Afunction is represented by the table. 3 CH 5-26 7 -50 The rate of change of the function represented in the table is -13 12 13 . For the given x- and y-values, the function is decreasing ​

The constant of proportionality of the graph is 8.

Constant of proportionality is the constant value of the ratio between two proportional quantities.

Given that, a table, of price of the number of pack of biscuits,

We are asked to find the constant of proportionality or unit rate that defines the relationship,

Unit rate is a rate for one of something.

Here, let us consider the number of packets be x and price be y,

x and y are proportional, therefore,

y = kx, here k is the constant of proportionality,

Put y = 8 and x = 1

8 = k

Similarly, if we check for other values we will get 8

[graph is attached]

Hence, the constant of proportionality of the graph is 8.

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The expression equal to 5¹/₃ is ∛5 (option B)

The definition of an expression in math is a statement composed of terms and operations. The terms may be constant (numbers), or variables with coefficients. The operations may be addition, subtraction, multiplication, or division.

Given is an expression, 5¹/₃,

Using indices rule,

b¹/ₐ = [tex]\sqrt[a]{b}[/tex]

Therefore,

5¹/₃, here b = 5, a = 3

Therefore,

5¹/₃ = ∛5

Hence, the expression equal to 5¹/₃ is ∛5 (option B)

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Answer:

it has 1 solution of 1/2 or decimal form of 0.5

The weight 60.5 kg is equal to approximately 133.38 pounds. This conversion was done using the formula 60.5 kg x 2.20462 lbs/kg = 133.37851 lbs.

We know that 1 kg is equivalent to 2.20462 pounds, which means that we can convert kilograms to pounds by multiplying the weight in kilograms by the conversion factor 2.20462.

So to convert 60.5 kg to pounds, we can use the following formula:

60.5 kg x 2.20462 lbs/kg = ? lbs

Multiplying 60.5 by 2.20462 gives us:

60.5 x 2.20462 = 133.37851

Therefore, 60.5 kg is equivalent to 133.37851 pounds.

Finally, we can round this result to two decimal places to get:

60.5 kg is approximately equal to 133.38 pounds.

So the final answer is that 60.5 kg is equivalent to approximately 133.38 lbs.

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The solution of the Equation is x=1  and y= -3.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

-3x + 7y = -18...........(1)

4x - 4y = 8.................(2)

Solving equation (1) and (2) we get

-12x + 28y = -72

12x - 12y = 24

____________

16y =  -48

y= -48/ 16

y = -3.

and, -3x + 7(-3) = -18

-3x = 3

x= -1

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Answer: C

Step-by-step explanation:

The golden ratio of Fibonacci, also known as the divine proportion, golden mean, or golden section, is a mathematical constant that is approximately equal to 1.618033988749895.

It is represented by the Greek letter phi (φ) and is found by dividing a line into two parts so that the longer part divided by the smaller part is also equal to the whole length divided by the longer part.

In mathematical terms, the golden ratio is expressed as:

φ = (1 + √5) / 2

The golden ratio is closely related to the Fibonacci sequence, which is a series of numbers where each number is the sum of the two preceding ones, usually starting with 0 and 1. The ratio of consecutive numbers in the Fibonacci sequence converges to the golden ratio as the sequence progresses.

For example, the first few numbers in the Fibonacci sequence are:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ...

As we divide each number by the one before it, we get closer and closer to the golden ratio:

1/1 = 1

2/1 = 2

3/2 = 1.5

5/3 = 1.666...

8/5 = 1.6

13/8 = 1.625

21/13 = 1.615...

34/21 = 1.619...

55/34 = 1.617...

89/55 = 1.618...

144/89 = 1.618...

As you can see, the ratio of consecutive numbers in the Fibonacci sequence approaches the golden ratio as the sequence progresses. This is why the golden ratio is often referred to as the golden ratio of Fibonacci.

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Noel delivered an average of 500 yards of ribbon per day from Tuesday to Monday.

The central value represents the typical or average value of all the numbers in the set.

