Solve using quadratic equation:
3x(^2)-2x+1=0
[^2 means 2 squared]

Answer:

that answer is incorrect!! you can check by typing in your browser calculator and typing (-51)^0 im teling you its wrong the answers 1 again answer is 1 you can also check tiger mathh

Step-by-step explanation:

The total sum of Adriana’s grades are:

sum of grades = 4 * 90

sum of grades = 360

If Adriana and Roberto has similar total sum, therefore the average of Roberto’s grades is:

Roberto average = 360 / 5 = 72

Answer:

72

The coefficient of kinetic friction is 0.58

To determine the coefficient of kinetic friction [tex](\(\mu_k\))[/tex], we can use the following approach:

1. Identify the horizontal component of the pulling force [tex](\(F_{\text{pull, horizontal}}\))[/tex] and set it equal to the force of kinetic friction [tex](\(f_k\))[/tex].

2. The equation for the horizontal component of the pulling force is:

[tex]\[ F_{\text{pull, horizontal}} = F_{\text{pull}} \cdot \cos(30^\circ) \][/tex]

3. The equation for the force of kinetic friction is:

[tex]\[ f_k = \mu_k \cdot N \][/tex]

4. Since the sled is on a horizontal surface, the normal force [tex](\(N\))[/tex] is equal to the weight of the sled [tex](\(m \cdot g\))[/tex], where m is the mass of the sled and g is the acceleration due to gravity.

Putting these equations together and setting them equal to each other because the sled is moving at constant velocity, we get:

[tex]\[ F_{\text{pull}} \cdot \cos(30^\circ) = \mu_k \cdot m \cdot g \][/tex]

Now, substitute the given values:

[tex]\[ 80 \cdot \cos(30^\circ) = \mu_k \cdot 20 \cdot 9.8 \][/tex]

Solve for [tex]\(\mu_k\)[/tex]:

 [tex]\[ \mu_k = \frac{80 \cdot \cos(30^\circ)}{20 \cdot 9.8} \][/tex]

Calculating this expression yields:

[tex]\[ \mu_k \approx 0.58 \][/tex]

So, the calculated coefficient of kinetic friction is approximately 0.58, which matches the provided answer.

Complete question:

A 20 kg sled is being pulled across a horizontal force at a constant velocity the pulling force has a magnitude of 80 N and it's directed at an angle of 30° above the horizontal determine the coefficient of kinetic friction.

Answer:

△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.

Step-by-step explanation:

We can see from the diagram that XYZ is not the same size as PQR.  This means there is no series of rigid motions, which preserve segment length, that maps PQR to XYZ.

Answer:

△PQR is not congruent to △XYZ because there is no sequence of rigid motions that maps △PQR to △XYZ.

Step-by-step explanation:

The probability that the product of the numbers they roll is even is, 2/3

We have to given that,

Geoff and Trevor each roll a fair six-sided die.

Here, Number of possible outcomes for Geoff,

1, 2, 3, 4, 5, 6

And, Number of outcomes for Trevor,

1, 2, 3, 4, 5, 6

Hence, Possible outcomes for product of the numbers they roll is even are,

2 x 1 = 2

2 x 2 = 4

2 x 3 = 6

2 x 4 = 8

2 x 5 = 10

2 x 6 = 12

3 x 2 = 6

3 x 4 = 12

3 x 6 = 18

4 x 1 = 2

4 x 2 = 8

4 x 3 = 12

4 x 4 = 16

4 x 5 = 20

4 x 6 = 24

5 x 2 = 10

5 x 4 = 20

5 x 6 = 30

6 x 1 = 6

6 x 2 = 12

6 x 3 = 18

6 x 4 = 24

6 x 5 = 30

6 x 6 = 36

Hence, Total possible outcomes = 24

And., Total outcomes = 6x 6 = 36

So, the probability that the product of the numbers they roll is even is,

P = 24 / 36

P = 12/18

P = 2/3

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Final answer:

The sentence 'The sum of 14 and Holly's age is 55' can be translated into the equation 14 + h = 55, where h represents Holly's age.

Explanation:

To translate the sentence into an equation, we identify the mathematical operations described by the sentence. The sentence 'The sum of 14 and Holly's age is 55' indicates an addition operation involving Holly's age and the number 14. Using the variable h for Holly's age, we form the equation 14 + h = 55. This is a simple linear equation where h represents an unknown value that can be solved for.

vertical angles equal each other so you have

 angle E = angle F

9x+12 = 3x +24

subtract 12 from each side

9x = 3x +12

subtract 3x from each other

6x =12

divide both sides by 6

x = 12/6 = 2

 x = 2

Final answer:

The probability that at least two more coin tosses are required to get the first head, after ten tails in a row with a balanced coin, is 50%.

