A bookstore has 45 copies of a bestseller available on Saturday morning. Twenty-one customers purchase the book that day. On Monday, a shipment of 25 books arrives and 14 copies are sold. Which statements are correct?

A The integer −21 represents the sale of 21 books.The integer −21 represents the sale of 21 books.

B After Monday's sales, 26 copies are available.After Monday's sales, 26 copies are available.

C The integer 25 represents the new shipment.The integer 25 represents the new shipment.

D After Monday's sales, 35 copies are available.After Monday's sales, 35 copies are available.

E The integer 14 represents the sale of 14 books.
(P.S it can have multiple answers)

The value of the linear equation 12x+10=54-10x, X=22.

An algebraic equation of the form y=mx+b is referred to as a linear equation involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a linear equation of two variables, where y and x are the variables.

Given that,

Moira chooses 10x on the left side of the equation,

And on the right side she chooses 10x

Given equation is 12x+10=54-10x

12x+10-10=54-10x-10 (subtract -10 on both sides)

12x=44-10x

12x-10x=44 (sending 10x on left side of the equation)

2x=44

X=22

Therefore the value of linear equation 12x+10=54-10x is X=22.

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Answer: Maybe D, I'm not sure

Step-by-step explanation:

When certain mapping in the plane has the following property: Each pair of points A and B is mapped to another pair or points A' B' such that quadrilateral AA'BB' is parallelogram, the transformation is reflection.

Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.

When a figure is translated, it is moved in any direction.

Flipping a figure over a line is called reflection.

Rotation is the process of turning a figure a specific amount around a point.

When we dilate a figure, we increase or decrease its size.

In this case, since the figure is flipped, over a line is called reflection.

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Step-by-step explanation:

b(h) = 212 - 1.72×h/1000

what is h, when b = 190 ?

190 = 212 - 1.72×h/1000

-22 = -1.72×h/1000

22000 = 1.72×h

h = 22000/1.72 = 12,790.69767... ≈ 12,791 ft

Answer:

log 75.

Step-by-step explanation:

log 25 + log 3​

= log (25*3)

= log 75

This is one of the laws of logs.

Answer:

9+8-6+6=29

Step-by-step explanation:

MATHAMATICS please check this i don't know x or×

The height of the Kudzu vine after 15 days is 8 m.

The initial measurement of length of Kudzu vine =

0.5 metres

Length of the Kudzu vine after seven days = 4 m

[tex]Let \: the \: (x _{1},y _{1}) =(0 ,0.5)[/tex]

[tex]Let \: the \: (x _{2},y _{2}) =( 7,4)[/tex]

The rate of the growth of the Kudzu vine per day is,

The slope formula is,

[tex]m = \frac{(y _{2} - y _{1}) }{ (x _{2} - x _{1}) }[/tex]

[tex]m = \frac{4 - 0.5}{7 - 0} [/tex]

[tex] = \frac{3.5}{7} [/tex]

= 0.5

Rate of growth of Kudzu vine per day is 0.5 per day.

Let the height of the Kudzu vine after fifteen days be y2.

The height of the Kudzu vine after fifteen days is,

[tex]m = \frac{(y _{2} - y _{1}) }{ (x _{2} - x _{1}) }[/tex]

[tex]0.5= \frac{y _{2} - 0.5 }{15 - 0} [/tex]

Now, multiplying 15 on both the sides. [tex]7.5 = y _{2} - 0.5[/tex]

[tex]y _{2} = 8[/tex]

Therefore, the height of the Kudzu vine after fifteen days is 8 m.

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The 17th term of the arithmetic progression (A.P) is given as 18.

An arithmetic progression (AP) is a succession in which the differences between each successive term are the same.

Now, as per the given question;

Then, the 17th term will be;

Apply the difference formula;

d = a₁₇ - a₁₆

a₁₇ = a₁₆ + d

a₁₇ = 21 + (-3)

a₁₇ = 21 - 3

a₁₇ = 18.

Therefore, the value of the 17th term of an AP is found to be 18.

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It is true that the expressions √3 + 5 and √2x/3y  cannot be simplified while the expression (x + y)3/2 can be simplified

Expressions are mathematical statements that are represented by variables, coefficients and operators

Expression 1

The expression is given as

√3 + 5

The above expression is a combination of a radical expression and an integer

The radical expression √3 cannot be simplified

This means that the expression √3 + 5 cannot be simplified

Hence, the expression √3 + 5  cannot be simplified

Expression 2

The expression is given as

√2x/3y

The above expression is a combination of radical expressions

However, the radical expressions do not have a common factor

This means that the expression √2x/3y cannot be simplified

Hence, the expression √2x/3y  cannot be simplified

Expression 3

The expression is given as

(x + y)3/2

Open the bracket

(x + y)3/2 = 3/2x + 3/2y

This means that the expression (x + y)3/2 can be simplified

Hence, the expression (x + y)3/2 can be simplified

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The measures of m [tex]\angle[/tex] A = 30º, m [tex]\angle[/tex] D = 30º, measure of arc AC = 60º and measure of arc BD = 60º.

The arcs exists congruent because they have equal measures.

Congruent arcs are arcs on circles that have the same degree measure and have congruent radii. A minor arc is one with a degree measure between 0º and 180º. A semicircle is an arc with a degree measure of 180º. A major arc is one with a degree measure between 180º and 360º.

If two arcs have the same length and are segments of congruent circles, they are congruent arcs. Because any circle is congruent to itself, two arcs of equal length that are part of the same circle are congruent arcs.

The measures of m [tex]\angle[/tex] A = 30º, m [tex]\angle[/tex] D = 30º, measure of arc AC = 60º and measure of arc BD = 60º.

The arcs exists congruent because they have equal measures.

The complete question is:

In this problem, you will investigate the relationship between the arcs of a circle that are cut by two parallel chords.

Use a protractor to find m \angle A and m \angle D. Then determine the measure of arc AC and BD. What is true about these arcs? Explain

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By substitution, the solution of the system of equations, 4p + 2q = 8 and q = 2p + 1, is (p , q) = (3/4 , 5/2).

A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.

There are three methods that can be used to solve system of linear equations.

1. Elimination

2. Substitution

3. Graphing

Using substitution method, given two linear equations in p and q,

4p + 2q = 8     (equation 1)

q = 2p + 1     (equation 2)

Since the second equation is already expressed in q in terms of p, substitute the second equation to the first equation.

4p + 2q = 8     (equation 1)

4p + 2(2p + 1) = 8

4p + 4p + 2 = 8

Combining all terms containing the variable p on one side and the constants on the other side of the equality, and solving for p.

4p + 4p + 2 = 8

4p + 4p = 8 - 2

8p = 6

p = 6/8

p = 3/4

Substitute the value of p in the second equation and solve for q.

q = 2p + 1

q = 2(3/4) + 1

q = 6/4 + 1

q = 5/2

Hence, the solution of the given system of equations is (p , q) = (3/4 , 5/2).

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The required value of the constant of proportion is 2.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of constant of variation

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion     —-- 1

Given the relation is y = 2x            —-- 2

On comparing both the equation 1 and 2, we have,

k = 2

Hence, the required value of constant of variation is 2.

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y - 9.1x - 3.6 = 0 is an equation of the line y=9.1 x+3.6 in standard form

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

Standard form of an equation is given as ax + by + c = 0

Here is given

⇒ y = 9.1 x+3.6

⇒ y - 9.1x - 3.6 = 0

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The number of falls per event is 3 (second option).

The number of falls per event can be determined by using the mathematical operation, division. Division is the process of splitting an amount into equal parts using another number. For example, to divide 12 by 3, 12 has to be divided into equal parts using 3.

The sign used to represent division is ÷. The other operations used in mathematics are addition, subtraction and multiplication.

The number of falls per event = total times Grady fell off the horse / number of rodeo events

156 / 52 = 3 times

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Hence, proved the reflective property of segment congruence.

We need to write a two-column proof for the property reflective property of segment congruence.

In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.

Two angles are congruent if and only if they have equal measures. Two segments are congruent if and only if they have equal measures. Two triangles are congruent if and only if all corresponding angles and sides are congruent.

Consider, XY≅AB

Prove that, AB≅XY

Proof: XY≅AB (given)

XY=AB (Definition of the congruent segment)

AB=XY (Symmetric property of equality)

AB≅XY (Definition of the congruent segment)

Hence, proved the reflective property of segment congruence.

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The range of given set of data is 15.

We have a set of numbers.

We have to determine its range.

The range is the difference between the smallest and highest number in a list.

According to the question, we have the following set of elements -

40, 41, 52, 54, 50, 39, 43, 54.

Arrange it in ascending order -

39  40  41  43  50  52  54  54

Now -

Range = Highest number - Lowest number

Range = 54 - 39

Range = 15

Hence, the range of given set of data is 15.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads..}[/tex]

[tex]\large\boxed{\text{What is the range of 40, 41, 52, 54, 50, 39, 43, 54 \bf ?}}[/tex]

[tex]\huge\textbf{To find your range, you have to..}}[/tex]

[tex]\large\boxed{\text{You have to find the difference between the largest number in the}}\\\\\large\boxed{\text{data plot from the smallest number in data plot.}}[/tex]

[tex]\huge\textbf{The range formula is..}[/tex]

[tex]\large\boxed{\rm{largest\ number - smallest\ number = range}}[/tex]

[tex]\huge\textbf{The data plot..}[/tex]

[tex]\large\boxed{\rm{40, \ 41, \ 52, \ 54, \ 50, \ 39, \ 43, \ 54}}[/tex]

[tex]\huge\textbf{Now let us answer the question..}[/tex]

[tex]\large\boxed{\rm{40, \ 41, \ 52, \ 54, \ 50, \ 39, \ 43, \ 54}}\\\\\large\boxed{\rm{The\ largest\ number\ in \ the \ plot\rightarrow 54}}\\\\\large\boxed{\rm{The \ smallest \ number\ in\ the\ data plot\rightarrow 39}}[/tex]

[tex]\huge\textbf{Your equation should be:}[/tex]

[tex]\large\boxed{\rm{54 - 39}}}\\\\\large\boxed{\rm{Simplify \ it}}\\\\\large\boxed{\rightarrow 15}}[/tex]

[tex]\huge\textbf{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{15}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

No

Step-by-step explanation:

-2(4-x) = 2x+8

Distribute the -2 on the left hand side

-2 *4 -2*-x = 2x+8

-8 +2x = 2x+8

They are not equal so it is not an identity

Answer: not an idenfity

Step-by-step explanation:

[tex]-2(4-x)=2x+8\\(-2)(4)+(-2)(-x)=2x+8\\-8+2x=2x+8\\2x-8\neq 2x+8[/tex]

The perimeter of parallelogram BCDE is 38 .

The plotting of the points B(2,-8), C(2, 1), D(-3, 5), and E(-3,-4) is given below.

Using distance formula , put [tex]x_1=2, \ y_1 =-8[/tex] and [tex]x_2=2, \ y_2 =1[/tex] in equation (1) , we get BC

      [tex]BC=\sqrt{(2-2)^2+(1-(-8))^2} \\BC=\sqrt{0+(1+8)^2} \\BC=\sqrt{(9)^2} \\BC= 9[/tex]

Using distance formula , put [tex]x_1=2, \ y_1 =1[/tex] and [tex]x_2=-3, \ y_2 =5[/tex] in equation (1) ,we get CD

       [tex]CD=\sqrt{(-3-2)^2+(5-1)^2} \\CD=\sqrt{(-5)^2+(4)^2} \\CD=\sqrt{25+16} \\CD=\sqrt{100} \\CD=10[/tex]

Using distance formula , put [tex]x_1=-3, \ y_1 =5[/tex] and [tex]x_2=-3, \ y_2 =-4[/tex] in equation (1) ,we get DE

       [tex]DE=\sqrt{(-3-(-3))^2+(-4-5)^2} \\DE=\sqrt{(-3+3)^2+(-9)^2} \\DE=\sqrt{0+81} \\DE=\sqrt{81} \\DE=9[/tex]

Using distance formula , put [tex]x_1=2, \ y_1 =-8[/tex] and [tex]x_2=-3, \ y_2 =-4[/tex] in equation (1) ,we get BE

     [tex]BE=\sqrt{(-3-2)^2+(-4-(-8))^2} \\BE=\sqrt{(-5)^2+(-4+8)^2} \\BE=\sqrt{25+(4)^2} \\BE=\sqrt{25+16} \\BE=\sqrt{100} \\BE=10[/tex]

Perimeter [tex]=10+10+9+9=38[/tex]

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The given sequence 10,20,30,40, ........... forms an arithmetic sequence. The common difference is found to be 10.

The difference between the two mathematical orders is a fixed value in Arithmetic Progression (AP). Another name for it is Arithmetic Sequence.

We'd come around a few specific words in AP that were labeled as:

Some formulas related to AP are-

Now, for the stated sequence is: 10,20,30,40, ...........

Let us suppose the first term is'a₁' = 10.

Let us suppose 'a₂' = 20 is the second term.

Let us suppose the third term is 'a₃' = 30.

Let us suppose the fourth term be 'a₄' = 40.

d = a₂ - a₁      

Substitute the values;

d = 20 - 10 = 10       ........(equation 1)

Now consider the other set;

d = a₃ - a₂    

d = 30 - 20 = 10      .......(equation 2)

Comparing equation 1 and 2, the common difference is same.

Thus, the given sequence forms an AP.

The common difference is found to be 10.

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After 25 minutes we will run out of the programs for the play.

An arithmetic sequence will yield a graph that is a straight line. A sequence is an arrangement of numbers in a particular pattern. The nth term of an arithmetic sequence is expressed as  nth term of the expression in form of the equation of a straight line is y = mx + b where;

m is the slope, b is the intercept, slope = d, y-intercept b = a -d.

total programs = 500          (given)

rate at which the audience members are filing into the theatre=20/minute

                                                                                                           (given)

the equation formed by analyzing the given data is

y = 500 - 20x

(x is the intercept that is the time taken to finish the programs )

for the programs to be finished  y should be = 0

0 = 500 - 20x                     ( putting value of y = 0)

500 = 20x                          ( like terms on same side and unlike on different)

x = 500/20

x = 25 minutes

Therefore, we can conclude that after 25 minutes we will run out of the programs for the play.

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The number of different 3-digit number if each of those digits is only allowed to be used once is 60

The digits are given as:

2, 4, 5, 7, 9

There are 5 digits represented in the above list

If each of those digits is only allowed to be used once, then we have the following possibilities

The number of 3-digit number codes is

Number =  5 * 4 * 3

Evaluate the product

Number = 60

Hence, the number of different 3-digit number if each of those digits is only allowed to be used once is 60

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Answer:

9

Step-by-step explanation:

given

10x + 3y = 2

then

10x + 3y + 7

= 2 + 7

= 9

The required first term is 100 and the common ratio is 1.1 and the 11th term is 285.

Geometric progression is a sequence of series whose ratio with adjacent values remains the same.

Here,
Orignal price iss 100
Appreciates 10% each year,
So price on next year = 100 + 100 * 10 / 100
So the price next year = 110
Similarly price on the next year becomes in a series = 100, 110, 121,
Now, the first term of geometric progression = 100
Common difference = 110 / 100 = 1.1
11 the term = 100 * 1.1 ¹¹
11the term = 285

Thus, the required first term is 100 and the common ratio is 1.1 and the 11th term is 285.

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Answer:

Volume = Length × Width × Height. Use this formula.

Put in 2 of the second spoon (1 teaspoon) and 1 of the third spoon (1/2 teaspoon).

Answer: f(2)=-10     f(-3)=15

Step-by-step explanation:

Let the number conceived be x.

Hence,

f(x)=(x+5)(-3)-2x+15

f(x)=-3x-15-2x+15

f(x)=-5x

Thus,

f(2)=(-5)(2)

f(2)=-10

f(-3)=(-5)*(-3)

f(-3)=15

The expression for diagonal of a rectangle is d= √ (a2 + b2).

Consider a rectangle PQRS in which let PR and QS be the diagonals.

Then, there are two triangles obtained and they are ΔRPS and ΔRPQ

The angle that is common between the two triangles is ∠p

The common side is PQ

Hence, PS=QR

Therefore, ΔRPS≅ΔRPQ

Also, QS=PR the diagonals of a rectangle are equal in length.

By using the Pythagorean theorem, the length of the diagonal of rectangle is                   d = √ (l2 + w2)

From the given data the length of the rectangle(l) PQ =a

The width of the rectangle(w) QR = b

Hence the expression for diagonal of rectangle is d= √ (a2 + b2).

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Answer:

The formula for a rectangle's diagonal is d=(a2 + b2).

Step-by-step explanation:

Let PR and QS be the diagonals of the rectangle PQRS.

Following that, two triangles—RPS and RPQ—are obtained.

The common angle between the two triangles is p.

PQ is the common side.

So, PS=QR.

Consequently, RPSRPQ

A rectangle's diagonals are also equal in length since QS=PR.

The Pythagorean theorem shows that d = (l2 + w2) is the length of the diagonal of a rectangle.

The length of the rectangle (l) PQ =a from the provided data

Rectangular width (w) = QR = b

Therefore, d=(a2 + b2) is the expression for the diagonal of a rectangle.

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The equivalent expression for the given expression is [tex]\frac{2.3^{15}}{0.9^{12}}[/tex]. Therefore, option D is the correct answer.

The given expression is [tex](\frac{2.3^{5} }{0.9^{4} } )^{3}[/tex].

We need to find the equivalent expression for the given expression.

Equivalent expressions are expressions that work the same even when they seem different. When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

Use [tex](\frac{a}{b} )^{m}=\frac{a^{m}}{b^{m}}[/tex] and [tex](a^{m} )^{n}=a^{m\times n}[/tex] to solve the given expression.

Now, [tex](\frac{2.3^{5} }{0.9^{4} } )^{3}=\frac{(2.3^{5})^{3} }{(0.9^{4})^{3} }[/tex]

[tex]=\frac{(2.3^{5\times3})}{(0.9^{4\times3})}[/tex]

[tex]=\frac{2.3^{15}}{0.9^{12}}[/tex]

The equivalent expression for the given expression is [tex]\frac{2.3^{15}}{0.9^{12}}[/tex]. Therefore, option D is the correct answer.

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The sentence "The isometric view is when an object is viewed from a corner" is True.

Isometric projection is used in technical and engineering drawings. Isometric view is a technique for visually representing three-dimensional objects in two dimensions along a vertical line. It is a 3-D drawing which is set out using 30-degree angles.

The Bottom View, the Left Side View, and the Rear View are three views of isometric drawings. Isometric, dimetric and trimetric drawings are three types of  axonometric drawings. Engineers, technical illustrators and sometimes architects use Isometric view.

The sentence "The isometric view is when an object is viewed from a corner" is True.

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The cost of 7 tickets will be $242.20.

In order to determine the cost of 7 tickets, the mathematical operation that would be used is multiplication. Multiplication is the process of determining the product of two or more numbers.

Multiplication is the process used to determine the result when a number is taken times. The sign used to represent multiplication is x. Other mathematical operations are addition, division and subtraction.

In order to determine the cost of 7 tickets, the cost of one ticket would be multiplied by 7.

Cost of 7 tickets = cost of one ticket x 7

$34.60 x 7 = $242.20

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