From Tuesday to Friday, Noel delivered 350 yards of ribbon per day, a total of 4 days. So, the total length of ribbon that he delivered during this period is

=> 4 * 350 = 1400 yards.

From Saturday to Monday, he delivered 700 yards of ribbon per day, a total of 3 days. So, the total length of ribbon that he delivered during this period is

=> 3 * 700 = 2100 yards.

To find the average length of ribbon that Noel delivered per day, we need to find the total length of ribbon he delivered in both periods and divide it by the total number of days.

The total length of ribbon he delivered in both periods is

=> 1400 + 2100 = 3500 yards.

The total number of days is

=> 4 + 3 = 7 days.

So, the average length of ribbon that Noel delivered per day is

=> 3500/7 = 500 yards.

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The equation 6x + 14x - 9 = 4( 5x + 1 ) has no solution.

Given the equation in the question;

6x + 14x - 9 = 4( 5x + 1 )

To solve the equation, first apply distributive property to remove the parenthesis.

6x + 14x - 9 = 4( 5x + 1 )

6x + 14x - 9 = 4 × 5x + 4 × 1

Multiply 4 and 5x

6x + 14x - 9 = 20x + 4 × 1

Multiply 4 and 1

6x + 14x - 9 = 20x + 4

Next, collect and add like terms.

Subtarct 20x from both sides

6x + 14x - 20x - 9 = 20x - 20x + 4

6x + 14x - 20x - 9 =  4

Add 9 to both sides

6x + 14x - 20x - 9 + 9 =  4 + 9

6x + 14x - 20x =  4 + 9

20x - 20x =  4 + 9

20x - 20x =  13

0 = 13

Therefore, there is no solution to the equation.

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The quadratic function is y = 1/3(x + 2)^2 - 5

The parent function of a quadratic function is represented as

y = x^2

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

vertical shrink of 1/3, shifts left 2 and down 5.

This means that

y = a(x + h)^2 + k

Where

a = 1/3

h = 2

k = -5

So, we have

y = 1/3(x + 2)^2 - 5

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Eigenvalues and eigenvectors can be found using a calculator by solving the equation Ax = λx, where A is a matrix, x is the eigenvector, and λ is the eigenvalue.

To solve this equation, you first need to calculate the determinant of the matrix A, which is written as |A|. If the determinant is not equal to zero, then you can calculate the eigenvalue by dividing the trace of the matrix (the sum of the diagonal elements) by the number of rows or columns of the matrix. The eigenvalues can then be substituted into the equation to solve for the corresponding eigenvector. For example, for a 2x2 matrix A, the eigenvalues can be found by calculating |A| and then solving the equation λ^2 - (trace of A) * λ + |A| = 0. The eigenvectors can then be found by plugging the eigenvalues into the equation Ax = λx and solving for x.

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The statement that is true regarding "96 multiplied by 11/8" is: G. The product is greater than 96.

To find the product of 96 and 11/8, we can multiply these two numbers:

96 x 11/8 = (96/1) x (11/8)

= 1056/8

= 132

So the product is 132.

Now we can check which statement is true:

F. The product is less than 11/8. This statement is false, since 132 is greater than 11/8.

G. The product is greater than 96. This statement is true, since 132 is greater than 96.

H. The product is between 11/8 and 96. This statement is false, since 132 is greater than both 11/8 and 96.

I. The product is equal to 96. This statement is false, since we have calculated that the product is actually 132.

The statement that is true is G. The product is greater than 96.

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Total cost to build the ramp is $1467.4. Santiago’s has over budget to build the ramp.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

Here,

Area of 2 rectangles is

2(Length×Width)

= 2(20×12)

= 480 square feet

Area of small rectangle = 12×8.5

= 102 square feet

Area of 2 triangles = 1/2×Base×Height

= 1/2 ×20×8.5

= 85 square feet

Total area = 480+102+85

= 667 square feet

Total cost to build the ramp = 667×2.20

= $1467.4

Santiago’s total budget for the materials to build the ramp and the foam pit is $3,000.

Hence, Santiago’s has over budget to build the ramp.

