Factor.
x^2-5x+6
A. (x+2)(x+3)
B. (x-5)(x-1)
C. (x-2)(x-3)
D. (x-6)(x+1)

Answer:

135

Step-by-step explanation:

Given:

\(x = 5\)

To determine a numerical value for the expression, simply substitute the value of "x" into the expression and simplify the expression, if necessary, to determine a specific number for the expression provided.

Therefore, the value of the expression \(5x^{2} + 2x\) when x = 5 is 135.

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Answer:

y = 2x - 4

Step-by-step explanation:

To solve this problem, we must first calculate the slope of the line AB using the formula:

\(\boxed{m = \frac{y_2 - y_1}{x_2 - x_1}}\)

where:

m ⇒ slope of the line

(x₁, y₁), (x₂, y₂) ⇒ coordinates of two points on the line

Therefore, for line AB with points A = (2, 5) and B = (4, 4) :

\(m_{AB} = \frac{5 - 4}{2 - 4}\)

⇒ \(m_{AB} = \frac{1}{-2}\)

⇒ \(m_{AB} = -\frac{1}{2}\)

Next, we have to calculate the slope of the line BC.

We know that the product of the slopes of two perpendicular lines is -1.

Therefore:

\(m_{BC} \times m_{AB} = -1\)      [Since BC and AB are at right angles to each other]

⇒ \(m_{BC} \times -\frac{1}{2} = -1\)

⇒ \(m_{BC} = -1 \div -\frac{1}{2}\)      [Dividing both sides of the equation by -1/2]

⇒ \(m_{BC} = \bf 2\)

Next, we have to use the following formula to find the equation of line BC:

\(\boxed{y - y_1 = m(x - x_1)}\)

where (x₁, y₁) are the coordinates of a point on the line.

Point B = (4, 4) is on line BC, and its slope is 2. Therefore:

\(y - 4 =2 (x - 4)\)

⇒ \(y - 4 = 2x - 8\)         [Distributing 2 into the brackets]

⇒ \(y = 2x-4\)

Therefore, the equation of line BC is y = 2x - 4.

Answer: 222 parts per hour

Step-by-step explanation: To find how many parts a manufacturer Can produce in 1 hour if it can produce 1,554 parts in 7 hours, then look for the unit rate. (1,554/7) To do this, simply divide 1,554 by 7, which gives you a final answer or result of 222. Hence, a manufacturer can produce 222 parts in 1 hour.

Answer:

222 parts

Step-by-step explanation:

1554 divided by 7 is 22.

Thank you Everyone for seeing this :D

The parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.

A parabola is a collection of points on a plane that are all at the same distance from a particular point and line. The point is called the focus of the parabola while the line is called the directrix. The directrix is perpendicular to a parabola's axis of symmetry and does not contact it.

As we know that the directrix is perpendicular to the axis of the parabola, now since the directrix is at x=-4, the parabola will be horizontal and will be opening either towards the left or the right.

As it is given that the vertex of the parabola is at (0,0) and we know that the parabola can not touch the directrix, therefore, the parabola's vertex will be at (0,0) and will open towards the right side. As shown below.

Hence, the parabola with vertex at (0,0) and directrix at x=-4, will open towards the right.

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Answer:

right

Step-by-step explanation:

Answer:

x = 7

Hope this helps :)

Explanation and Check part below.

Step-by-step explanation:

1. Isolate variable by doing the inverse operation which is in this case subtracting 9 on both sides of the equation.

3x + 9 = 30

- 9 - 9

3x = 21

2. Divide both sides of the equation by 3 since this is the inverse operation.

3x = 21

--- ---- <-------- fraction bar, divide

3 3

x = 7

Check:

3(7) + 9 = 30

21 + 9 = 30

30 = 30 ✓

Answer:

A

Step-by-step explanation:

Answer:

The ratio 9 to 12 is greater than 4 to 6.

9/12 = 3/4.

4/6 = 2/3.

3/4 is more.

