When y^3 is plotted against x, a straight linegraph is obtained, passing through the points (1,5) and (6,15). find y in terms of x

The correct equation to gives the proportional relationship of the graph is,

⇒ y = 6x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The graph is shown in figure.

Now, Let two points on the graph of line are (2, 12) and (4, 24).

Hence, The equation of line given the proportional relationship of the graph.

Thus, The equation of line is,

⇒ y - 12 = (24 - 12) / (4 - 2) (x - 2)

⇒ y - 12 = 12/2 (x - 2)

⇒ y - 12 = 6 (x - 2)

⇒ y - 12 = 6x - 12

⇒ y = 6x

Thus, The correct equation to gives the proportional relationship of the graph is,

⇒ y = 6x

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Answer:

Uncle Mike was 7 times as old as Sally 17 years ago.

Step-by-step explanation:

Let's call Uncle Mike's current age "x."

Sally is 12 years old, so x = 12 * 3 = 36 years old.

We are looking for years that must pass before Uncle Mike is only twice as old as Sally. So we need to find the age when x = 2 * (12 + n), where n is the number of years that have passed. Solving for n:

36 = 2 * (12 + n)

36 = 24 + 2n

12 = 2n

n = 6

So, six years must pass before Uncle Mike is only twice as old as Sally.

To find out how many years ago Uncle Mike was 7 times as old as Sally, we need to find the age when x = 7 * (12 - m), where m is the number of years ago. Solving for m:

36 = 7 * (12 - m)

36 = 84 - 7m

120 = 7m

m = 17

So, Uncle Mike was seven times as old as Sally 17 years ago.

The surface area of the rectangular prism is 174 in²

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism.

Given is a net for a rectangular prism, we need to find the surface area of the rectangular prism,

We know that,

The surface area of the rectangular prism = 2(lxb+bxh+hxl)

Length = l, height = h and b = breadth

Therefore, here we have, l = 9 in, b = 3 in and h = 5 in

Surface area = 2(9x3+3x5+5x9)

= 2(27+15+45)

= 2x87

= 174 in²

Hence, the surface area of the rectangular prism is 174 in²

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A two-column table method used to prove that the segments of the triangle are proportional, AE/EC = BD/DC, can be presented as follows;

Statement [tex]{}[/tex]                                       Reasons

1. AD bisects ∠BAC[tex]{}[/tex]                         Given

2. AE = ED     [tex]{}[/tex]                                   Given

3. ∠BAD ≅ ∠DAE [tex]{}[/tex]                            Definition  of bisected angle ∠BAC

4. ΔADE is an isosceles Δ [tex]{}[/tex]              Definition of isosceles triangle

5. ∠ADE ≅ ∠DAE [tex]{}[/tex]                            Base angles of an isosceles triangle

6. AB ║ DE [tex]{}[/tex]                                      Converse of alternate int. ∠ theorem

7. AE/EC = BD/DC [tex]{}[/tex]                           Thales theorem

A proportional relationship is one in which the elements of each ordered pair in the relationship are in the same proportion.

The details of the reasons used to prove the proportionality of the segments of the triangle are presented as follows;

Definition of bisected angle ∠BAC

An angle is bisected by a segment that divides it into two angles of the same measure.

Definition of isosceles triangle
An isosceles triangle is a triangle that has two sides that are congruent, or which have the same length.

Base angles of an isosceles triangles

The base angles of an isosceles triangle are congruent.

Converse of the alternate interior angle theorem

The converse of the alternate interior angles theorem states that if the alternate interior angles formed between two lines and a transversal are congruent, then the lines are parallel

Thales theorem

The Thales theorem states that a line drawn parallel to one of the sides of a triangle, such that it intersects the other two sides, then the line divides the other two sides proportionately.

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The binary representation of the number 4 is 101, which is a three-digit binary number where leftmost digit represents the MSB and the rightmost digit represents the LSB.

The binary fraction, 0.1, now has 1 added to it because the outcome is 1. The representation is finished because there is zero in the last decimal place of the number.

To convert 10 to binary, we can use the following steps:

Divide the decimal number 10 by 2. The remainder is 0, while the quotient is 5.

Write the remainder (0) as the least significant bit (LSB) of the binary representation.

To Divide the quotient (5) by 2. The remainder is 1, while the quotient is 2.

Write down the remainder (1) as the next bit in the binary representation.

As a result, 4 is represented in binary as 101

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A conversion factor is a mathematical expression that is used to convert a quantity from one unit of measure to another. It is a ratio that expresses the relationship between two different units of measurement.

There are many conversion factors used to convert one unit of measure to another. Here are some common conversion factors that you may find useful:

1 inch = 2.54 centimeters

1 foot = 0.3048 meters

1 mile = 1.609 kilometers

1 pound = 0.4536 kilograms

1 ounce = 28.35 grams

1 gallon = 3.785 liters

1 liter = 1000 milliliters

1 meter = 100 centimeters

1 kilometer = 1000 meters

1 square meter = 10.764 square feet

1 cubic meter = 35.315 cubic feet

1 atmosphere = 101.3 kilopascals

These are just a few examples of the many conversion factors that are used in various fields of science, engineering, and everyday life. It's important to know and use the appropriate conversion factor when converting units of measure to ensure accurate and meaningful results.

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Answer:

(1, - 2 )

Step-by-step explanation:

9x - 3y = 15 → (1)

3x + 3y = - 3 → (2)

add (1) and (2) term by term to eliminate y

(9x + 3x) + (- 3y + 3y) = 15 - 3

12x + 0 = 12

12x = 12 ( divide both sides by 12 )

x = 1

substitute x = 1 into either of the 2 equations and solve for y

substituting into (2)

3(1) + 3y = - 3

3 + 3y = - 3 ( subtract 3 from both sides )

3y = - 6 ( divide both sides by 3 )

y = - 2

solution is (1, - 2 )

Answer:

2(x-4)

Step-by-step explanation:

2 is common and (x-4) is the leftover.. simple as that.

The solution set for the inequality is,

''A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.''

Any relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 3 (8 - 4x) < 6 (x - 5)

Now, Simplify the inequality as,

⇒ 3 (8 - 4x) < 6 (x - 5)

⇒ 24 - 12x < 6x - 30

⇒ 24 + 30 < 6x + 12x

⇒ 54 < 18x

Divide by 18;

⇒ 54/18 < 18x/18

⇒ 3 < x

Hence, The solution of inequality on number line is,

⇒ A number line from negative 5 to 5 in increments of 1. An open circle is at 3 and a bold line starts at 3 and is pointing to the right.

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The width of the foil is 37//19 inches

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

Area of the rectangular piece of foil = 12 1/3 square inches

Length = 4 3/4 inches

The width is calculated as

Width = Area/Length

Substitute the known values in the above equation, so, we have the following representation

Width = (12 1/3)/(4 3/4)

Evaluate

Width = 37//19

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The EAN-13 code of Mr. Chips Nacho Cheese Flavor (100 g) 4-800016-653094 is valid.

To check the validity of the EAN-13 barcode, we need to perform a computation based on the numbers in the code. The EAN-13 code consists of 13 digits, where the first digit represents the number system, the next five digits represent the manufacturer code, the following five digits represent the product code, and the last digit is the check digit.

The check digit is calculated based on the previous 12 digits using a specific algorithm.

For the given EAN-13 code 4-800016-653094, we can extract the previous 12 digits as 480001665309. To calculate the check digit, we need to multiply the first, third, fifth, etc. digits by 3, and the second, fourth, sixth, etc. digits by 1, and then sum these products. In this case, the calculation is as follows:

(4x3) + 8 + (0x3) + 0 + (0x3) + 1 + (6x3) + 6 + (5x3) + 3 + (0x3) + 9 = 74

The check digit is then the smallest number that, when added to the sum above, results in a multiple of 10. In this case, the check digit is 6, since 74 + 6 = 80, which is a multiple of 10.

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The probability of Halston choosing two pieces of fruit that are not bananas is 69 %

First, find the total number of fruit :

=   3 + 4 + 2

= 9 fruit

The probability of picking a fruit that is not a banana the first time is :

= ( 3 + 4 ) / 9

= 7 / 9

The probability of picking a fruit that is not a banana the second time is :

= ( 3 + 4 - 1 ) / 9

= 6 / 9

The probability that two fruits are picked that aren't bananas is:

= 7 / 9 x 6 / 9

= 69 %

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The minimum number of rides Scott has to go on is 7 or more rides.

What is inequality ?

