subtract 5 from 12, then multiply by 4

Length of the line AB is 1.414 units and midpoint of AB is (3.5,5.5).

Given in the graph,

A(4,6)  and B(3,5)

Distance formula = [tex]\sqrt{(x1-x2)^{2} +(y1-y2)^{2} }[/tex]

                      AB =  [tex]\sqrt{(4-3)^{2} +(6-5)^{2} }[/tex]

                            = [tex]\sqrt{1^{2} +1^{2} }[/tex]

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

                            = 1.414 units

Midpoint = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2})[/tex]

Let midpoint of AB be C(x,y)

C = (x,y) = [tex](\frac{4+3}{2},\frac{6+5}{2})[/tex]

             = [tex](\frac{7}{2},\frac{11}{2})[/tex]

             = (3.5,5.5)

Hence, length is 1.414 units and midpoint is (3.5,5.5).

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In linear equation, 275 hamburgers were sold on Wednesday​ .

What in mathematics is a linear equation?

Let x = the number of hamburgers sold

Let x - 67 = the number of cheeseburgers sold

x + x - 67 = 483

2x = 483 + 67

2x = 550

x = 275

x = 275 hamburgers

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Answer:

The number of books bought in each store would be 4 The amount spent will be the same in either store.

Step-by-step explanation:

Comment

The question has to make the assumption that no matter how many books are bought from store 1, the shipping charge is 8 dollars. Otherwise there is no solution.

Givens

Book1: 10 and  8 dollars total for shipping

Book2: 12 dollars, no shipping costs.

Equation

12x = 10x + 8         Subtract 10x from both sides

Solution

12x - 10x = 10x - 10x + 8      Combine

2x = 8                                   Divide both sides by 2

2x/2 = 8/2

x = 4

The absolute value of the difference between the first and second numbers is 5.

Here we have to find the difference between the first and the second numbers.

There are three statements.

Let a, b, and c be the first, second, and third numbers respectively.

The first statement is that the sum of the three number is 96.

The second statement is that the first number is 6 times the third number.

a = 6c

The third statement is that the third number is 40 less than the second number.

c = b - 40

b = c + 40

The sum of the three numbers is 96.

a + b + c = 96

6c + c + 40 + c = 96

8c = 96 - 40

8c = 56

c = 7

As a = 6c and b = c + 40

Now put the value of c as 7 we have:

a = 6 × 7

= 42

b = 7 + 40

= 47

Difference between the first and second numbers= 47 - 42

= 5

Therefore the difference is 5.

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Answer:

y = [tex]\frac{4}{3}[/tex] x + 4

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 )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line

m = [tex]\frac{4-0}{0-(-3)}[/tex] = [tex]\frac{4}{0+3}[/tex] = [tex]\frac{4}{3}[/tex]

the line crosses the y- axis at (0, 4 ) ⇒ c = 4

y = [tex]\frac{4}{3}[/tex] x + 4 ← equation of line

Answer:10.75

Step-by-step explanation:

3/4 as a decimal is 0.75. add that to the 10 gives you 10.75

Answer: m=0

Step-by-step explanation: (-10,17) & (-9, 17) are 2 points away from each other on the x-axis, there is no difference in y. Therefore the answer is zero.

Using the exterior angles theorem, the measures of the named angles are:

m∠PQR = 51°

m∠PRQ = 96°

Based on the exterior angles theorem, the measure of the exterior angle of a triangle has an angle degree that is equal to sum of the interior angles of the triangle.

Therefore, the following equation would be set to find the value of x:

33 + 10x + 1 = 17x - 1

34 + 10x = 17x - 1

Combine like terms

34 + 1 = 17x - 10x

35 = 7x

35/7 = 7x/7

5 = x

x = 5

m∠PQR = 10x + 1 = 10(5) + 1 = 51°

m∠PRQ = 180 - (17x - 1) = 180 - (17(5) - 1) = 96°

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Answer:

-4

Step-by-step explanation:

(-2)^2 + 4(-2) =

= 4 - 8 =

= -4

Part A: polynomial in Standard form;-

bluef(x) = ax⁴ + bx³ + cx²+ dx + e

Part B: Closure property relates to polynomial;-

The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.

What is  Polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.

A.

Any of the following can be the fourth degree polynomial with two terms:

f1(x) = ax⁴ + bx³

f2(x) = ax⁴ + cx²

f3(x) = ax⁴ + dx

f4(x) = ax⁴ + e

a ≠ 0  in all four instances.

Explanation. Because each of the aforementioned polynomials fi(x)-s can be written in the form of f(x) by setting blue0 equal to (c,d,e), (b,d,e), (b,c,e), and (b,c,d), respectively, each of the aforementioned polynomials is in standard form.

B.

The polynomial's closer property for subtraction. When two polynomials of identical degrees with different leading coefficients are subtracted, a polynomial of the same degree is produced.

Example.

Let r(x) be defined as a₁x³ + a₂x² + a₃x + a₄

s(x) is equal to b₁x³ + b₂x² + b₃x + b₄

where a ≠ 0 ≠ b and a ≠ b both belong to a set of real or complex numbers called ai and bi.

If this is how subtraction is defined, then

r(x) - s(x) = [a₁x³ + a₂x² + a₃x + a₄] - [b₁x³ + b₂x² + b₃x + b₄]

r(x) - s(x) = (a₁ - b₁)x³ + (a₂ - b₂)x² + (a₃ - b₃)x + (a₄ - b₄)

Given that (a₁ - b₁) ≠ 0, r(x) - s(x) is similarly a polynomial of fourth degree in this situation.
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By using algebra properties, the quadratic equation y = x² - 4 contains the roots x = - 2 and x = 2.

In this problem we need to derive the quadratic equation that contains two roots: r₁ = - 2, r₂ = 2. We need to replace all roots in the factor form of the quadratic equation and expand it by algebra properties. First, replace the roots of the factor form of the quadratic equation:

y = (x - r₁) · (x - r₂)

y = (x + 2) · (x - 2)

Second, expand the expression derived in the previous step by algebra properties:

y = (x + 2) · x - (x + 2) · 2

y = x² + 2 · x - 2 · x - 4

y = x² - 4

Third, write the resulting expression:

y = x² - 4

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Answer:

A

Step-by-step explanation:

Answer:

b = (4/3), with rounding

Step-by-step explanation:

Area = A, in cm^2

n = days

A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]

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

Data:

n = 2, A = 1.8

A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]

1.8 =  [tex]A_{0}[/tex][tex]b^{2}[/tex]

n = 3, A = 2.4

2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex]

Although we are not given the initial area, we can still make the calculation since we have two data points and each has the same initial area, [tex]A_{0}[/tex].  Lets take the first equation and multiply it by b, in order to bring the [tex]b^{2}[/tex] to [tex]b^{3}[/tex]

1.8 =  [tex]A_{0}[/tex][tex]b^{2}[/tex]

b(1.8 =  [tex]A_{0}[/tex][tex]b^{2}[/tex])

1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]

We can know from the second equation that 2.4 = [tex]A_{0}[/tex][tex]b^{3}[/tex] .  We can eliminate this term in the above relationship by substituting 2.4:

1.8b = [tex]A_{0}[/tex][tex]b^{3}[/tex]

1.8b = 2.4

b =  1.3333

       or (4/3)

Check:

Does the value of (4/3) for b work for both data points?  To check this, we do need to assume an initial starting area.  Lets assume the starting area, [tex]A_{0}[/tex] = 1.

n = 2, A = 1.8, b = (4/3)

A(n) = [tex]A_{0}[/tex][tex]b^{n}[/tex]

1.8 =  1*[tex](4/3)^{n}[/tex]

1.8 =  1.78  Close enough?

n = 3, A = 2.4, b = (4/3)

2.4 = [tex]A_{0}[/tex][tex](4/3)^{n}[/tex]

2.4 = 1*[tex](4/3)^{3}[/tex]

2.4 = 2.37 Close enough?

The value of 150/4 to the nearest tenth is 37.50

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. . In a proper fraction, the numerator is less than the denominator. In improper fraction, the denominator is smaller to the numerator.

The value of 150/4 = 75/2= 37 1/2

1/2 in decimal is 0.5

Therefore 150/4= 37+ 0.5= 37.5

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The required value of "b" is 7, where the equation is y = -3x + 7.

As per the given table, we take the two points (9, 1) and (3,7).

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = -3, y₁ = 16

x₂ = 1, y₂ = 4

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

Substitute the values in the above equation,

y - 16 = [(4 - 16)/(1 - (-3))](x - (-3))

y - 16 = (-12/4)(x+3)

y - 16 = -3(x+3)

y - 16 = -3x - 9

y = -3x - 9 + 16

y = -3x + 7  ....(i)

Compare the given equation y = mx + b with the above equation, and we get

b = 7

Therefore, the required value of "b" is 7.

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The inequality for this graph is:

x<2

The dimension of each corral should be 25 feet in width and 33⅓ feet in length so that the enclosed area will be a maximum.

Adjacent rectengular corral has length and width with area formula as below.

A = L × W

Given:

Because the dimension of adjacent rectangular corrals are the same, so:

W = 4x

L = 3y

3y + 4x = 200

[tex]y = \frac{200 - 4x}{3} [/tex]

There are two adjacent rectangular corrals, so:

A = 2×L×W

[tex]A = 2 \times \frac{200 - 4x}{3} \times \: x [/tex]

A = ⅓(400x–8x²)

We can differentiate to get the maximum area:

⅓×(400x–8x²) = 0

400–16x = 0

16x = 400

x = 25 feet

Substitute x value (width) to get y value (length):

y = (200–4(25)) ÷ 3

y = (200–100) ÷ 3

y = 100 ÷ 3

y = 33⅓ feet

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The average of aa and bb is 740.

The result of adding together and dividing by the total number of numbers or variables is the arithmetic mean, which is also known as the average or average value. In statistics, the arithmetic mean is significant. Central tendency is measured using the arithmetic mean. By giving each observation the same amount of weight, it enables us to determine the frequency distribution's center for a quantitative variable (in contrast to the weighted arithmetic mean).

Given,

Arithmetic mean = 1515

Total number of values = 5

Formula:

Sum/Total = Arithmetic mean

33 + 55 + 77 + aa + bb/ 5 = 1515

165 + aa + bb = 7575

aa + bb = 7575 - 165

aa + bb= 7410

The average of aa and bb is 740.

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The record-holder ate 6.205 kilograms of hot dogs.

We are given that 73/10 hotdogs per minute is the record for the most hot dogs eaten and one hot dog and bun has a mass of 85 grams. Also, one kilogram is equal to 1,000 grams. Solving this problem would involve converting units.

In order to find out how many kilograms of hot dogs the record holder ate, we first need to convert 85 grams to kilograms. Since a kilogram is equal to 1,000 grams, 85 grams = 85 / 1,000 = 0.085 kilograms.

Then, we multiply 0.085 by 73 to get 6.205. We can conclude that the record-holder ate 6.205 kilograms of hot dogs.

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29 elements are there in total for sets A, B, and C

Since  we are provided the  values of pair-wise intersections which are: |A∩B|=|A∩C|=|B∩C|= 7 and  the  three sets have common is |A∩B∩C| = 2 and individual sets  were having |A|=19 ,|B|=|15 and |C|=14. The formula we are referring to for calculating the  total  elememets altogether is A∪B∪C|=|A|+|B|+|C|−|A∩B|−|A∩C|−|B∩C|+|A∩B∩C|, where |A|,|B|,|C|quantity for individual sets,|A∩B|,|A∩C|,|B∩C| are the intersection subsets in a pairwise, and|A∩B∩C| is the intersection subset for the three sets altogether.

So substituting the  know values in the  above format, we get  

=> |A∪B∪C|= 19+15+14-7-7-7+2

=>|A∪B∪C|=29

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The number of books bought by the school is 92.

Here it is given that the school spend $925 to buy new books for the library.

The cost of each book is $9.95

So we have to find the number of books that can be bought.

By dividing the total money spent by the cost of each book we get the number of books bought.

Let n be the number of books bought.

n × 9.95 = Total money spend on the books

As we know the total money spend on the books is $925.

So we get:

925 = n × 9.95

n = 925/ 9.95

= 92

Therefore the total number of books bought is 92.

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Answer:

It line splits the graph of a quadratic equation into two mirror image, or basically means every point on the parabola on one side of the axis will be a mirror image of the other side of the parabola.

np :d

The value of x are, x = 9, x = -9.

What is undefined expression?

A mathematical expression that consists of a number of variables and arithmetic operations but has no known solution is referred to as an undefined expression. Any expression that has the symbol ∞ in any part of its expression or that has zero in the denominator is regarded as being undefined.

When the denominator is zero, a rational expression cannot be defined. Set the denominator equal to zero and solve the ensuing equation to get the values that render a rational expression undefined.

So, to find the x - values set denominator equal to zero.

[tex]x^2 - 81 = 0\\x^2 = 81\\x = \sqrt{81}[/tex]

x = ± 9

Therefore, the value of x are, x = 9, x = -9.

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Answer:

2561.2785

Step-by-step explanation:

All you gotta do is calculate and times 78.93 x 32.45