Answer:

ok wirrudi 123 alf8 434 21 3dis w

University researchers published a paper on ride-sharing, finding positive changes in transportation patterns and potential benefits in reducing congestion and emissions.



University researchers recently published a working paper aimed at investigating the impact of ride-sharing services. The primary objective of the study was to determine whether ride-sharing contributes to positive changes in transportation patterns and to assess its potential benefits. The researchers collected and analyzed extensive data on ride-sharing usage, public transportation ridership, and traffic patterns in various cities. Their findings indicate that ride-sharing has indeed led to notable shifts in transportation behavior, including increased usage of shared rides and decreased reliance on private car ownership.



The study suggests that these changes have the potential to reduce congestion, lower emissions, and enhance accessibility in urban areas. However, further research is needed to explore long-term implications and address potential challenges related to equity, public transportation integration, and overall sustainability.



Therefore, University researchers published a paper on ride-sharing, finding positive changes in transportation patterns and potential benefits in reducing congestion and emissions.

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Answer:

1.) the student got 16 questions correct

2.) 81% showed up

3.)75%

The written description of the relationship between the variables as discussed in the task content is; Choice C; You leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally you continue at a slower (but constant) speed than before.

According to the task content, the time (hours) is plotted on the x-axis while the distance (miles) is plotted on the y-axis.

Since the graph is described by a line, it follows that it's slope is constant and consequently, its distance covered increases to 2 hours. This signifies driving.

Also, since the distance covered is constant through 3 hours, it follows that no distance is covered in that time and hence, speed is zero which signifies a stop.

Ultimately, when the distance increases through 6 hours, it follows that although the speed is constant, it is slower than the first 2 hour distance.

Therefore, Choice C correctly represents the interpretation of the relationship between the variables.

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Answer:

\( \sf \: x=34\)

Step-by-step explanation:

Let's solve your equation step-by-step.

x/2 = 17/1

Step 1: Cross-multiply.

x/2 = 17/1

x*(1)=(17)*(2)

x=34

Answer:

X = 6y-2 is the easier substitution for another equation because all you have to do is just plug in the equation into the value of x.

Answer:

Step-by-step explanation:

Answer:

1.

9x²y -10x²y = -1x²y

2.

8w - 6w = 2w

Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

Option (c) is the correct one.

The expression for the given statement i.e. 5 less than twice a number is 3 is 2n - 5 = 3.

Given, a statement

5 less than twice a number is 3

we have to find an expression for the given statement

Let the number be n,

So the twice of the number be 2n,

5 less than twice a number be 2n - 5,

So, the expression for the given statement be

2n - 5 = 3

Hence, the expression for the given statement be

2n - 5 = 3

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The statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

Given data:

7, 11, 12, 18, 20, 22, 43.

To find out whether the last observation is an outlier or not, let's use the three standard deviation criterion.

That is, if a data value is more than three standard deviations from the mean, then it is considered an outlier.

The formula to find standard deviation is:

S.D = \sqrt{\frac{\sum_{i=1}^{N}(x_i-\bar{x})^2}{N-1}}

Where, N = sample size,

             x = each value of the data set,

    \bar{x} = mean of the data set

To find the mean of the given data set, add all the numbers and divide the sum by the number of terms:

Mean = $\frac{7+11+12+18+20+22+43}{7}$

          = $\frac{133}{7}$

          = 19

Now, calculate the standard deviation:

$(7-19)^2 + (11-19)^2 + (12-19)^2 + (18-19)^2 + (20-19)^2 + (22-19)^2 + (43-19)^2$= 1442S.D

                                                                                                                               = $\sqrt{\frac{1442}{7-1}}$

                                                                                                                                ≈ 10.31

To determine whether the value of x = 43 is an outlier, we need to compare it with the mean and the standard deviation.

Therefore, compute the z-score for the last observation (x=43).Z-score = $\frac{x-\bar{x}}{S.D}$

                                                                                                                      = $\frac{43-19}{10.31}$

                                                                                                                      = 2.32

Since the absolute value of z-score > 3, the value of x = 43 is considered an outlier.