Explanation:

The student is asking about the probability of a specific outcome in a sequence of coin tosses. Given that we have already tossed a balanced coin ten times and obtained zero heads, we want to calculate the probability of having to toss the coin at least two more times to get the first head. The probability of getting a head on any given coin toss is 0.5. To get the first head in at least two more tosses means we need a tail (T) on the next toss and then any outcome (H or T) after that. Therefore, we calculate the probability as follows:

The combined probability is the product of the two individual probabilities, which is 0.5 * 1 = 0.5 or 50%. Hence, the probability that we must toss the coin at least two more times to obtain the first head is 50%.

Following the 4-step method of problem-solving offers the benefits of structured decision-making and enhanced clarity in identifying and addressing core issues. These advantages significantly contribute to effective decision-making and successful implementation of solutions.

The 4-step method, involving identification, planning, execution, and evaluation, provides a structured framework for tackling problems. In the identification phase, _Step 1_, issues are precisely pinpointed, aiding in accurate problem definition, crucial for effective decision-making. For instance, in a business scenario, if sales decline is the issue, this step helps clarify if it's due to product quality, marketing, or market changes, enabling focused decision-making.

Moving to the planning phase, _Step 2_, where strategies and solutions are devised, this structured approach ensures that all potential solutions are thoroughly explored, enhancing the quality of decisions made. This step involves a rigorous evaluation of each potential solution, ensuring a comprehensive understanding of their viability and implications.

During the execution phase, _Step 3_, the structured plan is put into action, benefiting from the earlier clarity and well-thought-out decisions. For example, if a marketing strategy was identified as a solution, this phase would involve implementing the chosen strategy with a clear roadmap, minimizing errors and optimizing resources.

Lastly, the evaluation phase, _Step 4_, allows for the assessment of the implemented solution's effectiveness. By systematically analyzing the outcomes against predefined metrics, this step ensures continuous improvement and learning from the process, contributing to more informed decision-making in the future. This structured approach, therefore, not only facilitates effective decision-making but also ensures successful implementation and ongoing refinement of solutions.

Here is complete question;

"What are two benefits of following the 4-step method of problem-solving, and how do they contribute to effective decision-making and solution implementation?"

we know that

The angle marked in the figure is the angle CEB

The vertex is the intersection point of the line CD and the line AB

The intersection point is the point E

therefore

The answer is

Point E is the vertex of the angle CEB

12/3 = 4

 it was dilated with a scale factor of 4

The time they read together, is the sum of their individual study time.

Ronny read 1.14 hours longer than her brothers combined

The given parameters are:

[tex]\mathbf{Ronny = 2.75\ hours}[/tex]

[tex]\mathbf{Older\ Brother= 1.18\ hours}[/tex]

[tex]\mathbf{Younger\ Brother= 0.43\ hours}[/tex]

The combined time her brothers studied is:

[tex]\mathbf{Both = Older + Younger}[/tex]

Substitute known values

[tex]\mathbf{Both = 1.18\ hours + 0.43\ hours}[/tex]

Evaluate like terms

[tex]\mathbf{Both = 1.61 \ hours}[/tex]

The time Ronny read longer is calculated as follows:

[tex]\mathbf{Time = Ronny- Both}[/tex]

Substitute known values

[tex]\mathbf{Time = 2.75\ hours - 1.61\ hours}[/tex]

Evaluate like terms

[tex]\mathbf{Time = 1.14\ hours}[/tex]

Hence, Ronny read 1.14 hours longer than her brothers combined

Read more about time at:

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Answer:

Numbers: 11, 7 and 44

Expressions: n, n - 4, 4n

Step-by-step explanation:

We have that A + B + C = 62, where A, B and C represent numbers.

We know that the 2nd number (B) is equal to the first number (A), diminished by 4. This means B = A - 4  

We also know that the 3rd number (C) is four times the first (A), that is to say 4*A. This means C = 4*A

If we replace this information in the first expression, we have

A + B + C = A + (A - 4) + (4*A) = 62

We change an equation of 3 variables to an equation of just one. Now we solve it putting together the terms that have the variable A:

A + A - 4 + 4*A = 62

2A + 4A - 4 + 4 = 62 + 4

6A = 66

A = 11

Our first number is 11, now we find B and C:

B = A - 4 = 11 - 4 = 7

C = 4A = 4*11 = 44

So, the numbers are 11, 7 and 44

If we change the A for a "n", the expressions that represent the numbers are n, n - 4 and 4n

The minimum value of the function y=3x^2-12x+10 is found using the vertex form, and it is -2. This value corresponds to the y-coordinate of the vertex of the parabola.

To find the minimum value of the function y=3x^2-12x+10, we can use the vertex form of a quadratic equation, or complete the square method. We also know that a quadratic function with a positive coefficient for the x^2 term opens upwards and has a minimum value at its vertex. To get the vertex form, we complete the square:

y = 3(x^2 - 4x) + 10
y = 3(x^2 - 4x + 4 - 4) + 10
y = 3((x-2)^2 - 4) + 10
y = 3(x-2)^2 -12 + 10
y = 3(x-2)^2 - 2

Now, the vertex of this parabola is at (2, -2). As this is the vertex of a parabola that opens upwards, the y-coordinate of this point gives us the minimum value of the function, which is -2.