Shirley buys 5 bottles of soda. She has a coupon for $0.55 off the regular price of each bottle. After using the coupons. The total cost is 5.20. what is the regular price of the soda?

Hence, if one trigonometric function of x is tangent, the value of x is arctan [tex]\frac{1}{\sqrt{5} }[/tex]. We can start solving this equation by isolating one of the trigonometric functions.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, particularly right triangles. It is a fundamental part of geometry, and is also used in other areas such as physics, engineering, and navigation.

Trigonometry functions such as sine, cosine and tangent are used to describe the ratios between the sides of a right angled triangle, These functions are periodic and defined for all real numbers.

Since the tangent and cotangent functions are reciprocals of each other, we can multiply both sides of the equation by the reciprocal of the tangent function:

[tex]\frac{1}{tan(x)}[/tex] = [tex]\frac{1}{2} * \frac{1}{cot(x)}[/tex]

Now we can use the fact that the cotangent function is the reciprocal of the tangent function to write:

[tex]\frac{1}{tan(x)}[/tex] =[tex]\frac{1}{2} * \frac{1}{\frac{1}{tan(x))} }[/tex]

Solving for tan(x) we get:

tan(x) = [tex]\frac{1}{\sqrt{5} }[/tex]

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The solution of the inequality −2(−3x+4) − 5 > −3(x+7) − 19 is x > -3.

Inequalities are mathematical expressions involving the symbols >, <, ≥ and ≤.

Therefore, let's solve the inequality as follows:

−2(−3x+4) − 5 > −3(x+7) − 19

let's open the brackets on both sides

−2(−3x+4) − 5 > −3(x+7) − 19

6x - 8 - 5 > -3x - 21 - 19

6x - 13 > -3x - 40

add 13 to both sides of the inequality

6x - 13 > -3x - 40

6x - 13 + 13 > -3x - 40 + 13

6x > -3x - 27

add 3x to both sides of the inequality

6x + 3x > -3x + 3x - 27

9x > -27

divide both sides by 9

x > -27 / 9

Hence,

x > -3

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The point where the triangle's three altitudes connect is known as the orthocentre.

The circumcentre is the center of a triangle's circumcircle. It can be found as the point of intersection of the perpendicular bisectors of the triangle.

The letter H is frequently used to denote the orthocentre.

The kind of triangle determines where the orthocentre is.

The orthocentre will be located inside an acute triangle.

The orthocentre will be outside of an acute triangle.

Finally, the orthocentre will be the vertex at the correct angle if the triangle is right.

Thus, The point where the triangle's three altitudes connect is known as the orthocentre.

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Where the properties of the triangle are given, by angle sum property the value of x in the expression (2 x + 10) +  (6 x + 1) +79 =180  is 11.25

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 °.

2 horizontal and parallel lines are intersected by 2 diagonal lines to form a triangle with exterior angles.

The top angle of the triangle is (2 x + 10) °. The bottom right angle of the triangle is 79°.

The exterior angle to the bottom left angle is (6 x + 1) °.

By angle sum property

(2 x + 10) +  (6 x + 1) +79 =180

8x+11 + 79 =180

8x+11=180-79

8x+11 =101

8x = 90

x = 11.25

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Answer:

31 levels

Step-by-step explanation:

Zoey already has 25 points

So she needs at least 850-25 more points to beat the high score

850-25 = 775

So Zoey needs at least 775 points more

Since she earns 25 points for each level, if she has to play L levels to beat the high score, she will need at least 25L points and that should be greater than or equal to 775

Therefore the inequality is
25L ≥ 775

Dividing by 25 on both sides of the inequality gives:

L ≥ 775/25

which simplifies to L ≥ 31

So Zoey needs at least 31 levels before she can break the record

Let W be the inverse of AB. Then WAB = I and (WA)B = l. Therefore, matrix B is invertible by part (j) of the IMT by letting C = WA.

We have A and B are two n × n matrices and AB is invertible. We have to prove that B is invertible by showing a valid reason given by one of the four options:

Option (a) False:

The first option is not valid proof. since W is the inverse of A B would imply WAB = I, as multiplying a matrix by its inverse will produce the identity matrix of the corresponding order. Here stated that WAB = B, which is invalid.

Option (b) False:

It is true that AB invertible implies [tex]$(A B)^{\top}$[/tex] is invertible but this does not imply B is invertible (not a valid statement).

Option (c) False:

A B is invertible does not mean [tex]$A=B^{-1}$[/tex]. Since [tex]$A=B^{-1}$[/tex] implies AB = I, but AB need not be only the identity matrix. So these statements are invalid.

Option (d) True:

W being inverse of AB, this gives WAB = I

(WA) B = I since matrix multiplication is associative.