Therefore, the statement "Using the three standard deviation criterion, the last observation (x=43) would be considered an outlier" is true.

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The ellipses centered at the origin that runs through the points (1, 2), (2, 2), and (3, 1) is mathematically given as

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

Generally, the equation for three points is mathematically given as

a+2b+4c=1.....1  for the variable (1, 2)

4a+4b+4c=1.....2  for the variable (2, 2)

9a+3b+c=1.....3  for the variable (3, 1)

Step 1

Here we solve equations 1 and 2 simultaneously to find the value of b

Therefore

equ 2-equ1

3a+2b=0

b=-1.5a....4

Step 2

We solve equations 1 and 3 simultaneously to find the value of c

Where

9*equ1-equ3 gives

-15b-35c=-8

c=8-15b

subbing equ 4 we have

c=8+22.5a ....5

Step 3

Put values of b and c in equation 2, and we have

4a-6a+32+90a=1

a=-31/88

a=-0.3523

The value of b will be

b=-1.5*a

b=0.5284

The value of b will be

c=8-22.5*a

c=15.9268

Step 4

In conclusion, the equation is given as

By substituting the values of a b and c into the general formula we have

-0.3523x^2 0.5284xy 15.9268y^2 = 1.

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The graph of g(x) is the graph of f(x) stretched vertically and reflected over the axis.

The correct option is C.

We can compare the graphs of two functions f(x)=x² and g(x)=-2/3 x² by determining their vertices, domain, range, axis of symmetry, and shape of the graphs. The vertex of f(x)=x² is at the origin (0,0), which means that the parabola opens upward and is symmetrical around the y-axis.

The domain is all real numbers, and the range is y≥0. The axis of symmetry is the y-axis. On the other hand, the vertex of g(x)=-2/3 x² is also at the origin, and it opens downward. It is also symmetrical around the y-axis. The domain is all real numbers, and the range is y≤0.

The axis of symmetry is the y-axis, just like f(x).It is important to remember that g(x) is the negative of f(x), which indicates that g(x) is reflected across the x-axis. Furthermore, the stretch factor is 2/3, which makes the graph of g(x) flatter than the graph of f(x) and it is  stretched vertically and reflects over x axis(option c).

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Answer:

Rose plants has the greatest number of plants that can be put in one row that is 27

Step-by-step explanation:

If you wanted to plant 45 sunflowers and 81 rose plants in your garden you have to see which one has more and you get rose plants.all you have to do is subtract 1 from 81 and then put it with sunflowers.

Answer:

the first answer

Step-by-step explanation:

1/8 of the absolute value is 1/8 positive

anything from the absolute value is positive because absolute value is the value of how far away the number is from zero.

Answer:

-1/8

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

Based on an srs of 22 observations from a normal population, the value of the t statistic (±0.01) is -16.49.

To find the value of the t statistic, we first need to calculate the test statistic t. The formula for t is:

t = (mean - μ) / (s / √n)

Where mean is the sample mean, μ is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.

In this case, we have:
mean = 7.2
μ = 100 (under the null hypothesis)
s = 5.1
n = 22

Plugging these values into the formula, we get:

t = (7.2 - 100) / (5.1 / √22) = -16.49 (rounded to two decimal places)

The t statistic has a t-distribution with 21 degrees of freedom (df = n-1). We are testing the null hypothesis that the population mean is equal to 100 against the alternative hypothesis that it is less than 100. This is a one-tailed test with a significance level of α = 0.05.

Looking at the t-distribution table with 21 degrees of freedom, we find that the critical value for a one-tailed test with α = 0.05 is -1.721. Since our calculated t statistic (-16.49) is less than the critical value (-1.721), we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the population mean is less than 100.

Therefore, the value of the t statistic (±0.01) is -16.49.