An inequality is a mathematical statement that compares two quantities, expressing that one is greater than, less than, or equal to the other. Inequalities are often represented using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

According to the question:

Let's start by finding an expression for the total cost of each amusement park in terms of the number of rides, x. For Amusement Park A, the total cost is:

Total cost for Amusement Park A = 40 + 2.5x

This is because there is a $40 entry fee plus $2.50 for each ride.

For Amusement Park B, the total cost is:

Total cost for Amusement Park B = 30 + 4x

This is because there is a $30 entry fee plus $4.00 for each ride.

To find the minimum number of rides Scott has to go on so that the total charge at amusement park A costs less than the total charge at amusement park B, we can set up an inequality comparing the total cost of the two amusement parks:

40 + 2.5x < 30 + 4x

This inequality is saying that the total cost for Amusement Park A is less than the total cost for Amusement Park B. We want to solve for x, which represents the minimum number of rides that Scott has to go on to make Amusement Park A cheaper than Amusement Park B.

To solve for x, we can simplify the inequality:

40 + 2.5x < 30 + 4x

10 < 1.5x

6.67 < x

So the minimum number of rides Scott has to go on to make Amusement Park A cheaper than Amusement Park B is 7 (rounded up from 6.67). Therefore, if Scott goes on 7 or more rides, Amusement Park A will be cheaper than Amusement Park B.

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Answer:

Step-by-step explanation:

At a simple annual interest rate of 3%, the following formula might be used to determine the annual interest for a $4200 principal:

Interest is calculated as follows: Principal * Rate * Time

Where,

Capital = $4200

Rate = 3% (expressed as a decimal by dividing by 100) (expressed as a decimal by dividing by 100)

t = one year

When we enter the values, we obtain:

Interest is equal to $4200 multiplied by 0.03 times one.

Therefore, $126 would be the annual interest for a $4200 principal at a basic annual interest rate of 3%.

Answer:

.28

Step-by-step explanation:

you subtract Lucas's from karim's hight wich is .56 then devid in by 2 wich is .28

We know that :1 oz. to ml = 29.57353 ml, 2 oz. to ml = 59.14706 ml and so on. Therefore, based on the above information:

14 oz. to ml. = 414.0294156 milliliter.

Milliliter:

A milliliter (ml) equals 1/1000 of a liter or 0.001 liter. The liter (Commonwealth English spelling liter, US English spelling liter) is a unit of volume. There are two official symbols. The Latin letter el is l and L in both cases. The liter is not an SI unit but can be used with SI. The SI unit of volume is the cubic meter (m³).

Fluid Ounce:

A fluid ounce is actually a fairly simple unit of measurement. In the Imperial system, one ounce of liquid is 28.41306 ml, whereas in the US it is 29.57353 ml.

These measures are important to know if you want to convert fluid ounces to ml. This is a very old dimension and many have decided it is worth using. I need to find the difference between British fluid ounces and US fluid ounces. A British fluid ounce is 1/160 of an imperial gallon and a US fluid ounce is based on a gallon of wine which is 231 cu. inch.

We know that:

1 milliliter = 0.0351951 oz.

Therefore,

milliliter (mL) = Ounce Value × 29.5735296

⇒ mL = 14 × 29.5735296

⇒ mL = 414.029

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The sequence types are (a) arithmetic seqience and (b) geometric seqience

a) an annual raise of $3,500

Given that the annual rase ie $3500

This is an arithmetic seqience

And it means that there will be an addition of $3500 in the salary each year

So, we have

Common difference = 3500

b) an annual raise of 5% of his current salary.

Given that the annual rase is 5% of the current salary

This is a geometric seqience

And it means that the raise would be 5% of previous salary

So, we have

Common ratio = 1.05

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Answer:

56

Step-by-step explanation:

Plotting the relationship between the number of hours studied and exam results reveals a negative correlation curve, where the exam results get worse as the number of hours studied rises.

The point (10,70) would be plotted on the negative correlation curve, for instance, if a student spent 10 hours studying and received a 70 on their exam. A downward sloping negative correlation curve would result as study time increased and exam score decreased. A graph illustrating the relationship between two variables, where an increase in one variable is accompanied by a drop in the other, is called a negative correlation curve. Numerous various types of situations, such as the amount of hours studied and exam results, might demonstrate this type of link. Exam scores typically decline as the amount of study time increases.

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The constant of variation for the subscription cost based on the number of weeks is $7.5.

What is Slope?

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

The straight line passes through the point

(4, 30), (8, 60) and (12, 90)

so, slope of line passing through the points

m = (60- 30)/ (8-4)

m = 30/ 4

m = 7.5

Thus, the constant of variation is $7.5.

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Answer:

Step-by-step explanation:

A surface analysis chart is a type of weather map that displays information about the current pressure and wind patterns over a particular region. The chart provides a snapshot of the weather conditions at a specific point in time and helps meteorologists to identify and track the location, movement, and development of high- and low-pressure systems, fronts, and other weather features.

The surface analysis chart typically shows a map of the Earth's surface with various meteorological symbols and information, including isobars (lines of equal pressure), fronts (boundaries between different air masses), and wind direction and speed. The chart may also include information about temperature, precipitation, and cloud cover.

Surface analysis charts are used in weather forecasting, air traffic control, and other applications where an understanding of current weather conditions is important. They provide important information for short-term weather forecasting, such as predicting the location of fronts and the development of thunderstorms, and for long-term weather planning, such as determining the most suitable routes for shipping or aviation.

we can conclude that 2.2 is less than 14/4.

what is fraction ?

A fraction is a mathematical representation of a part of a whole or a ratio between two quantities. It is typically represented as a top number (numerator) divided by a bottom number (denominator), separated by a horizontal line.

For example, the fraction 3/4 represents three parts out of four equal parts of a whole. The numerator (3) represents the number of parts, while the denominator (4) represents the total number of parts that make up the whole.

According to the question:
To compare 2.2 and 14/4, we can convert 14/4 to a decimal:

14/4 = 3.5

Now we can see that 2.2 is less than 3.5. Therefore, we can say that:

2.2 < 14/4

Another way to compare them is to convert both numbers to a common denominator. In this case, the common denominator of 2.2 and 14/4 is 10:

2.2 = 22/10

14/4 = 35/10

Now we can see that:

22/10 < 35/10

Therefore, we can conclude that 2.2 is less than 14/4.

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Amy Folsom will need to make 64 trips to deliver 40 cords of wood with her small pickup truck.

To find the number of trips needed to deliver 40 cords of wood, we can use the following formula:

Number of trips = Total amount of wood / Amount of wood per trip

In this case, the total amount of wood is 40 cords and the amount of wood per trip is 5/8 cord.

Plugging these values into the formula, we get:

Number of trips = 40 / (5/8)

Number of trips = 40 * (8/5)

Number of trips = 64

Therefore, Amy Folsom will need to make 64 trips to deliver 40 cords of wood with her small pickup truck.

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Answer:

108

Step-by-step explanation:

5^2 + 45 - 67 + 15x                     when  x = 7

= 5^2 + 45 - 67 + 15(7)

= 25 + 45 - 67 + 105

= 70 - 67 + 105

= 3 + 105

= 108

So, the answer is 108

The number of students that have veggies as a snack is equal to 51 students.

In Mathematics, a circle graph is sometimes referred to as a pie chart and it can be defined as a type of graph that is used for the graphical representation of the proportional relationship between each part to a whole, especially by dividing a circle into various sectors or sections.

Since there are 300 students at York Middle School, the number of students that have veggies as a snack can be calculated as follows;

Number of students that had veggies = 17/100 × 300

Number of students that had veggies = 0.17 × 300

Number of students that had veggies = 51 students.

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Assuming that each of the five children had the same amount of cards before the exchange, the total number of cards in the game was twenty.

Amount is the term used to describe a quantity or size of something it will stop to use to refer your numbers of object items are people with as well as measure of money time and distance.

The exchange between the children meant that each of them gave away four cards, for a total of twenty cards being given away. Thus, before the exchange there were forty cards in the game. After the exchange, each of the five children had ten cards, and only half of those cards were played with, meaning that the total number of cards in the game was twenty.

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If you can only pick one answer, the most correct choice would be (d) all real numbers up to and including 2, and any other values for which we have data.

This choice is the most general and inclusive, as it covers all possible values of time, including non-integer values, and any other values for which we have data on the population of E. coli bacteria.

However, if the answer choices are restricted to the given options, the most appropriate answer would be (c) all integers up to and including 2, and any other values for which we have data, since the given table only provides data for integer values of time up to 2 hours.

Step-by-step explanation:

3/2x + 12 = -y

divide all sides by -1

-y/-1 = (3/2x)/-1 + 12/-1

y = -3/2x - 12