what is the solution to the system
line 1: y= -2x-4
line 2: y=2/5x + 16/5

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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When two positive fractions are multiplied the product is always less than the factors.

Fraction is defined as the number of compositions that constitutes the Whole. In mathematics, fraction is a number that is expressed as a proportion, as 1/2 or 2/3. The number on the bottom represents the total number of parts of one unit, while the number on the top is the portion of the unit being considered.

here,

Let's assume an example,

1 / 8 × 1 / 9 = 1 / 72

So as we see in the above example,

1 / 8 and 1/ 9 is a positive fractions and their product is less than their own factors.

Thus, when two positive fractions are multiplied the product is always less than the factors.

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Jacinta's pattern is correct for question A.

Jacinta's pattern is not correct for question B.

A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.

We have two types of fractions.

Proper fraction and improper fraction.

A proper fraction is a fraction whose numerator is less than the denominator.

An improper fraction is a fraction where the numerator is greater than the denominator.

Example:

1/2, 1/3 is a fraction.

3/6, 99/999 is a fraction.

1/4 is a fraction.

We have,

Jacinta's:

Fractions are 1/3 and 1/5 (say).

Product.

= 1/3 x 1/5

= 1/15

Now,

1/15 < 1/3

1/15 < 1.5

For Question A:

We can assume that,

The fractions are 1/3 and 3/4.

Their product.

= (1/3) x (3/4)

= 3/12

= 1/4

1/4 < 1/3

1/4 < 3/4.

So,

Jacinta's pattern is correct.

For Question B.

The fractions are 2/5 and 4/7.

Their product.

= (2/5) x (4/7)

= 8/35

We see that,

8/35 < 2/5

8/35 >  4/7

So,

Jacinta's pattern is not correct.

Thus,

Jacinta's pattern is correct for question A.

Jacinta's pattern is not correct for question B.

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The complete question.

A) The two fractions are 1/3 and 3/4

B The two fractions are 2/5 and 5/7

Double integration in polar coordinates involves integrating a function over a two-dimensional region in the polar coordinate system. This is done by setting up a double integral in terms of r and θ, and integrating first with respect to r and then with respect to θ.

Double integration in polar coordinates involves integrating a function over a two-dimensional region in the polar coordinate system. The steps to double integrate a function in polar coordinates are as follows:

1. Determine the limits of integration for r and θ. These limits define the region over which the function will be integrated. Typically, the limits are determined by the boundaries of the region in the xy plane.

2. Write the function to be integrated in terms of r and θ. The function must be expressed in polar coordinates for integration in polar coordinates.

3. Set up the double integral by writing the function in polar coordinates, multiplying by the appropriate factors of r and integrating with respect to r first and then θ.

4. Integrate the function with respect to r, using the limits of integration for r determined in step 1.

5. Integrate the result from step 4 with respect to θ, using the limits of integration for θ determined in step 1.

The general form of a double integral in polar coordinates is:

∫∫f(r, θ)r dr dθ

where f(r, θ) is the function to be integrated, and r and θ are the polar coordinates.

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Converting 1 pound to 2 cups is mainly used for cooking and baking. One pound equals two cups.

Pound:

A pound is a unit of mass used to measure the weight of dry ingredients. It is expressed in "pounds" and equals 16 ounces in the traditional American system. On the other hand, there are two types of pounds used in England, the common American pound (avoirdupois pound) and the British imperial pound, which are slightly different from each other. So remember the pounds used in the recipe book you're working on.

Cups:

Cups are an important tool for measuring ingredients in the kitchen. It is mainly used for measuring the volume of liquid ingredients such as water, milk, butter, etc. or for measuring dry grain or powder ingredients such as coffee beans, chocolate chips, flour, sugar, etc.

There are two types of measuring cups:

Measuring cups are normally supplied with a printed weighing scale. We can fill the cup with ingredients according to this scale. Liquid measuring cups are usually made of a transparent material such as glass or plastic. This makes it easier to fill accurately.

According to the Question:

1 cup = ½ lb

To calculate how many pounds are in a given number of cups, you can do it with the following simple formula:

Pounds = Cups × ½

Or, Pounds = Cups × 0.5

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In The equation, A equal to 2,400 plus quantity 1 plus 0.031 over 4 end quantity all raised to the power of 4 times t, represents the amount of money earned on a compound interest savings account, A. The value 0.031 represents the interest rate, which means the annual compounded interest rate is 3.1%.

The general compound interest equation is given as:

Formula:

A = P(1 + r/n)^nt

A = final amount or future value

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Compounding interest involves computing interest on both the principal and the accumulated interest.

On the other hand, the simple interest method does not compute interest on accumulated interest.

Thus, the correct representation of the value 0.031 is the compound interest rate as 3.1%.

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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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Answer:

$320

------------------

Original price of 4 chairs:

Cost after mark down by 20%:

Answer:

450.092

Step-by-step explanation:

4 × 100 = 400

5 × 10 = 50

9 × 1/100 = 0.09

2 × 1/1000 = 0.002

400 + 50 + 0.09 + 0.002 = 450.092

Answer:

the answer is number of orange marble/number of times

which might be 1/12 because you didn't specify

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:

The volume of water in a pool can be calculated using the following formula:

Volume (in gallons) = Length (in feet) x Width (in feet) x Average Depth (in feet) x 7.5

For example, if your pool is 20 feet long, 15 feet wide, and has an average depth of 5 feet, the volume of water in your pool would be:

20 x 15 x 5 x 7.5 = 5625 gallons

Note: If you prefer metric units, the formula for volume in liters would be:

Volume (in liters) = Length (in meters) x Width (in meters) x Average Depth (in meters) x 1000

It's important to note that this formula assumes a standard rectangular or square pool shape. If your pool has a more complex shape, you may need to measure the volume in smaller sections and add the volumes together to get the total volume.

The percent change from the first value to the second is 20%.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

The first number= 48

The second number= 60

Now, difference=60-48=12

Here,

=(60-48) x 100/48

=1200/48

=20

Therefore, the percentage change will be 20%.

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The number of chocolates that Steve have left is 4848 - 88 chocolates

Algebraic expressions are expressions having a composition of terms, variables, coefficients, factors and constants.

They are also composed of mathematical operations, such as;

From the information given, we have that;

Then, the number of chocolates he has is 4848 - 88

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The change in temperature each hour is 6 °C.

Unit rate is the amount of one quantity for a unit amount of the other quantity.

In other words it compares 1 unit of some quantity with different amount of another quantity

Given that,

In a lab, a substance was cooled by 18 °C over a period of 3 hours at a constant rate.

Since the rate at which the substance is cooling down is constant,

Amount by which substance cooled down in 3 hours = 18 °C

Amount by which substance cooled down in 1 hour = 18 °C / 3 = 6 °C, which is the unit rate.

Hence the unit rate of the change in temperature is 6 °C per hour.

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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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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:30

Step-by-step explanation:

use the word Pemdas

P-parenthesis

e-exponent

m-Multiplication

d-divide

a-Add.

s-Subtract.

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 solution to the given fraction polynomial is expressed as; (x - 4)/(x + 4)

The polynomial fraction expression is;

[(6x² - x - 1)/(3x² + 25x + 8)] * [(x² + 4x - 32)/(2x² + 7x - 4)]

Let us reduce each of the terms to their factors;

6x² - x - 1 = (3x + 1)(2x - 1)

3x² + 25x + 8 = (3x + 1)(x + 8)

x² + 4x - 32 = (x - 4)(x + 8)

2x² + 7x - 4 = (2x - 1)(x + 4)

Thus, we now have;

[(3x + 1)(2x - 1)/((3x + 1)(x + 8))] * [((x - 4)(x + 8))/(2x - 1)(x + 4))]

Common terms will cancel out to get;

(x - 4)/(x + 4)

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1. <1 and <7 are supplementary.

2. <1 and <3 are supplementary.

3. <2 and <6 are congruent angles.

Supplementary angles are two angles that add up to 180 degrees. In other words, they are angles that "complete" each other, forming a straight line. If two angles are supplementary, they are said to be "supplementary to each other."

Congruent angles are angles that have the same measure. They are written with the symbol "≅" and are read as "is congruent to." Two angles are congruent if they have the same degree measure.

1. Angles 1 and 7 add up to 180 degrees, therefore, they are supplementary.

2. Also, angles 1 and 3 are supplementary.

3. Angles 2 and 6 are corresponding angles, therefore, they are congruent angles.

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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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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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Answer:

x = 2

Step-by-step explanation:

7 [tex]\frac{1}{3}[/tex] x - 5 [tex]\frac{1}{2}[/tex] = 4x + 1 [tex]\frac{1}{6}[/tex] ( change mixed numbers to improper fractions )

[tex]\frac{22}{3}[/tex] x - [tex]\frac{11}{2}[/tex] = 4x + [tex]\frac{7}{6}[/tex]

multiply through by 6 ( the LCM of 3, 2, 6 ) to clear the fractions

44x - 33 = 24x + 7 ( subtract 24x from both sides )

20x - 33 = 7 ( add 33 to both sides )

20x = 40 ( divide both sides by 20 )

x = 2

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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Answer: The x-intercepts of the line are points where the y-coordinate is equal to 0. The x-intercepts of this line are (-2, 0) and (3, 0). The y-intercept is the point where the x-coordinate is equal to 0, which in this case is (0, 4).

Step-by-step explanation:

The most appropriate measure of center is median.

option B.

The choice of measure of center (i.e., the most appropriate way to summarize the "typical" value of a dataset) depends on the distribution of the data and the research question being addressed. In general, the most commonly used measures of center are the mean and the median.

The mean is the arithmetic average of a dataset, and is often used as the measure of center for datasets that follow a normal or symmetrical distribution, where the data are roughly evenly distributed around a central value.

The median, on the other hand, is the middle value of a dataset when the values are arranged in order from smallest to largest.

For the given data, it is not evenly distributed but it is arranged from the smallest to the largest, so we can use median as the most appropriate measure of center.

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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.

Answer:

2(x-4)

Step-by-step explanation:

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

The perimeter of the original parallelogram is 22/9 * √3

The vertices of the parallelogram are A, B, C, and D, with AB parallel to CD and AD parallel to BC.

The parallel lines intersect the sides of the parallelogram at E, F, G, and H.

The side length of the equilateral triangle is s.

The three regions have the same area, hence, the area of each region is 1/3 of the total area of the parallelogram.

Let's the area of the parallelogram as A.

The area of the equilateral triangle is (s²√3)/4

This area is one-third of A

(s²√3)/4 = A/3

s² = 4A/(3√3)

Considering the whole parallelogram;

AB is parallel to CD, hence, triangle AEF is similar to triangle BGF

Also, AD is parallel to BC, hence, triangle ADE is similar to triangle BCF.

AE/EB = BF/FG AD/DE

AE/EB = BC/CF

Expressing AE, BF, AD, and BC in terms of s:

AE = s/3 (perimeter of the equilateral triangle is 1)

EB = 2s/3

BF = 2s/3

FG = s/3

AD = (2s + 2EB)/3

AD = (2s + 4s/3)/3

AD = 10s/9

DE = (2s + 2AE)/3

DE = (2s + 2s/3)/3

DE = 8s/9

BC = (2s + 2FG)/3

BC = (2s + s/3)/3

BC = 7s/9

CF = (2s + 2BF)/3

CF = (2s + 4s/3)/3

CF = 10s/9

Now we can find the perimeter of the parallelogram:

Perimeter = 2(AB + AD)

Perimeter = 2(EB + BC)

Perimeter = 2(2s/3 + 7s/9)

Perimeter = 4s/3 + 14s/9

Perimeter = (22s/9)

Substituting s² = 4A/(3√3) from the earlier equation, we get:

Perimeter = (22/9)√3

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