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A quadrilateral with congruent diagonals is a rectangle. In a rectangle, the opposite sides are parallel and equal in length, and all interior angles are 90 degrees. The diagonals in a rectangle are congruent, which means they have the same length.

This property distinguishes rectangles from other quadrilaterals such as squares, rhombuses, parallelograms, kites, isosceles trapezoids, and trapezoids. Although squares and rhombuses also have congruent diagonals, they possess additional properties that rectangles do not have, such as all sides being equal in length for both squares and rhombuses, and all angles being 90 degrees for squares.

On the other hand, parallelograms, kites, isosceles trapezoids, and trapezoids do not have congruent diagonals. Therefore, a quadrilateral with congruent diagonals is a rectangle.

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75% of the beads are green in color.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Chase ordered a set of beads

He received 4,000 beads in all.

3,000 of the beads were green.

We need to find the  percentage of the beads were green of 4000.

x/100×4000=3000

40x=3000

Divide both sides by 40

x=75%

Hence, 75% of the beads are green in color.

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Answer:

Scale factor = 2.5.

Step-by-step explanation:

Work out the lengths of the corresponding sides.

The scale factor is the ratio of one side to the other.

Take the smallest length in both triangles.

Blue triangle:

length = √((7.5-2.5)^2 + (12.5-5)^2) = 9.0139 units.

Red triangle:

length = √((3-1)^2 + (5-2)^2) =3.6056

So the scale factor

= 9.0139/ 3.6056

= 2.5.

Answer:

First we have the function f(x) = 27*x  - 67.5

It has an x-intercept at (a, 0)

This means that:

f(a) = 0 = 27*a - 67.5

Solving the above equation we can find the value of a.

0 = 27*a - 67.5

67.5 = 27*a

67.5/27 = a = 2.5

Now let's look at equation g(x).

It is a linear equation, remember that a linear equation can be written as:

g(x) = y = A*x + B

Where:

A is the slope, and B is the y-intercept.

If the line passes through the points (x₁, y₁) and (x₂. y₂), the slope can be written as:

A = (y₂ - y₁)/(x₂ - x₁)

In this case we can select any two points from the table, for example, I will use the second and third points:

(1, 39) and (2, 32.5)

Then the slope is:

A = (32.5 - 39)/(2 - 1) = -6.5/1 = -6.5

Then the equation is something like:

g(x) = y = -6.5*x + B

B is the y-intercept, to find this value, we can use one of the two points we used before.

For example, (1, 39) means that g(1) = 39

Then:

g(1) = -6.5*1 + B = 39

     = B = 39 + 6.5 = 45.5

Then the equation for g(x) is:

g(x) = -6.5*x + 45.5

Now, we know that g(x) has an x-intercept at (b, 0)

this means that:

g(b) = 0 = -6.5*b + 45.5

6.5*b = 45.5

b = 45.5/6.5 = 7

Then the difference between b and a is:

b - a = 7 - 2.5 = 4.5

b is equal to a plus 4.5

And the ratio is:

b/a = 7/2.5 = 2.8

b is 2,8 times larger than a.

The correct statement is:

a. As analogue to digital conversion is a dynamic process, each conversion takes a finite amount of time called the quantization time.

Analog-to-digital conversion is the process of converting continuous analog signals into discrete digital representations. This conversion involves several steps, including sampling, quantization, and encoding.

During the quantization step, the continuous analog signal is divided into discrete levels or steps. Each step represents a specific digital value. The quantization process introduces a finite amount of error, known as quantization error, due to the approximation of the analog signal.

Since the quantization process is dynamic and involves the discretization of the continuous signal, it takes a finite amount of time to perform the conversion for each sample. This time is known as the quantization time.

During this time, the analog signal is sampled, and the corresponding digital value is determined based on the quantization levels. The quantization time can vary depending on the specific system and the required accuracy.

Therefore, statement a. accurately states that analog-to-digital conversion is a dynamic process that takes a finite amount of time called the quantization time for each conversion.

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