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"Your question is incomplete, probably the complete question/missing part is:"

The material Santiago will use to build the ramp cost $2.20 per square foot. Find the total cost of materials for the ramp? All sides are; 21.7, 20, 12 for perimeter and 8.5 for the height.

Santiago’s total budget for the materials to build the ramp and the foam pit is 3,000. With his current design, will he be over budget or under budget, and by how much?

Using the geometric mean theorem, the value of x is approximately 8.2.

The right triangle altitude theorem, also known as the geometric mean theorem, is a basic concept in geometry that connects the altitude of a right triangle to the two line segments it creates on the hypotenuse. According to the theorem, the altitude is equal to the geometric mean of the two line segments.

Using the theorem, we have:

14 = √(x * 24)

14² = 24x

196 = 24x

x = 196/24

x ≈ 8.2

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The system of equations that has a solution of approximately (1.8, –0.9) are: x+2y=0 and 6x-5y=15

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

Here, we have,

we are given the following equations:

i) x-2y= 4

ii) 4x+5y= 8

iii) 6x-5y=15

iv) x+2y=0

Required:

Which system of equations has a solution of approximately (1.8, –0.9).

To find the approximate equations, substitute x and y for  1.8 and  -0.9 into all the equations respectively and check the resulting values

i) Substitute (1.8, -0.9) in x-2y= 4:

1.8 - 2(-0.9) = 4.

1.8 + 1.8 = 4.

3.6 ≠ 4.

ii) Substitute (1.8, -0.9) in 4x+5y= 8

4(1.8) + 5(-0.9) = 8

7.2 - 4.5 = 8.

2.7 ≠ 8.

iii) Substitute (1.8, -0.9) in 6x-5y=15

6(1.8) - 5(-0.9) = 15.

10.8 + 4.5 = 15

15.3 ≠ 15.

This equation has a solution that is close, therefore it is correct.

iv) Substitute (1.8, -0.9) in x+2y=0

1.8 + 2(-0.9) = 0.

1.8 - 1.8 = 0.

0 = 0.

x + 2 y = 0 has the exact value, therefore it is also correct.

The system of equations that has a solution of approximately (1.8, –0.9) are: x+2y=0 and 6x-5y=15

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The following equations should be used to calculate the cylinder's surface area = SA = 2πr² + 2πrh. As a result, the suggested options do not include the correct approach.

Where h is the cylinder's height and r is the cylinder's radius.

The radius is equal to half of the diameter, or 1.6 feet, given that the diameter is 3.2 feet. And it stands 3.8 feet in height.

As a result, the following is the appropriate formula to get the cylinder's surface area:

SA is = 2.16 plus 2.16.3.8 square feet.

When we abbreviate the phrase, we get:

SA = 2.56 + 2.08 square feet

SA = 5.12 plus 12.16 square fee

SA = 17.28 square feet.

As a result, the suggested options do not include the correct approach.

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The surface area of the given cylinder is given by the equation:

    SA =  2π (1.6)² + 3.2π(3.8) square feet

What is meant by a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. One of the fundamental three-dimensional shapes in geometry is the cylinder, which has two distant, parallel circular bases. At a predetermined distance from the centre, a curved surface connects the two circular bases. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases.

The surface area of the cylinder is the sum of the area of the curvilinear surface and the areas of the top and bottom circular bases.

Now the area of the curved surface  = 2πrh

Area of bases = πr² + πr² = 2πr²

where,

  r = radius of the cylinder

   h = height of the cylinder

Given,

 r = 3.2 / 2 = 1.6 feet

h = 3.8 feet

Substituting,

Surface area SA = 2πrh + 2πr² = 2π * 1.6 * 3.8 + 2π (1.6)²

                                                =  2π (1.6)² + 3.2π(3.8) square feet.

Therefore the surface area of the given cylinder is given by,

    SA =  2π (1.6)² + 3.2π(3.8) square feet.

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To indicate that one value is greater than, less than, or equal to another, an inequality in a word problem is written using mathematical symbols like, >, or.

