Given the standard form, what is the x co-ordinate of the vertex of a quadratic function?

The number of different ways to plan his trip is 240240

The given parameters are

Places, n = 14

Stops, r = 5

From the question, we understand that the places are in specific order

This represents permutation

So, the number of different ways to plan his trip is

Ways = \(^nP_r\)

This gives

Ways = \(^{14}P_5\)

Apply the permutation formula

Ways = 14!/9!

Evaluate

Ways = 240240

Hence, the number of different ways to plan his trip is  240240

Read more about permutation at:

https://brainly.com/question/11732255

#SPJ1

Answer:

Las dimensiones del rectángulo son:

ancho = 16 cm

largo = 20 cm

Step-by-step explanation:

Consideración:

La formula del perímetro de un rectángulo es:

perímetro = 2(largo + ancho)

25% más grande = 125% = 125/100 = 1.25

Planteamiento:

2(a+b) = 72

b = 1.25a

a = longitud del ancho

b = longitud del largo

Desarrollo:

de la primer ecuación del planteamiento:

a+b = 72/2

a+b = 36

b = 36 - a        Ec. 3

Igualando la segunda ecuación del planteamiento con la Ec. 3:

1.25a = 36 - a

1.25a + a = 36

2.25 a = 36

a = 36/2.25

a = 16

de la Ec. 3:

b = 36 - a

b = 36 - 16

b = 20

Comprobación:

de la primera ecuación del planteamiento:

2(a+b) = 72

2(16+20) = 72

2*36 = 72

Answer:

Let x be the normal cost for an individual.

Given that Keith and his friends purchase the group package which costs $78 for 6 people. and that is $3 less per person. Since there are 6 people, it is $18 less.

The equation that represents this is

6x + 18 = 786x+18=78

6x = 966x=96

x = 16x=16

The normal cost for an individual is $16.

Step-by-step explanation:

The perimeter of the rectangle is, 3y + 1 feet.

What is perimeter?

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to determine a rectangle's or square's perimeter. In this instance, the rectangle's length is represented by x and its width by y.

P = x + x + y + y represents the perimeter, P.

Let the length of triangle is 7.5y + 8 feet and the width of triangle is 6y - 7.5 feet.

So, the perimeter of rectangle is,

Perimeter = 2(length + width)

                = 2(7.5y + 8 + 6y - 7.5)

                 = 2(1.5y + 0.5)

Perimeter = 3y + 1

Hence, the perimeter of the rectangle is, 3y + 1 feet.

To know more about perimeter, click on the link

https://brainly.com/question/25092270

#SPJ1

Answer:

Step-by-step explanation:

The translation 5 to the right adds 5 to the x-value.

The translation 1 unit down subtracts 1 from the y-value.

  (x, y) ⇒ (x+5, y-1)

P(0, 0) ⇒ P'(0+5, 0-1) = P'(5, -1)

Q(2, 4) ⇒ Q'(2+5,4-1) = Q'(7, 3)

R( 5, 2) ⇒ R'(5+5, 2-1) = R'(10, 1)

Answer:

P'[5,-1], Q' [7,3], R'[10,1]

Step-by-step explanation:

Since the object translates 5 unit to the right and 1 unit down ;it means the value of X will move 5 units positively and the value of y will decrement by 1 of its original value to create the image.

Answer:

idk if this helps but here:

Cutoff points are a crucial piece of calculus and are among the main things that understudies find out about in a calculus class. So, finding the constraint of a capacity implies figuring out what esteem the capacity approaches as it draws nearer and more like a specific point.

Step-by-step explanation:

The evaluation of the constraints with regards to the production of the polo and t-shirts, and to maximize the profit, using linear programming indicates that we get;

a. x = The number of polo shirts produced, y = The number of t-shirts produced

b. The inequalities representing the constraints are;

2·x + y ≤ 84

x + 2·y ≤ 106

x ≤ 36

x ≥ 0, y ≥ 0

c. P = 30·x + 22·y

d. Please find attached the graph of the feasible region

To maximize profit, the company should produce;

21 polo shirts and 43 t-shirts

Linear programming is a method used for optimizing (maximizing or minimizing a value) operations with some specified constraints.

a. The details indicates that the question is related to linear programming. Let x represent the number of polo shirt produced, and let y represent the number of t-shirts produced.

x = The number of polo shirt produced

y = The number of t-shirts produced

b) The constraints are;

Pattern and cutting section; 2·x + y ≤ 84

Sewing section; x + 2·y ≤ 106

Sales constraints; x ≤ 36

The values of x and y are non negative, numbers, therefore;

x ≥ 0, y ≥ 0

c) The objective of the company is to maximize profit, P, therefore, the objective function is; P = 30·x + 22·y

d) The graph can be plotted from the constraint inequalities, by making y the subject in the inequalities that includes both x and y as follows;

2·x + y ≤ 84, therefore; y ≤ 84 - 2·x

x + 2·y ≤ 106, therefore; y ≤ 53 - x/2

x ≤ 36

Please find attached the graph of the inequalities, showing the feasible region which is the polygon with boundaries which are the lines representing the constraints.

The objective function evaluated at the vertices of the feasible region indicates that we get;

\(\begin{tabular}{ | l | l | c | }\cline{1-3}(x, y)& 30\cdot x + 22\cdot y & P(\$) \\ \cline{1-3}(0, 53 & 30\times 0 + 22\times 53 & 1166 \\\cline{1-3}(21, 42.5 & 30\times 21 + 22\times 42.5 & 1565 \\\cline{1-3}(32, 12) & 30\times 36 + 22\times 12 & 1344 \\\cline{1-3}(36, 0) & 30\times 36 + 22\times 0 & 1080 \\\cline{1-3}(0, 0) & 30\times 0 + 22\times 0& 0 \\\cline{1-3}\end{tabular}\)

The feasible region and the objective function indicates that the values of x and y that maximizes the profit is; (x, y)  = (21, 42.5)

Therefore, to maximize profit, the number of polo and t-shirts the company should produce are 21, and 42.5 ≈ 43 respectively.

Learn more on linear programming here: https://brainly.com/question/29750786

#SPJ1

Answer:

a is what I have for your answer

Both Jeremy and Aksa could be right, depending on how they are counting the cubes for finding the volume of a prism.

A prism is a three-dimensional solid shape with a constant cross-section, usually a polygon. It is characterized by two identical end faces, parallel and congruent bases, and straight lateral faces connecting the bases.

Both Jeremy and Aksa could be right, depending on how they are counting the cubes.

If the prism has a square base with 4 cubes along each side, then there would be 16 cubes in each layer. If there are 4 layers, then the total volume would be 16 x 4 = 64 cubic units.

However, if the prism has a rectangular base with 6 cubes along one side and 4 cubes along the other side, then there would be 24 cubes in each layer. If there are 4 layers, then the total volume would be 24 x 4 = 96 cubic units.

Therefore, the answer depends on the shape of the prism and how the layers are counted.

To know more about Prism visit:

https://brainly.com/question/23963432

#SPJ1

Answer:

x=4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Given

5x + 2 = 22

5x = 22 - 2

5x = 20

x = 20 / 5

x = 4

Answer:

181

Step-by-step explanation:

im just guessing so it's probably not right

Answer:

Let x be the number of additional outfits.

5 + x < 11

(A) The slope of the secant line to f(x) from input value -3 to input value 0 is -5, while (B) the slope of the secant line to f(x) from input value x to input value x + h is 3h + 4.

Given the function f(x) = 3x² + 4x + 1, we are required to find the slope of the secant line to f(x) (also known as the average rate of change of f) from input value -3 to input value 0, and also from input value x to input value x + h.

(a) The slope of the secant line to f(x) (a.k.a, the average rate of change of f) from input value -3 to input value 0 is: We are required to find the slope of the line that passes through the two points (-3, f(-3)) and (0, f(0)). Here, the input value -3 corresponds to x = -3, and the input value 0 corresponds to x = 0. Substituting these values in the given function, we have f(-3) = 3(-3)² + 4(-3) + 1 = 16f(0) = 3(0)² + 4(0) + 1 = 1Hence, the slope of the secant line to f(x) from input value -3 to input value 0 is:\($$\frac{f(0) - f(-3)}{0 - (-3)} = \frac{1 - 16}{3} = -5$$\)

Therefore, the slope of the secant line to f(x) from input value -3 to input value 0 is -5.

