the whole price increase with the taxes:

[tex] \frac{33.19 \times 6.5\%}{100\%} = 2.15735[/tex]

And finally, let's add this number and the old price together:

$33.19 + $2.15735 = $35.34735 ≈ $35.35

The expression 3z^2 - 27 can be simplified by factoring out the greatest common factor (GCF), which is 3:

3z^2 - 27 = 3(z^2 - 9)

Now, we can simplify the expression further by recognizing that the term inside the parentheses is the difference of squares, which can be factored as:

z^2 - 9 = (z + 3)(z - 3)

Substituting this back into our original expression, we get:

3z^2 - 27 = 3(z^2 - 9) = 3(z + 3)(z - 3)

Therefore, the simplified form of the expression 3z^2 - 27 is 3(z + 3)(z - 3).

A) Surface area of Can is 276.32 [tex]cm^2[/tex].

B)The reason is that the top of the can has to be open to be used as a pencil holder. Therefore, you do not have to include the area of the top which is  [tex]\pi r^2[/tex] .

What is surface area?

A three-dimensional object's surface area is the space it takes up when viewed from the outside.

Here the given radius = 4 cm and height h = 9 cm.

A) Now using cylinder surface area formula then,

=> Surface area SA = [tex]\pi r^2+2\pi rh[/tex] square unit.

=> SA = [tex]3.14\times4^2+2\times3.14\times4\times9[/tex]

=> SA = [tex]3.14\times16[/tex]+ 226.08

=> SA = 50.24+226.08

=> SA = 276.32 [tex]cm^2[/tex]

B) Here top of the paint is used to open a pencil holder. So we don't need bottom circle area. [tex]\pi r^2[/tex] is the formula for the area of a circle which means you can use it to calculate the area of the top of the can.

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Answer:

D

Step-by-step explanation:

23 - (-8)

23 + 8 = 31°

The temperature rose 31 degrees.

l-8 -23l = l-31l = 31  Absolute value is asking the distance from zero.

Helping in the name of Jesus.

The area of the shape is 331km²

The area of shape is the space enclosed within the perimeter or the boundary of a given shape. Area is measured in units².

The shape above can be divided into 4 shapes.

The area of the first triangle = 1/2 bh

= 1/2 × 14 × 21

= 7× 21

= 147km²

The area of the first rectangle = l× b

= 14 × 5

= 70km²

The area of the second triangle = 1/2 bh

= 1/2 × 10× 18

= 10× 9

= 90km²

area of the second rectangle = l × b

= 4 × 6

= 24 km²

area of the shape = 147+90+70+24 = 331km²

Therefore the area of the shape is 331km²

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Corrected analysis of errors : Vertex: (-2, -8), x-intercepts: (-1,0) and (6,0), y-intercept: (0,-8), Axis of symmetry: x = -2

What are the errors?

There are multiple errors in the given analysis which are given below.

1. The x-coordinate of the vertex is incorrectly given as 1 instead of -2.

2. The y-coordinate of the vertex is incorrectly given as 8 instead of -8.

3. The x-coordinate of the axis of symmetry is incorrectly given as 1 instead of -2.

4. The given x-intercepts are incorrect. The correct x-intercepts are (-1,0) and (6,0).

5. The given y-intercept is incorrect. The correct y-intercept is (0,-8).

Corrected analysis:

Vertex: (-2, -8)

x-intercepts: (-1,0) and (6,0)

y-intercept: (0,-8)

Axis of symmetry: x = -2

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Answer:

sorry for my pen!......

Using the law of sine, the missing side of the triangle is approximately 4.01 units.

The law of sines states that for any triangle ABC with sides a, b, and c opposite to angles A, B, and C respectively

a / sin(A) = b/sin(B) = c / sin(C)

Using this law, we can find the missing side b as follows:

b/sin(B) = c/sin(C)

Since angle B and angle C are complementary, we can find angle C as:

C = 180 - A - B = 180 - 58 - 48 = 74 degrees

Now we have

b/sin(48) = 5/sin(74)

Solving for b, we get

b = (5 x sin(48))/sin(74) ≈ 4.01 units

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The given question is incomplete, the complete question is;

use the law of sines to find the missing side of the triangle