The spring musical cost $600 for costumes and $450 for the stage materials.

Answer:

C(x) = 25 + 1.5x

Step-by-step explanation:

A function is a mathematical equation that describes how two variables are related. To write a function that models the cost of having a carpet installed, we can use the information provided in the problem.

The cost of having a carpet installed is:

C(x) = 25 + 1.5x

Where C(x) represents the total cost of the carpet installation and x represents the number of square yards of carpet.

25 is a fixed cost for delivery , and $1.5 is cost per sq yard.

So, C(x) = 25 + 1.5x this function is representing the cost of having a carpet installed in x sq yard.

The first step in solving an inequality is to isolate the variable on one side of the inequality sign. This is also known as "clearing the inequality" of the variable. This can be done by using inverse operations such as addition, subtraction, multiplication, and division.

For example, if the inequality is 3x + 2 > 7, the first step is to isolate the variable x by subtracting 2 from both sides:

3x + 2 > 7

3x > 5

Then, divide both sides by 3 to get x > 5/3

This is the first step in solving an inequality, as now the variable x is isolated on one side of the inequality sign, and it's clear what the inequality is asking for.

It's important to note that when solving inequalities, it's crucial to keep the direction of the inequality sign the same, meaning if you multiply or divide by a negative number, you need to switch the direction of the inequality sign as well.

Also, it's important to check if the inequality is not valid, if the operation you are doing creates a division by zero, it will be an invalid inequality.

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The price of the adult ticket is $9

Word problems are sentences describing a 'real-life' situation where a problem needs to be solved by way of a mathematical calculation.

Set up equations to represent the problem.

Let the A and S represent the prices of adult and student ticket respectively. So we can write:

4A + 10S = 106 --- (1)

4A + 9S = 99  --- (2)

Subtracting (2) from (1) will give:

S = 7

Put S = 7 into (1):

4A + 10S = 106

4A + 10(7) = 106

4A + 70 = 106

4A = 106 - 70

4A = 36

A = 36/4

A = 9

Thus, the price of the adult ticket is $9

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Answer:

B.  x + 10 ≥ 70;  x ≥ $60

Step-by-step explanation:

Given:

The equation that models the given parameters is:

To solve for x, subtract 10 from both sides of the equation:

[tex]\implies x+10-10 \geq 70-10[/tex]

[tex]\implies x \geq 60[/tex]

Therefore, Kelvin needs to withdraw at least $60 from the bank.

Answer:

x = 0.25y + 7/12

Step-by-step explanation:

12x - 3y = 7

12x = 3y + 7

x = 0.25y + 7/12

One solution exists for the given equation.A linear equation with one variable has only ever one solution.

A linear equation with one variable has only ever one solution. The unique solution of a linear equation is the location at which LHS and RHS are identical when substituted.

The solution must be an ordered pair when there are two linear equations operating simultaneously (x, y). In this case, the ordered pair will fulfill the set of equations.

Given:

2x + 5y = 4

-4x - 13y = 9

Now,

a 1 = 2,  b1 = 5 , = -4

a2 = -4 , b2 = -13, = 9

Now,  = 2 / -4

= 5 / -13

As, a1/ a2 = 2/-4

b1 / b2 = 5 /-13

Thus, the relationship mentioned above reflects intersecting lines.

So, there is only one solution to the given problem.

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The Order of the ordered pair is defined as the specific way in which the ordered pair is written having a composition of the x coordinate and the y coordinate .

What is Ordered Pair ?

The Ordered Pair is defined as the pair of numbers in a specific order.

For Example :  (x,y) , here for the given ordered pair , the element x is called as the abscissa and the element y is called as the ordinate .

The Order of the Ordered Pair (x,y) is the first element always represents the abscissa that means the x coordinate and the second element should always represent ordinate that means the y coordinate .

For Example : for the ordered pair (2,4) , the x coordinate of the point is 2 and the y coordinate of the point is 4 .

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When t = 3, the exponential function has a value of 59.375.

The exponential function is a mathematical function denoted by f(x)=\exp or e^{x}. Unless otherwise indicated, the word refers to a positive-valued function of a real variable, however it can be extended to complex numbers or applied to other mathematical objects such as matrices or Lie algebras. A mathematical function of the following type is an exponential function: f (x) = an x, where x is a variable and an is a constant known as the function's basis. The transcendental number e, which is about 2.71828, is the most often encountered exponential-function base.

Here,

Given the exponential function h (t) = 475(0.5)^t

When t = 3

h(3) = 475(0.5)^3

h(3) =59.375

h(3) = 59.375

The exponential function when the value of t is 3 is 59.375.

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The maximum number of drinks Liam can buy is 4 without over exceeding his price.

Unitary method:

The unit method is a method of obtaining a single-unit value from a multiple-unit value and obtaining a multiple-unit value from a single-unit value. This is the method used for most calculations in mathematics. This method is useful when solving problems involving proportions and proportions, algebra, geometry, and more.

The unit method allows us to find missing values. For example, if a pack of juice costs $5. Then you can easily see that the cost is 5 packages, or $25.

According to the Question:

If Liam has $30 to spend and he must buy at least 9 drinks and tacos altogether, it means that,

$3.50 for 5 tacos

⇒ 3.50 x 5 =  $17.50

Now,

9 - 5 tacos = 4 drinks

Cost of 4 drinks x $2 = $8

The total price :

$17.50 + $8 = $25.50 out of $30 price limit

Thus, the number of drinks that she could buy is 4.

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Answer:

271.2

Step-by-step explanation:

Write it down and remove the decimals and do long multiplication. After that, count the decimal points and add them back ro the answer

Answer:

271.2

Step-by-step explanation:

move the decimal point 2 places to the right in the two numbers and multiple

[tex]2825 \times 960 = 2712000 [/tex]

and then move you decimal point 4 places to the left so your finally answer should be 271.2

The slope of the equation of the line 3f - s = 24 is 3.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Therefore, let's model the equation of the line y = mx + b to 3f - s = 24. Then, we can locate the slope in the equation.

Hence,

3f - s = 24.

add s to both sides of the equation

3f - s + s = 24 + s

3f = 24 + s

subtract 24 from both sides of the equation

3f = 24 + s

3f - 24 = 24 - 24 + s

s = 3f - 24

Therefore, the slope is 3.

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The answer is the point (5, -27) and no other solution.

The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.

Given here: The equation y=-6x+23

Checking for  (5, -27) we get -27=-6×5+23

                                                      =-27

Hence, The answer is the point (5, -27)

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A constant polynomial is a polynomial with a degree of 0, meaning it has no variable terms. The only possible constant polynomial is the term with a coefficient of 3, which is 3.

This can be seen by looking at the formula for a polynomial, which is:

P(x) = a0 + a1x + a2x2 + ... + anxn,

where a0 is the constant term, a1 is the linear term, a2 is the quadratic term, and so on. Since this polynomial has no variable terms (x = 0), the only possible constant polynomial is the term with a coefficient of 3.

To calculate the value of a constant polynomial, you simply substitute 0 for x in the equation above. For example, in the polynomial 3, the value would be 3 when x = 0.

P(0) = 3

Therefore, the answer is option b, 3.

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The (2,1) is a solution of the system of equations is shown. A formula that expresses the connection between two expressions on either side of a sign. Typically, it has a single variable and an equal sign.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

2 + 3·1 = 5

5 = 5

1 = -2 +3

1 = 1

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Answer:

5.6 or 28/5

Step-by-step explanation:

We know that A = 8 and B = 4

The expression is A/5 + B

8/5 + 4

The answer in decimal is 5.6

The answer in fraction is 28/5

Answer: You can make more bracelets than necklaces. ✅

Step-by-step explanation:

You have 2.88 meters of copper wire and 5.85 meters of aluminum wire.

With 2.88 meters of copper wire, you can make 12 bracelets because each bracelet needs 0.24 meters of copper wire.

With 5.85 meters of aluminum wire, you can make 9 necklaces because each necklace needs 0.65 meters of aluminum wire.

So you can make 12 bracelets and 9 necklaces.

Therefore you can make more bracelets than necklaces.

An ordered pair is a pair of numbers that are usually represented in the form of (x, y) and it is used to indicate the position of a point in a coordinate system or a Cartesian plane.

Another example is an ordered pair (-2, 1) representing a point in the coordinate system located 2 units to the left of the y-axis and 1 unit above the x-axis.

In this way, any point in a coordinate system can be represented by an ordered pair.

In summary, the ordered pair is a way to represent a point in a coordinate system and it is made up of two numbers (x, y), where x represents the horizontal position and y represents the vertical position of the point in the coordinate system.

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The student whose measurement had the greatest percentage error is Tenicia with a measurement of 23mm.

Percentage error refers to the difference between the estimated value and the actual value which is then expressed as a percentage. In the question given, the students and their values are; Layne, 26 mm, Tenicia, 23 mm, and Juan 25 mm.

Juan was the only student who had no error in the value obtained because she got the exact figure of 25 mm. Tenicia recorded the greatest value because the difference between the actual and estimated value was apart with so much difference. Her error was an 8% error.

25 -23/25 × 100

= 8%

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Answer:

The total number count we are looking at from the numbers 30 to 65 is 36. So that is a total of 72 digits making up this numbers from 30 to 65. Also, we can see that the whole range of numbers 0 to 9 is being used for this range

A polygon having seven sides and seven angles is called a heptagon. Seven straight sides and seven corners, or vertices, make up a heptagon. It's also referred to as a "septagon" at times.

A seven-sided polygon is called a heptagon. A closed figure with seven vertices, it is. Another name for a heptagon is a septagon.

There are various sorts of hexagons, depending on the angles and diagonals.

Regular and Irregular Heptagons

Concave and Convex Heptagon

The following are some heptagon's characteristics:

(1) The inner angles of a heptagon add up to 900 degrees.

(2) A heptagon's outside angles add up to 360 degrees.

(3) The internal angle of a normal heptagon measures approximately 128.57 degrees.

(4) The size of a typical heptagon's central angle is roughly 51.43 degrees.

(5) There are fourteen diagonals in a heptagon.

(6) Convex heptagons are another name for regular heptagons.

(7) A heptagon has a total of five triangles.

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Yes, the square of any number like X² is always positive.

Example:

If we calculate the square of a negative number, let's say -x, where x > 0, then (-x) (-x) = x².

Here, x² > 0.

Hence, the square of any number like X² is always positive.

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Translation type of transformation can be defined as moving a figure to a new location with no change to the size or shape of the figure.

Now, According to the question:

Type of Transformation:

There are four types of transformation in geometry, namely translation, reflection, rotation, and dilation. In translation, it slides the figure in any direction while in reflection, it flips the figure over a point or a line. Also, in rotation the figure turns, while in dilation the figure is either enlarged or reduced.

The type of transformation can be defined as moving a figure to a new location, without any change in the figure's size or shape being called translation. In translation, the figure merely slides or moves in the same direction and distance.

Therefore, the answer is Translation.

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The pattern of the sequence 1 1 2 3 5 8 13 is that each term is obtained by adding the previous term and the term before that.

The sequence 1 1 2 3 5 8 13 is also a famous example of the Fibonacci sequence. The Fibonacci sequence is a sequence of numbers in which each term is the sum of the two preceding terms. In this case, the first two terms of the sequence are 1 and 1, and the rest of the terms are obtained by adding the previous two terms.

It's also possible to express the pattern of the Fibonacci sequence by using the formula, F(n) = F(n-1) + F(n-2) where F(n) is the nth term of the sequence.

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A polynomial is factored when it is broken down into the sum of two or more other polynomials. For instance, f (x) = x 2 + 5 x + 6 can be broken down into f(x) = (x+3)(x+2) and f(x) = x2 + 5 x + 6.

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

A polynomial is factored when it is broken down into the sum of two or more other polynomials. For instance, f (x) = x 2 + 5 x + 6 can be broken down into f(x) = (x+3)(x+2) and f(x) = x2 + 5 x + 6.

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Answer:

1,400

Step-by-step explanation:

y=mx+b

plug in 460 for b

y=mx+460

plug 20 for m

y=20x+460

and when graphed on a graph you would see the answer

The value of x for the given expression is,

⇒ x = 5/44

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The algebraic expression is,

'' 4 times x plus one third equals one third times x plus 4''.

Now, The mathematical expression is,

⇒ 4x + 1/3 = 1/3 (x + 4)

Solve for x as;

⇒ 4x + 1/3 = 1/3x + 3/4

⇒ 4x - 1/3x = 3/4 - 1/3

⇒ 11/3x = 5/12

⇒ x = 5 × 3 / 12×11

⇒ x = 15/ 132

⇒ x = 5/44

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Triangle MNO with sides m = 20, n = 14 and angle m ∠ M = 51° can have two possible configurations.

In this problem we have the knowledge of two sides and an angle of triangle MNO, where angle M is opposite to side m. First, determine the possible values for angle N by law of sine:

n / sin (m ∠ N) = m / sin (m ∠ M)

14 / sin (m ∠ N) = 20 / sin 51°

sin (m ∠ N) = (14 / 20) · sin 51°

sin (m ∠ N) = 0.544

There are two possible values for angle N: m ∠ N₁ ≈ 32.957°, m ∠ N₂ ≈ 147.043°. The existence of two different angles indicates that two distinct triangles can be formed.

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Answer:

x = 92

y = 92

Step-by-step explanation:

164 + 102 + 90 + x + x = 540

2x + 356 = 540

2x = 184

x = 92

Answer:

[tex]y= \frac{x}{2x−1}[/tex]

Step-by-step explanation:

To find the inverse function, swap x and y, and solve the resulting equation for x.

If the initial function is not one-to-one, then there will be more than one inverse.

So, swap the variables: y=x/2x−1 becomes x=y/2y−1.

Now, solve the equation x=y/2y−1 for y.

y=x/2x−1