(b) The slope of the secant line to f(x) (a.k.a, the average rate of change of f) from input value x to input value x + h is: We are required to find the slope of the line that passes through the two points (x, f(x)) and (x + h, f(x + h)). Hence, the slope of the secant line to f(x) from input value x to input value x + h is: \($$\frac{f(x + h) - f(x)}{(x + h) - x} = \frac{3(x + h)² + 4(x + h) + 1 - (3x² + 4x + 1)}{h}$$$$= \frac{3x² + 6xh + 3h² + 4x + 4h + 1 - 3x² - 4x - 1}{h} = \frac{3h² + 4h}{h} = 3h + 4$$\)

Therefore, the slope of the secant line to f(x) from input value x to input value x + h is 3h + 4.

For more questions on secant line

https://brainly.com/question/31033097

#SPJ8

We can complete the blanks with the following ratios:

(7.5 mi/1) * (1 mi/ 5280 ft) * (400ft/1 yd) * (3 ft/1 ft) =33 flags

Since we do not need a flag at the starting line, then 32 flags will be required in total.

To solve the problem, we would first convert 400 yds to feet and miles.

To convert to feet, we multiply by 3. This gives us: 400 yd * 3 = 1200 feet.

To convert to miles, we would have 0.227 miles.

Now, we divide the entire race distance by the number of miles divisions.

This gives us:

7.5 mi /0.227 mi

= 33 flags

Learn more about miles-to-yards conversion here:

https://brainly.com/question/1609225

#SPJ1

Answer:

1. The minimum head breadth that will fit the clientele is of 3.95-in.

2. The maximum head breadth that will fit the clientele is of 9.25-in.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Mean of 6.6-in and a standard deviation of 1.1-in.

This means that \(\mu = 6.6, \sigma = 1.1\)

1. What is the minimum head breadth that will fit the clientele?

The 0.8th percentile, which is X when Z has a p-value of 0.008, so X when Z = -2.41.

\(Z = \frac{X - \mu}{\sigma}\)

\(-2.41 = \frac{X - 6.6}{1.1}\)

\(X - 6.6 = -2.41*1.1\)

\(X = 3.95\)

The minimum head breadth that will fit the clientele is of 3.95-in.

2. What is the maximum head breadth that will fit the clientele?

The 100 - 0.8 = 99.2nd percentile, which is X when Z has a p-value of 0.992, so X when Z = 2.41.

\(Z = \frac{X - \mu}{\sigma}\)

\(2.41 = \frac{X - 6.6}{1.1}\)

\(X - 6.6 = 2.41*1.1\)

\(X = 9.25\)

The maximum head breadth that will fit the clientele is of 9.25-in.

In the given parallelogram ABCD the values for variables are - g = 6, y = 5 and x = 4.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

We know that in a parallelogram, opposite sides are congruent and parallel, and diagonals bisect each other.

Using this information, we can set up equations to solve for the variables.

From the given information, we have -

AE = CE = 2x - 5 = 5x - 17 (since diagonals bisect each other at point E)

BE = x + 2

DE = BE = (x + 2) = g (since diagonals bisect each other at point E)

We also know that opposite sides of a parallelogram are parallel.

Therefore, 10 is parallel to 2y, which means they have the same slope. We can write this as -

10/1 = 2y/1

10 = 2y

y = 5

Now we can use equation (1) to solve for x -

2x - 5 = 5x - 17

12 = 3x

x = 4

Finally, we can use x to solve for g -

(x + 2) = g

(4 + 2) = g

g = 6

Therefore, the values of x, y, and g are 4, 5, and 6, respectively.

To learn more about parallelogram from the given link

https://brainly.com/question/3050890

#SPJ1

Answer:

Mauricio's score for each event is 7.

Step-by-step explanation:

Mauricio scored a total of 34.42 points in five gymnastic  events.

We can round off his score as 35.

To find Mauricio's score for each event, divide total score and no of events as follows :

\(n=\dfrac{35}{5}\\\\=7\)

Hence, Mauricio's score for each event is 7.

n⁴ - 2n³ - 23n² + 24n + 144 is the standard form of given zeroes.

What is a linear equation in mathematics?

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.

                              A linear equation is an equation that raises a variable to the first power. ax+b = 0 is an example of a 1 variable. x is a variable and a and b are real numbers.  

Roots : -3(mult . 2), 4(mult.2)

the function is given as

     f(n) = (n + 3)² (n - 4)²

         = (n + 3) (n + 3 ) ( n - 4 ) ( n - 4)

        = (n² + 6n + 9) (n² - 8n + 16 )

        = n⁴ - 8n³ + 16n² + 6n³ - 48n² + 96n + 9n² - 72n + 1

collecting like term,

    f(n) = n⁴ - 2n³ - 23n² + 24n + 144

Learn more about Linear equation

brainly.com/question/11897796

#SPJ1

Given statement solution is :-  The Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

To find the sum of 4 + 20, we simply add the two numbers together:

4 + 20 = 24

As for the given vectors, let's perform the requested calculations:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 4 + (-4), -2 + (-32) > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 7 - (-8), -3 - (-30) > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 5 + 2, -11 + 0, 0 + 0, 0 + 0 > = < 7, -11, 0, 0 >

Therefore, the Vector Calculations and Addition results are as follows:

ü -< -3, -7 > = < -3, -7 >

=< 4, -2 > - < -4, -32 > = < 0, -34 >

< 7, -3 > - < -8, -30 > = < 15, 27 >

< 5, -11 > + < 2, 0, 0, 0 > = < 7, -11, 0, 0 >

And 4 + 20 = 24.

For such more questions on Vector Calculations and Addition

https://brainly.com/question/31866215

#SPJ11

Answer:

\(f(x)=4(x+6)^2-134\)

Step-by-step explanation:

We are required to write the function\(f(x) = 4x^2 + 48x + 10\) in vertex form.

First, bring the constant to the left-hand side.

\(f(x) -10= 4x^2 + 48x\)

Factorize the right hand side.

\(f(x) -10= 4(x^2 + 12x)\)

Take note of the factored term(4) and write it in the form below.

\(f(x) -10+4\Box= 4(x^2 + 12x+\Box)\)

\(\Box = (\frac{\text{Coefficient of x}}{2} )^2\\\\\text{Coefficient of x}=12\\\\\Box = (\frac{12}{2} )^2 =6^2=36\)

Substitute 36 for the boxes.

\(f(x) -10+4\boxed{36}= 4(x^2 + 12x+\boxed{36})\)

\(f(x) -10+144= 4(x^2 + 12x+6^2)\)

\(f(x) +134= 4(x+6)^2\\f(x)=4(x+6)^2-134\)

The function written in vertex form is \(f(x)=4(x+6)^2-134\)

Answer:

C

Step-by-step explanation:

I just finished the unit test on Edge. and got a 100% and I selected "c" as my answer.

Based on the information, we can infer that the tables are completed as follows: 5, 10, 15, 4, 8.

To complete the table of the ratios we must take into account the information provided in the fragment. According to the above, in box A for every two markers there are 5 pencils and in box B for every three markers there are 4 pencils. Then the ratios would be the following:

Box A

box B

Learn more about pencils in: https://brainly.com/question/20606782

#SPJ1

Answer:

\(Q = \frac{k}{14}\)

Step-by-step explanation:

Given

k and 14

Required

Determine the quotient

Quotient implies that we divide k by 14.

So, the quotient (Q) of k and 14 is:

\(Q = \frac{k}{14}\)

Answer:

513.45

Step-by-step explanation:

use intelligence

Answer:

S:{4}

Step-by-step explanation:

The inequality is
4x + 6 < 2x + 12

Subtract 2x from both sides:
4x - 2x + 6 < 2x - 2x + 12
2x + 6 < 12

Subtract 6 from both sides:
2x + 6 - 6 < 12 - 6
2x < 6

Divide both sides by 2
x < 3

So any value of x such that x ≥ 3 will make this statement false

In the answer choices, the only value that satisfies this conditionis the value 4

Answer:

In response to tissue injury, the body initiates a chemical signaling cascade that stimulates responses aimed at healing affected tissues. These signals activate leukocyte chemotaxis from the general circulation to sites of damage. These activated leukocytes produce cytokines that induce inflammatory responses [7].

Step-by-step explanation:

The Mann-Whitney U test is not appropriate for a comparison of two means in a causal comparative study.

To determine if two samples are likely to come from the same population, researchers employ the Mann Whitney U test, also known as the Mann Whitney Wilcoxon Test or the Wilcoxon Rank Sum Test (i.e., that the two populations have the same shape). When a continuous level variable is measured across all observations in two groups and we wish to test if the distribution of this variable differs between the two groups but we are unable to assume normality in both groups, we use the Mann-Whitney test.

Here,

Mann-Whitney test In a causal comparative investigation, comparing two means is not acceptable using the U test.

To know more about Mann-Whitney U test,

https://brainly.com/question/24341709

#SPJ4

The company can utilise anticipated value or mean to establish the average number of clients they can expect based on the probability distribution.

To compute the expected value, the company would multiply each value by its associated probability and then sum the results. This would provide the company with an estimate of the typical number of new clients they may expect in the forthcoming tax season.

This information discusses Backen and Hayes LLC's, a New York State accounting company, projections for the number of new clients seeking tax help during the forthcoming tax season. The company created a probability distribution for the number of new clients, with different numbers reflecting the number of clients and their associated probabilities.

For instance, the company has a 5% chance of acquiring 20 new clients, a 20% chance of acquiring 25 new clients, and so on. The likelihood of the company receiving 30 new clients is 25%. The firm's receiving 45 or 50 new clients has the lowest likelihood (10%).

For more such questions on Probability distribution, click on:

https://brainly.com/question/28021875

#SPJ4

Answer:

\(y=-\frac{4}{5}x-\frac{21}{5}\)

Step-by-step explanation:

The fastest way is to use point-slope form with \(m=-\frac{4}{5}\) and \((x_1,y_1)=(-4,-1)\):

\(y-y_1=m(x-x_1)\\y-(-1)=-\frac{4}{5}(x-(-4))\\y+1=-\frac{4}{5}(x+4)\\y+1=-\frac{4}{5}x-\frac{16}{5}\\y=-\frac{4}{5}x-\frac{21}{5}\)

To graph the line passing through (-4,-1) with slope m = -4/5, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting m = -4/5, x = -4, and y = -1, we can solve for b:

-1 = (-4/5)(-4) + b

-1 = 3.2 + b

b = -4.2

Therefore, the equation of the line is:

y = (-4/5)x - 4.2

To graph the line, we can plot the given point (-4,-1) and then use the slope to find additional points. Since the slope is negative, the line will slope downwards from left to right. We can find the y-intercept by setting x = 0 in the equation:

y = (-4/5)x - 4.2

y = (-4/5)(0) - 4.2

y = -4.2

So the y-intercept is (0,-4.2).

Using this point and the given point (-4,-1), we can draw a straight line passing through both points.

Here is a rough sketch of the graph:

     |

     |

     |     *

     |    /

     |   /

     |  /

-----*--------

     |

     |

     |

     |

     |

The point (-4,-1) is marked with an asterisk (*), and the y-intercept (0,-4.2) is marked with a dash. The line passing through these two points is the graph of the equation y = (-4/5)x - 4.2.

Using the probability concept, it is found that:

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

Item a:

Then:

P(star) = 3/8 = 0.375 = 37.5%.

Item b:

Then:

P(not diamond) = 7/8 = 0.875 = 87.5%.

Item c:

Then:

P(flower) = 1/4 = 0.25 = 25%.

Item d:

\(p = \frac{2}{8} = \frac{1}{4}\)

Out of 100:

\(\frac{1}{4} \times 100 = \frac{100}{4} = 25\)

You would expect to spin a heart 25 times.

A similar problem is given at https://brainly.com/question/16256175