WA is the inverse of B, as multiplying WA by B produces the identity matrix I. Hence, this is valid proof to show that B is invertible.

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HL congruence is the principle that states that two triangles are congruent if they have two sides and the included angle equal. An example of HL congruence is shown below:

Triangle ABC is congruent to triangle DEF because they have two sides, AB and BC, and the included angle, ∠B, equal.

AB = DE

BC = EF

∠B = ∠D

HL congruence is an important concept in geometry that states that two triangles are congruent if they have two sides and the included angle equal. This means that if two triangles have the same lengths for two of their sides, and the angle between those two sides is the same, then the triangles are congruent. This principle is useful in geometry because it allows us to determine whether two triangles are congruent without needing to calculate any other lengths or angles.

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To solve a complex fraction with a whole number, you will need to first simplify the fraction by dividing the numerator and denominator by the same number.

A complex fraction is a fraction that contains another fraction within its numerator or denominator. To solve a complex fraction with a whole number, you will need to first simplify the fraction. This can be done by dividing the numerator and denominator of the fraction by the same number. Once the fraction has been simplified, you can further reduce the fraction as much as possible by cancelling out common factors. Finally, you can divide the numerator by the denominator of the fraction to find the answer as a whole number. It is important to note that the answer can also be in the form of a mixed number, depending on the result of the division.

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You must first simplify the fraction by dividing the numerator and denominator by the same amount in order to solve a complex fraction with a whole number.

A fraction that includes another fraction in either the numerator or denominator is referred to as a complicated fraction. You must first simplify the complex fraction in order to solve it with a whole number.

To achieve this, divide the fraction's numerator and denominator by the same number. After the fraction has been made simpler, it can be further decreased as much as feasible by removing frequent elements.

To find the solution as a whole number, divide the fraction's numerator by its denominator. It is significant to remember that, depending on how the division turned out, the solution could possibly take the shape of a mixed number.

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the answer to the question of how many thousands of units of corn can Congo produce in one week is 20. In conclusion, Congo can produce number - 20 thousands of units of corn in one week.

The table identifies how many thousands of units of corn and diamonds the united states and congo can produce in one week. The table shows that Congo can produce 20 thousands of units of corn in one week. Therefore, the answer is 20.

The given table provides information on how many thousands of units of corn and diamonds the United States and Congo can produce in one week. According to the table, the United States can produce 60 thousands of units of corn and 10 thousands of units of diamonds. On the other hand, Congo can produce 20 thousands of units of corn and 5 thousands of units of diamonds. Thus,The table identifies how many thousands of units of corn and diamonds the united states and congo can produce in one week. The table shows that Congo can produce number -  20 thousands of units of corn in one week. Therefore, the answer is 20.

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Answer:

C) 20

Step-by-step explanation:

I got it right on the test

x²+√2x+3  and x²+√2x+6  are expressions that are not polynomial. (Option a and Option b)

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

A polynomial function is one that uses only non-negative integer powers or positive number coefficients of such a variables in such an expression like the quadratic function, cubic equation, and so on.

For the algebraic expression to be called a  polynomial, the exponents in the algebraic expression should be non-negative integers. Also if an algebraic expression has a radical in it then it can not be called a polynomial.

a) x²+√2x+3. This expression is not a polynomial as the polynomial expression does not contain any radicals. √2 here is a radical root.

      ⇒   Hence, option a is not a polynomial expression.

b) x²+√2x+6.This expression is also not a polynomial expression as it has a radical √2 present in the expression.

      ⇒   Hence, option b is not a polynomial expression.

c) x³+3x²-3. This expression can be termed as a polynomial expression since all of the variables have positive integer exponents.

     ⇒    Hence, option c is a polynomial expression.

d) 6x+4​. This expression is also a polynomial expression as all of the variables have positive integer exponents.

      ⇒   Hence option d is a polynomial expression.

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Answer:

[tex] x 2 + 4x + 4[/tex]

Step-by-step explanation:

yes

The speeds of each train are 355.4 miles per hour and 365 miles per hour

From the question, we have the following parameters that can be used in our computation:

This means that

Train 1 + Train 2 = 720.4

Train 2 = 9.6 + Train 1

Substitute Train 2 = 9.6 + Train 1 in Train 1 + Train 2 = 720.4

Train 1 + 9.6 + Train 1 = 720.4

So, we have

2Train 1 = 710.8

Divide both sides by 2

Train 1 = 355.4

Recall that

Train 2 = 9.6 + Train 1

So, we have

Train 2 = 9.6 + 355.4

Evaluate

Train 2 = 365

Hence, the speeds are 355.4 and 365

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A possible equation to represent the situation described is  x (total of markers)= 90 + (15 x 3) and the diagram is attached below.

An equation can be defined as a mathematical expression that shows equality of two mathematical expressions. Due to this, equations include the symbol =.