Determine the values that the inequality will compare before using the correct mathematical symbol to express the relationship between them in a word problem. Once the values have been determined, represent the relationship between them using the proper mathematical symbol. For instance, the inequality would be phrased as "x > 5" if the problem stated that "x is greater than 5". Other possible symbols for inequalities are (less than), (less than or equal to), and (more than) (greater than or equal to). It is crucial to always use the appropriate mathematical symbols when creating an inequality since they are needed to indicate the direction of the comparison. Moreover, make sure to incorporate all essential components, including the values being compared, the mathematical symbol, and the equals sign, if required. These procedures can be used to effectively write an inequality in a word problem.

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Answer:

3

Explanation:

Based on the given conditions, formulate: 3

Cross out the common factor: 3

get the result:3

Answer: 3

Answer:

2$

Step-by-step explanation:

10/5=2

Answer:-8

Step-by-step explanation:

f(x)=-3x-2

f(2)=-3(2)-2

-6 - 2=

-8

Expressions that are tested by the 'if' statement is called conditions.

A condition is an expression that evaluates to either 'True' or 'False', and it determines whether the code block within the 'if' statement is executed. The 'if' statement allows the program to make decisions and execute different codes based on whether the condition is 'true' or 'false'. For example, in Python, an 'if' statement might look like this:

if x > 10:

   print("x is greater than 10")

In this example, the condition being tested is 'x > 10', which will evaluate as 'True' or 'False' depending on the value of x. If the condition is 'True', then the code block within the 'if' statement (in this case, the print statement) will be executed. If the condition is 'False', then the code block within the 'if' statement will be skipped.

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The total cost to put a new floor on both the court and its border is; $61776

The parameters given are;

Initial length = 84 ft

Initial Width = 46 ft

Now, since the court has a border that is 10 ft wide, it means that we will add 20 ft to the initial length and width to get the new measurements. Thus;

New length = 84 + 20 = 104 ft

New Width = 46 + 20 = 66 ft

Thus;

Area = 104 * 66

Area = 6864 sq.ft

Thus;

Total Cost = 6864 * 9

= $61776

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Answer:

24

Step-by-step explanation:

Write 10% as 10/100

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have 10/100 of 240 = 10/100×240

Therefore, the answer is 24

Answer:

Step-by-step explanation:

12

Answer:

350

Step-by-step explanation:

Using the proportion from part (a):

14/n = 20/500

Cross-multiplying, we get:

20n = 14 × 500

Dividing both sides by 20, we get:

n = 14 × 500 / 20 = 350

Therefore, about 350 seventh graders participate in the contest.

The two zeros of the equation are -3,8.

The zeros of any equation lie on the x axis.On x axis y=0.The zeros can be found by substituting y=0 and finding the corresponding y values.

here, we have,

The given equation is :

f(x) = x² - 5x - 24

Comparing it with quadratic equation

y = ax^2+bx+c

We have a=1,b=-5,c=-24.

To find the zeros we substitute y=0.

x² - 5x - 24= 0

WE need to find two numbers which on multiplication will give us ac that is 1(-24)=-24.The same numbers on addition should give us b=-5.

The two numbers are -8 and 3.-8 times 3=-24 and -8+3=-5.

The factors of the equation are (x+8)(x-3)=0

making  both factors =0 we have:

x+8=0 and x-3=0

Solving for x

x=-8 and x=3.

Hence, The two zeros of the equation are -3,8.

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The appropriate values in the table will be:

Cost selling price

1. 1

2. 3

3. 5

From the information, the store sells a toy car for $1 less than twice what it costs to make the car.

It should be noted that the selling price when the cost price is $1 will be:

= (2 × $1) - $1

= $1

It should be noted that the selling price when the cost price is $2 will be:

= (2 × $2) - $1

= $3

It hould be noted that the selling price when the cost price is $3 will be:

= (2 × $3) - $1

= $5

The equation that shows the relationship will be:

Selling price = 2c - 1

The selling price when cost price is $4 will be:

=(2 × $4) - 1

= $7

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Answer: 7/14

Step-by-step explanation: