Can you solve this sum?
If you can show me how to made it step by step.​​

For the quadratic function y = ax² + bx + c , for which graph passes through the points (2, 31), (3 , 45) , (1, 19) is given by y = x² + 9x + 9.

As given in the question,

Standard form of quadratic function,

y = ax² + bx + c

Graph of the quadratic function passes through the points  (2, 31),

(3 , 45) , (1, 19) .

When passes through (2, 31)

31 = 4a + 2b + c __(1)

Passes through (3,45)

45 = 9a + 3b + c  __(2)

Passes through (1, 19)

19 = a + b + c __(3)

Multiply 9 to (3) and subtract (2) from it,

9a + 9b + 9c =171

9a +3b + c = 45

      6b + 8c = 126 ____(4)

Now, Multiply 4 to (3) and subtract (1) from it,

4a + 4b + 4c =76

4a +2b + c = 31

      2b + 3c = 45____(5)

Multiply 3 to (5) and subtract (4) from it,

6b + 9c = 135

6b + 8c =126

       c = 9

Substitute c= 9 in (5) we get,

2b + 3(9) = 45

⇒ b = 9

Now , substitute b = 9, c = 9 in (3) we get,

a + 9 + 9 = 19

⇒ a = 1

Required quadratic function is :

y = x² + 9x + 9  

Therefore, for the quadratic function y = ax² + bx + c , for which graph passes through the points (2, 31), (3 , 45) ,(1, 19) is given by y =x² + 9x + 9.

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Correlation coefficient = 0.945 ( approx) and weight of a student increases as the height of the student increases.

What is correlation coefficient?

A statistical indicator of the strength of a linear link between two variables is the correlation coefficient. Its values may be between -1 and 1.

Main Body:

Here, value of x are  =58, 59, 60, 62, 63, 64, 66, 68, 70

Value of y are,  =   122, 128, 126, 133, 145, 136, 144, 150, 151.

∑x = 570, ∑y= 1236, ∑ = 36234, ∑ = 170694

∑xy=78617

Thus the correlation coefficient r =

formula is in the image,

Where n is the number of the term.

here n = 9

thus, correlation coefficient

r= [tex]\frac{9*78617- 570*1236}\sqrt{{9*36234- (570^{2} )}\sqrt{9*170794- (1235)^{2} }[/tex]

Thus, r= 0.94452987512

Which is closed to 0.95 and less than 1.

Therefore, weight of a student increases as the height of the student increases.

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Answer:

The numbers are:

4 and 11

Step-by-step explanation:

a + b = 15      Eq. 1

3a - 1 = b        Eq. 2

Replacing Eq. 2 in Eq, 1

a + (3a - 1) = 15

a + 3a = 15 + 1

4a = 16

a = 16/4

a = 4

From Eq. 1:

a + b = 15

4 + b = 15

b = 15 - 4

b = 11

Check:

From Eq. 2:

3a - 1 = b

3*4 - 1 = 11

12 - 1 = 11

Answer:

Step-by-step explanation:

138

The standard form of the equation of the given straight line is 4x + (-7)y = 13.

We are given an equation. The equation is linear in nature. The equation represents a straight line. The equation is given below.

8x = 26 + 14y

We need to convert this equation to standard form. The standard form of an equation for a straight line is given below.

Ax + By = C

We need to rearrange the given equation so that it matches the correct format. The equation is written below.

8x - 14y = 26

We can simplify the equation further by dividing the whole equation by two.

4x + (-7)y = 13

Hence, the standard form of the equation is 4x + (-7)y = 13.

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Differentiation of   [tex]\frac{2x-3}{2x+1}[/tex]  is [tex]\frac{8}{4x^{2}+4x+1}[/tex] .

Differentiation formula for  [tex]\frac{d}{dx}(\frac{u}{v}) = \frac{v\frac{d}{dx} - v\frac{d}{dx}}{v^{2} }[/tex]

Here, u = 2x - 3

          v = 2x + 1

[tex]\frac{d}{dx}u[/tex] = 2

[tex]\frac{d}{dx}v[/tex] = 2

[tex]v^{2} = (2x+1)^{2}[/tex]

    [tex]= 4x^{2}+4x+1[/tex]

Putting the values,

[tex]\frac{d}{dx}(\frac{2x-3}{2x+1}) = \frac{(2x+1)(2)-(2x-3)(2)}{4x^{2}+4x+1}[/tex]

              [tex]=\frac{4x+2-(4x-6)}{4x^{2}+4x+1}[/tex]

              [tex]=\frac{4x+2-4x+6}{4x^{2}+4x+1}[/tex]

              [tex]=\frac{8}{4x^{2}+4x+1}[/tex]

Hence, Differentiation of   [tex]\frac{2x-3}{2x+1}[/tex]  is [tex]\frac{8}{4x^{2}+4x+1}[/tex] .

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The Bar graph, Line graph and Report displays the counter in decimal format.

Selecting a counter displays information about that counter's collected data as a chart type. The bar graph, line graph and report displays the current value of each performance counter in decimal format.

Line graph: - Line graph, also known as a line chart or line plot, is commonly drawn to show how something changes over a period of time. scientists and engineers use these graphs to understand and derive meaning from large chunks of data.

Bar graph: - This are the pictorial representation of data, in the form of vertical or horizontal rectangular bars, where the  length of bars are proportional to the measure of data. They are mostly used in business and finance, but they can also be found in other contexts. This can be used to show the distribution of different heights of students in a class.

Report: -  A report is a document that presents information in an organized format for a specific audience and purpose. All the skills and the knowledge of the professionals are communicated through reports. Reports help the top line in decision making. A rule and balanced report also helps in problem solving.

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The area of the floor in the scale drawing is 20 square inches.

Firstly calculating the width of scale drawing. For this we will equate the two fractions.

Length/width (rectangle) = length/width (scale drawing)

Let the width of scale drawing be x

24/30 = 4/x

x = 4×30/24

Performing multiplication on Right Hand Side of the equation

x = 120/24

Performing division on Right Hand Side of the equation

x = 5

So, the area of scale drawing = length × breadth

Area of scale drawing = 4 × 5

Performing multiplication on Right Hand Side of the equation

Area of scale drawing = 20 square inches

Hence, the area is 20 square inches.

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The cost of one cup of coffee in terms of x and y is x/12y.

Given in question,

Cost of 12 grams coffee = x dollars

   Cost of 1 gram coffee = x/12 dollars

1 gram coffee make cups = y

                   Cost of 1 cup = (x/12)/y

                                          = x/12y

Hence, the cost of one cup of coffee in terms of x and y is x/12y.

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The revised coordinates for the indicated site are (6, 3).

Given information;

Location of Point n (3, 5). The new coordinates will be if point n is moved 2 units down and 3 units right.

To get new coordinates we have to transform given points;

Transformation of the coordinate system: 

Defining new coordinate systems on the plane frequently involves coordinate transformations. The transformation's u- curves are representations of vertical lines with the form u- constant, while the v- curves are representations of horizontal lines with the form v- constant.

∴ (3, 5) ⇒ (3 + 3, 5 - 2)

           ⇒ (6, 3)

Hence, (6, 3) are the new coordinates of the given point.

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Answer: 8 months

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

3 6 and 7  = 82 °

1 4 5 8 = 180 - 82 = 98 °

The amount of water needed to drink with their 50 guests is 900 liters.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

In a town, 100 people need 600 liters of water to drink every day.

This can be written as,

100 people = 600 liters of water

50 guests are added.

The number of people = 100 + 50 = 150 people.

Now,

100 people = 600 liters of water

Multiply 150/100 on both sides.

150 people = 150/100 x 600 litres of water

150 people = 900 liters of water

Thus,

The amount of water needed to drink with their 50 guests is 900 liters.

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The equation that describes the proportional relationship between the distance she runs in miles, and her running speed, in miles per hour, when she runs, is:

d = 0.5v.

A proportional relationship is a special case of a linear function, with intercept zero, in which the output variable is given by the multiplication of the input variable and the constant of proportionality, given as follows:

y = kx

The distance as a function of the velocity and of the time in hours, is given as follows:

d = vt.

30 minutes is half an hour, hence the constant of the proportional relationship is given as follows:

v = 0.5.

Then the equation is:

d = 0.5v.

In which:

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The equation 3n = 6 has a solution n = 2.

An equation is an expression that shows the relationship between two or more numbers and variables.

We have to find that which equation below is n = 2 a solution.

Then substitute n = 2;

3n = 6

3(2) = 6

This equation has a solution n = 2.

2. n-1=2

Then substitute n = 2;

2 - 1 = 1

The solution of the equation is not n = 2

3. 9+n=12

Then substitute n = 2;

9 + 2 = 11

The solution of the equation is not n = 2

4. 3+n=8

Then substitute n = 2;

3 + 2 = 5

The solution of the equation is not n = 2

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For the given sequence of transformation mapping of pentagon ABCDE onto pentagon A"B"C"D"E" is given by Line reflection followed by a translation.

As given in the question,

Given sequence of transformation mapping of pentagon ABCDE onto pentagon A"B"C"D"E" is given by :

a. dilation followed by a rotation :

Here dilation means enlarge or reduced the original shape which is not true for the given pentagon ABCDE.

b. translation followed by a rotation :

Translation means moves around a fixed point by certain degrees that is horizontal or vertical shift.

Not true.

c. Line reflection followed by a translation:

In this case preimage is flipped across the line or get reflected.

True.

d. Line reflection followed by a line reflection:

Here  fixed line is or a line is used as mirror . You get a image of the original.

Not true.

Therefore, for the given sequence of transformation mapping of pentagon ABCDE onto pentagon A"B"C"D"E" is given by Line reflection followed by a translation.

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Answer:

- [tex]\sqrt{5}[/tex]

Step-by-step explanation:

using the rule of radicals

[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]

simplifying radicals

[tex]\sqrt{20}[/tex]

= [tex]\sqrt{4(5)}[/tex]

= [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex]

= 2[tex]\sqrt{5}[/tex]

and

[tex]\sqrt{45}[/tex]

= [tex]\sqrt{9(5)}[/tex]

= [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex]

= 3[tex]\sqrt{5}[/tex]

Then

4[tex]\sqrt{20}[/tex] - 3[tex]\sqrt{45}[/tex]

= 4(2[tex]\sqrt{5}[/tex] ) - 3(3[tex]\sqrt{5}[/tex] )

= 8[tex]\sqrt{5}[/tex] - 9[tex]\sqrt{5}[/tex]

= - [tex]\sqrt{5}[/tex]

Answer:

below

Step-by-step explanation:

The angle dimensions given for each triangle sum to 180 °

so

(x+10)  +  y+15   + 70 = 180     Simplifies to

x +y = 85

and

x + 20    + 50 + 60 = 180 °    simplifies to

x = 50°     use this value in the underlined equation to find y = 35°

Answer:

1. 104

2. 38

3. 38

Step-by-step explanation:

3x + 66 = 180

3x = 114

x = 38

The solutions are;

The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.

The critical value with a level of significance ‘of 0.01’ and degrees of freedom ‘of 3’ is 3.747.

The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.

Given;

Let's say you randomly choose n = 4 measurements from a normal distribution. If you were constructing the following confidence intervals, compare the standard normal z values with the appropriate t values.

(a) 80% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 1.2 and the column value is 08.

The critical value with a level of significance is 1.28.

α = 1 - 0.80 = 0.20

α/2 = 0.10

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with a level of significance ‘of 0.10’ and degrees of freedom ‘of 3’ is 1.533.

(b) 98% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 2.3 and the column value is 03.

The critical value with a level of significance is 2.33.

α = 1 - 0.98 = 0.02

α/2 = 0.01

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with level of significance ‘0.01’ and degrees of freedom ‘3’ is 3.747

(C) 90% confidence interval:

The z-value is obtained as shown below:

The level of significance is;

Locate the probability in the z table. Then, the corresponding row value is 1.6 and the column value is 04.

The critical value with a level of significance is 1.64.

α = 1 - 0.90 = 0.10

α/2 = 0.05

The t-value is obtained as shown below;

From the information, the sample size is 4.

df = n - 1 = 4 - 1

              = 3

The critical value with a level of significance ‘of 0.05’ and degrees of freedom ‘of 3’ is 2.132.

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Answer:

The correct answer is: c) 3r + 6s

Step-by-step explanation:

the first 3 pounds are always going to be r dollars, then every additional pound will be s dollars.

Since we have a package that weighs 9 pounds; 3 pounds will cost r dollars and 6 pounds wills cost s dollars.

example:

lets say that r = 10 and s = 5

the first 3 pounds will cost 10 dollars and then every pound after would be 5 dollars

so:  

3(10) + 6(5)

This is just an example, since we don't know the actual values of r and s, we just use those variables.

The possible days Wendy goes to the library are Monday and Thursday.

The number of books that Wendy reads is 12 books.

From the information, when she goes to the library she always reads 3 books and she also goes to the bookstore to read books twice a week.

In this case, the total books read in two weeks will be:

= (2 × 3) × Number of weeks

= (2 × 3) × 2

= 6 × 2

= 12

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Kelly's knitting speed is 2.92 feet per hour

From the question, the given parameters are:

Length of knot = 38 foot

Time to cover this length = 13 hours

The speed of the knitting the scarf is calculated as

Speed = Length of knot /Time to cover this length

Substitute the known values in the above equation

So, we have the following equation

Speed = 38/13

Evaluating the quotient in the above equation, we have

Speed = 2.92

Hence, the speed of knotting the scarf is 2.92 feet per hour

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Answer: 204 miles

Step-by-step explanation:

Inequality can be used to represent the situation is s + l <= 2 and 20s + 15l >= 185.

Given:

Edith tutors after school for which she gets paid at a rate of $20 an hour. she has also accepted a job as a library assistant that pays $15 an hour. she will work both jobs, but she is able to work no more than a total of ll hours a week, due to school commitments.

Edith wants to earn at least $185 a week working a combination of both jobs.

Let s and l be the hours of school and library.

s + l <= 2

20s + 15l >= 185.

Therefore Inequality can be used to represent the situation is s + l <= 2 and 20s + 15l >= 185.

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Answer:

70/3

Step-by-step explanation:

[tex]f(0)=\frac{140}{1+5e^{-2(0)}} \\ \\ =\frac{140}{1+5(1)} \\ \\ =\frac{140}{6} \\ \\ =\frac{70}{3}[/tex]

x > 5 represents a line with an open circle at 5 and going indefinitely toward infinity.

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given inequality is  - 3(2x - 5) < 5(2 - x).

- 6x + 15 < 10 - 5x.

- x < - 5.

x > 5 (think of moving x to make it positive).

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Answer:

12

Step-by-step explanation:

y it equal to 12 is

-48÷-4=12