A possible equation to represent this situation is:

x = 90 + (15 x 3)

In this equation:

X = Number of total markers

90 = Number of markers left after the first markers were given to the teachers

15 = Number of markers given to the teachers

3 = Number of teachers

In this way, we know that the total of markers is equivalent to ninety markers plus forty-five markers as fifteen markerts were given to three different teachers.

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Answer:

Volume= πr^2h

Step-by-step explanation:

if you plot the values in above given formula

V≈0.058m³

V≈3562.57in³

The graph of function g is a reflection of the graph of function f in the x-axis. This means that the transformation that took place to produce function g was a reflection in the x-axis.

Transformation is the process of changing something into a different state or form. It can refer to physical, emotional, spiritual, or psychological changes. It can involve transformation of an object, person, or situation. Transformation is often associated with growth and development and can require significant effort and dedication. Transformation can be used to make positive changes in our lives and ultimately lead to a better future. It is a process of self-discovery and can be a powerful tool for personal growth and development.

This means that for each x-value in function f, the corresponding y-value in function g is the negative of the y-value in function f.

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The largest share is equivalent to 180.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that $360 is divided in the ratio 2 : 7 : 9.

We can write the equation as -

2x + 7x + 9x = 360

18x = 360

x = 20

For the largest share, the largest share is equivalent to 9x. The largest share will be -

9 x 20 = 180

Therefore, the largest share is equivalent to 180.

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The expression that can be used to calculate the rate per second in which the machine launches the balls is given as follows:

A. 32/4.

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

As the graph of the function has a constant slope and an intercept of zero, it represents a proportional relationship.

The rate per second is equivalent to the constant of proportionality of the function.

From the graph, when x = 4, y = 32, meaning that the rate can be calculated as follows:

4k = 32

k = 32/4

k = 8.

Meaning that option A is correct.

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Answer:

..................................

Answer: the answer is D. The panels already on the garage produce 600 watts of energy

Step-by-step explanation:

any starting energy would be above zero with there already being solar panels! So that leads to a y-intercept! Whatever the line starts at will tell you the amount of energy you get from the starting panels:) I hope this is helpful!

For 44.1 miles, the option {A} is cheaper than option {B}.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign "=".

Given is that you can rent a car via two options. Option A charges $30 per day plus $0.07 per mile. Option B charges $0 per day, but $0.75 per mile

We can write the equations for each case as -

A(x) = 30 + 0.07x

B(x) = 0.75x

Now, for option {A} to be cheaper, we can write -

A(x) < B(x)

30 + 0.07x < 0.75x

30 < 0.75x - 0.07x

30 < 0.68x

x > (30/0.68)

x > 44.1 miles

Therefore, for 44.1 miles, the option {A} is cheaper than option {B}.

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Answer:

see below

Step-by-step explanation:

1st polynomial = 4q + 3b + 2c

2nd polynomial= -6a +4b -2c -2

Subtracting 2nd from 1st ,

= 4a -3b +2c - (-6a +4b -2c -2)

= 4a - 3b + 2c +6a -4b +2c +2

group like terms ,

=(6a +4a)-(4b +3b) +(2c+2c)+2

= 10a -7b +4c +2

since the highest degree of any variable is 1 so its degree is 1.

And we are done!

-Rishabh

The tutorial feature such  as begin thinking about the lesson’s main topic is important part.

The multi-step project is one that can be utilized in leading different kinds of examination and they help in an examination  as a lab project.

The student on the creatures and assists us with really taking a look at about the information by giving us similar warm-up questions and furthermore comprise of sorts of the illustration movement.

In this way the response to a short multi-project is a warm-up question.

Therefore, the undertaking incorporates different kinds of exercises and these should be visible in the inquiry, glossary joins, ace tests, and information checks.

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Correct question:

Drag each tutorial feature to its learning purpose.

Tiles

Warm-Up question

Glossary link

Knowledge check

Lesson Activity

Mastery test

Pairs

Begin thinking about the lesson’s

main topic.

arrowBoth

Make sure you’ve met the lesson’s

overall learning objective.

arrowBoth

View the definition of an important

lesson word.

arrowBoth

Do a short, multistep project or

investigation.

arrowBoth

See if you’re getting the main idea

or developing an important skill in

the lesson.

arrowBoth

Answer:

Step-by-step explanation:

when you divide you get 43. something but you can't have half of a chair so you should get another one making it 44 chairs

if wrong i'm sorry.

[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{13})\hspace{10em} \stackrel{slope}{m} ~=~ - 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{13}=\stackrel{m}{- 2}(x-\stackrel{x_1}{(-7)}) \implies y -13= -2 (x +7) \\\\\\ y-13=-2x-14\implies {\Large \begin{array}{llll} y=-2x-1 \end{array}}[/tex]

Based on the provided information regarding measurement, the way 3 in Kali's number compares to the 3 in Lauren's number is that Kali's digit is in the ones place and Lauren's digit is in the hundreds place.

Measurement refers to the process of comparing an unknown quantity with a standard of the same quantity. It quantifies the characteristics of an object or event, which we can compare with other things or events. It is the most commonly used term when dealing with the division of a quantity. When considering measurement, the value before decimals reads as ones, tens, hundreds etc. As Kali measures a countertop in the classroom that is 5,743 mm long or 5,743.0 mm the 3 just before the decimal is one place. As Lauren finds that the distance on a map between New York City and Washington D.C. is drawn as 364.1 mm, the 3 is hundreds place. Therefore, Kali's digit is 1/100 of the value.

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The Estimated answer is 0.

A benchmark is a whole number or fraction that is easy to use when you estimate. The benchmarks 0, 1/2, and 1 are particularly useful when estimating sums and differences of fractions.

When Numerator value is close to 0 and Denominator value is not close to 0 then the benchmark is 0.

For Examples : 1/2 , 3/16 , 2/25 , 9/100

When Numerator value is about 1 half of denominator value then the benchmark is 1/2.

For Examples : 3/8 , 9/16 , 11/25 , 52/100

When Numerator value and Denominator value are close to each other then the benchmark is 1.

For Examples : 7/8 , 14/16 , 23/25 , 95/100

1/4 ≤ 23/40 ≤ 3/4 so round it to 1/2.

1/4 ≤ 11/30 ≤ 3/4 so round it to 1/2.

Estimating:

1/2 - 1/2 = 0

Therefore, the estimated answer is 0.

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The estimation will be  0

Now, According to the question:

What is estimating in math?

Estimating in math is a way of approximately calculating an answer (getting a ‘rough answer’) to check its accuracy (the ‘right answer’). You shouldn’t need to use a calculator or any written methods when estimating, even with large numbers or decimal numbers.

When Numerator value is close to 0 and Denominator value is not close to 0 then the benchmark is 0.

For Examples : [tex]\frac{1}{2} ,\frac{3}{16},\frac{2}{25},\frac{9}{100}[/tex]

When Numerator value is about 1 half of denominator value then the benchmark is 1/2.

For Examples : [tex]\frac{3}{8} ,\frac{9}{16} , \frac{11}{25} , \frac{52}{100}[/tex]

When Numerator value and Denominator value are close to each other then the benchmark is 1.

For Examples : [tex]\frac{7}{8} , \frac{14}{16} , \frac{23}{25} , \frac{95}{100}[/tex]

1/4 ≤ 23/40 ≤ 3/4 so round it to 1/2.

1/4 ≤ 11/30 ≤ 3/4 so round it to 1/2.

Then, the Estimating:

[tex]\frac{1}{2}-\frac{1}{2}[/tex] = 0

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The diagonal of a rhombus is a line lump that joins any two non-adjacent apexes of a rhombus.

A rhombus has two diagonals that cut each other at right angles, thus, they form 4 right-angled congruent triangles.

When the opposing vertices of a rhombus are joined, they form the diagonals of a rhombus. A rhombus has two diagonals that oppose each other at 90 degrees. Observe this rhombus to identify its diagonals and their properties listed in the following section.

The diagonals of a rhombus are line segments that are unavoidable between the opposite vertices of the rhombus. The quality of the diagonals of the rhombus are listed below.

The diagonals of a rhombus cut each other at right angles.

The diagonals of a rhombus may not be fundamentally equal.

The two diagonals cleave the rhombus into four congruous right-angled triangles.

The length of the diagonals can be calculated by different methods like using the Pythagoras theorem or by using the area of the rhombus.

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a) The point (4, 6) represent the cost for 4 scoops will be $6.

b) The unit cost will be $1.5.

c) The cost of 12 scoops will be $18.

d) If the unit rate was $1.75 per scoop then the graph will be change.

e) if the unit rate was $1.75 per scoop for the point (4, 6), then the point become (4, 7).

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Given that;

The graph shows the cost of buying scoops of gelato.

Now,

By the graph we get;

The point (4, 6) represent the cost for 4 scoops will be $6.

And, The cost of 4 scoops = $6

Hence, The unit cost = 6/4

                                 = $1.5

So, The cost of 12 scoops = 12 × $1.5

                                        = $18

Now if the unit rate was $1.75 per scoop then the graph will be change by the unit cost of scoop.

And, if the unit rate was $1.75 per scoop for the point (4, 6).

Then , The cost of 4 scoops = 4 x $1.75

                                            = $7

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The complete question is shown in image.

Answer:4(-4)+5=72

Step-by-step explanation: