How many solutions does the system of equation posses 2x 4y 10 3x 6y 12?.

Divide all three of the numbers in the ratio by the same number until they cannot be divided exactly any further to simplify a ratio with three numbers.

For instance, make the ratio simpler by using the numbers 20: 5: 10. 20, 5, and 10 may all be divided by 5 perfectly.

The 20:5:10 ratio can be expressed as 4:1:2.

By combining the ratio's numbers together, determine the total number of pieces.

Divide the supplied sum by the total number of parts to determine the value of each component in the ratio.

Divide the original ratio by the sum of each component's values.

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Answer:

[tex] \sf \: g = 12[/tex]

Step-by-step explanation:

Given equation,

→ 156 = 13g

Now the value of g will be,

→ 156 = 13g

→ 13g = 156

→ g = 156 ÷ 13

→ [ g = 12 ]

Hence, the value of g is 12.

The average rate of change of an function g(x) = 4ˣ  from x₁ = -1 to x₂ = 3 is 15.9375

The average rate of change of an function can be determine by using the formula below:

average rate of change = (g(x₂)- g(x₁)) / [x₂- x₁]

From the given information, g(x) = 4ˣ and x₁ = -1, x₂ = 3

For g(x) = 4ˣ:

average rate of change =  (4³ -  4⁻¹) / (3-(-1))

                                      = (63.75)/4

                                     = 15.9375

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The scale used for measuring the intensity of the earthquake is Richter Scale.

American seismologists Charles F. Richter and Beno Gutenberg developed the Richter scale (ML), a numerical indicator of an earthquake's size, in 1935. The height of the greatest seismic wave, as measured by the logarithm of its amplitude (height), is used to calculate the earthquake's magnitude.

Although the original Richter scale has been supplanted by other, more precise scales in modern science, the Richter scale is still frequently used incorrectly in news reporting of earthquake severity as a catch-all name for the logarithmic scale that earthquakes are measured on.

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The subtraction is not commutative because the order in which we subtract numbers affects the result.

Commutative property is applicable only for addition and multiplication processes. Thus, it means we can change the position or swap the numbers when adding or multiplying any two numbers.

The commutative property of subtraction does not apply to all real numbers. Subtraction is not commutative because the order in which we subtract numbers affects the result. For example, if we subtract 3 from 5, we get 2. But if we subtract 5 from 3, we get -2. The commutative property only applies to addition because a + b = b + a for all real numbers.

hence, the subtraction is not commutative because the order in which we subtract numbers affects the result.

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The Cartesian product of A = {1, 2} and B = {a, b} is A × B = {(1, a), (1, b), (2, a), (2, b)}

We know that the Cartesian Product of sets M and N is defined as the set of all ordered pairs (x, y) such that x belongs to set M and y belongs to set N.

It is denoted as M × N = {(x,y) | x ∈ M and y ∈ N}

For example, consider a set P = {1, 2}

and set M = {3, 4, 5},

From the definition of the Cartesian Product of P and M,

P × M = {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}

In this question we have been given two sets A = {1, 2} and set B = {a, b}

Using the definition of Cartesian product,

A × B = {(1, a), (1, b), (2, a), (2, b)}

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The selling price of the TV is 300 euro (250 euro original price + 20% VAT).

What is VAT(Value Added Tax) ?

VAT stands for Value Added Tax, it is a consumption tax that is added to the price of goods and services. VAT is imposed on most goods and services in many countries around the world, and it is usually a percentage of the sale price. The percentage can vary depending on the country and the type of goods or services being sold.

To calculate the VAT, we can use the formula:

VAT = (original price x VAT percentage) / 100

So, in this case:

VAT = (250 x 20) / 100 = 50

Now we add the VAT to the original price to find the selling price:

selling price = original price + VAT

250 + 50 = 300 euro.

Therefore , The selling price of the TV is 300 euro (250 euro original price + 20% VAT).

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VAT = (original price x VAT percentage) / 100

So, in this case:

VAT = (250 x 20) / 100 = 50

Now we add the VAT to the original price to find the selling price:

selling price = original price + VAT

250 + 50 = 300 euro.

Therefore , The selling price of the TV is 300 euro (250 euro original price + 20% VAT).

Yes, the number, 4225, is a perfect square because it can be expressed as square of 65 which is a whole number, i.e., 4225 = 65².

In mathematics, a square number or perfect square is an integer that is the product of some integer with itself. For example, 25 is a square number, it is equals to 5² and can be written as 5×5. A perfect square always represented as second power of a number. Perfect Square Formula : Let us consider if N is a perfect square of a whole number x, then it can be written as N = product of x and x = x². So, the perfect square formula is, N = x². We have a number 4225. Now, we resolve 4225 into prime factors, we get, 4225 = 5×5×13×13 = 5×13×5×13

= 65×65 = (65)²

Hence, the square of 65 results 4225. Therefore, 4225 is a perfect square.

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Answer:

-6x² + 35x - 36.

Step-by-step explanation:

(-2x + 9) (3x - 4)

=-2x ( 3x - 4) + 9 (3x - 4)

=-6ײ + 8x + 27x - 36.

=-6x² + 35x - 36.

The intersection of two sets is the set of elements that are common to both sets. In this case, Set A = {5, 6, 7, 8} and Set B = {7, 8, 9, 10}. Therefore, the intersection of Set A and Set B is {7, 8}.

Therefore, the number that is in the intersection of sets A and B is D: 7

It's important to note that both numbers 7 and 8 are in the intersection of the sets, but the question is asking for only one number.

Answer:

Step-by-step explanation:

I think that the numbers 10-(2-3990

Answer: 32

Step-by-step explanation:

The number of push-ups did sara did during gym class if for every 7 push-ups Dulce can do, Sara can do 6 is 24 push ups.

Number of push ups Dulce can do : number of push ups Sara can do

Let

number of push ups Sara does = x

7 : 6 = 28 : x

7/6 = 28/x

cross product

7 × x = 28 × 6

7x = 168

divide both sides by 7

x = 168/7

x = 24

Therefore, Sara does 24 push ups during the gym class.

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Answer:

. . . they are on the same plane

Step-by-step explanation:

I don't know how else this could be answered with the information given,

m<1=64

m<2=150

The equation is m+64=150

m= 86

There is no solution for the given equation "-15y + 7 + 17y = 2y + 70".

We are given an equation.

"-15y + 7 + 17y = 2y + 70"

We have to calculate the number of solutions to the given equation.

"-15y + 7 + 17y = 2y + 70"

Rearrange the terms

-15y + 17y + 7 = 2y + 70

Combine like terms

2y + 7 = 2y + 70

Subtraction property of equality

2y - 2y = 70 - 7

Combine like terms

0 = 61

But it is not possible.

Thus, there is no solution for the given equation -15y + 7 + 17y = 2y + 70.

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The factors of 9x² – 3x – 20 is (3x+4)(3x−5).

A number or other mathematical object is factorized or factored when it is written as the product of numerous factors, usually smaller or simpler things of the same kind.

Factorization in mathematics is the method of dividing a large number into tiny ones that, when multiplied together, give you the original number. Factorization is the split of a number into its factors or divisors.

We can also format it as

9x²−3x−20=9x²−15x+12x−20

by avoiding the everyday language

9x²−3x−20=3x(3x−5)+4(3x−5)

hence, we do

9x²−3x−20=(3x+4)(3x−5)

Factorization, also known as factoring, is the process of dividing or decomposing a thing into factors that, when multiplied together, form the original number, matrix, etc.

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Answer:

6x²-22x+

Step-by-step explanation:

perimeter=2(L+W)

L=3x²-12x

W=2+x

perimeter=2(3x²-12x+2+x)

=2(3x²-11x+2)

6x²-22x+4=0

Answer:

  28 +8√5 ≈ 45.89 cm

Step-by-step explanation:

You want the perimeter of an isosceles trapezoid with bases 10 and 18 cm and height 8 cm.

The length of each side of the trapezoid is the hypotenuse of a right triangle with legs 4 and 8:

  c² = a² +b²

  c² = 4² +8² = 16 +64 = 80

  c = √80 = 4√5 . . . . . . length of one side of the trapezoid

The perimeter is the sum of the lengths of the sides and the bases:

  10 + 18 + 2(4√5) = 28 +8√5 . . . . . cm

The perimeter is 28 +8√5 ≈ 45.89 cm.

The vertical portion of this plane's path is 81 degrees because it is travelling at a 90-degree angle of depression. She will have 393.3 yards remaining after multiplying 450 by 45 by 126.

The vertical component of this plane's angle of descent is 81 degrees, or 90 degrees. The landing field is no longer in this location. This is the landing area. I have 450 points and a 126-degree angle. Since this is not a right triangle, I will apply the law of sins.

I'm going to perform my x over my sin of 45, which is equivalent to my 450 yards over the 126 point. I'll multiply 126 times by 45 times to get 450 times. Divide both sides by 126 degrees; we'll do that. She will have 393.3 yards remaining after multiplying 450 by 45 by 126.

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Answer:

69.44

Step-by-step explanation:

now is 100%

100%=1

12%=0.12

1.12*62=69.44

Answer:12

Step-by-step explanation:

It would take approximately 12.6 years for the value of the car to be $700.

To find out how long it would take for the value of the car to be $700, we can use the formula for exponential decay. The value of the car after t years is:

[tex]V(t) = V_0 \times (1/2)^{(t/k)}[/tex]

Where V₀ is the initial value of the car, t is the time in years, k is the time constant in years, and (1/2) is the decay constant.

Given:

V₀ = $13,000

V(t) = $700

k = 3

Now you can solve for t:

[tex]700 = 13,000 \times (1/2)^{(t/3)}[/tex]

Take the natural logarithm of both sides:

[tex]ln(700) = ln(13,000 \times (1/2))^{(t/3))}[/tex]

[tex]ln(700) = ln(13,000) + ln((1/2)^{(t/3)})[/tex]

ln(700) = ln(13,000) + (t/3) × ln(1/2)

t = 3 × (ln(700) - ln(13,000))/ln(1/2)

t = 12.6 years (rounded to the nearest tenth of a year)

Thus, it would take approximately 12.6 years.

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The question seems to be incomplete the correct question would be:

A new car is purchased for $13,000 and over time its value depreciates by one-half every 3 years. How long, to the nearest tenth of a year, would it take for the value of the car to be $700?​

The inverse of f(x) = log₁₀(x) is 10ˣ.

A logarithm is an exponent to which a base must be raised to generate a given number. Expressed mathematically, x is the logarithm of n to the base a if ax = n, in which case one writes x = logₐn.

A logarithm is defined using an exponent.

aˣ = b ⇔ logₐb = x

Here, "log" stands for logarithm. The arrow's right part is read as "Logarithm of b to the base a is equal to x".

We have the function,

f(x) = log₁₀(x)

Let y = f(x)

⇒y = log₁₀(x)

⇒[tex]10^{y}[/tex] = x

∴[tex]f^{-1}[/tex](x) = 10ˣ

--The given question is incomplete; the complete question is

"What is the inverse of  f(x) = log₁₀(x)?"--

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Vertices A(-5, -3) , B(-3, -5) , C(-5, -7) , and D(-7, -5) is a rectangle

Generally, Based on the given vertices, ABCD is a rectangle. A rectangle is a four-sided polygon with four right angles, and the coordinates provided satisfy that definition.

A rhombus is a four-sided polygon with all sides congruent and opposite angles congruent, and a square is a rectangle with all four sides congruent.

Since all sides are not congruent, it is not a rhombus or a square.

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The mean of the sample is 10 and median is 10.5

The mean of the sample is given by: (∑ tour day)/ n

where n is number of visitors  

∑ tour day =12 + 7 +9 + 10 + 11 +11

=> 60

so ∑ tour day = 60

n = 6

so mean = 60 /6

=> 10

so the mean of the sample is 10.

The median of the list is found by sorting the element in ascending order and then find the average of middle most value

so after sorting the list in ascending order we get:

7 , 9, 10 , 11 , 11 , 12

so the median = (10 +11 )/2

=> 10.5

so the median of the list is 10.5

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Complete question:

The tourit bureau of the Hawaiian Iland urveyed a ample of United State tourit a they left to return home. The tourit were aked how many day they pent on their viit. Their repone were a follow.

12,7,9,10,11,11

Find the mean and median of this sample of numbers. Round your answer to two decimal places.

Angela check out 12 library book and Inola check out 1/3v then Inola checked out 12 - 3 = 9 books.

What is algebra ?

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It is a way to represent mathematical relations and to reason about them. Algebraic concepts include using variables (such as x or y) to represent unknown values, using operations such as addition, subtraction, multiplication and division.

We know that ,

Angela = 12 books

Inola = 1/3v less than Angela

To find the value of v, we can set up the proportion ,

12 = v + 1/3v

We can then solve for v by multiplying both sides by 3 ,

12*3 = 3v + v

36 = 4v

So, v = 9

Inola checked out 1/3v less than Angela, which is ,

1/3 * 9 = 3

So, Angela check out 12 library book and Inola check out 1/3v then Inola checked out 12 - 3 = 9 books.

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The distance between pylon B and pylon C is 1017.60 m, using the Pythagorean theorem.

The Pythagorean Theorem, also known as Pythagoras' Theorem, states that the area of the large square is equal to the sum of the areas of the two smaller squares.

In terms of algebra, the triangle's a and b are its legs, and its hypotenuse is equal to its product, a2 + b2 = c2.

Since it provides the foundation for the definition of distance between two points in Euclidean geometry, the theorem is crucial. Anyone who took geometry in high school, in my opinion, cannot possibly fail to remember it long after other math concepts have been completely forgotten because it is so fundamental and well-known.

Using Pythagorean theorem

The hypotenuse is the Distance from pylon B to pylon C

c = [tex]\sqrt{a^2 + b^2}[/tex]

Distance from pylon B to pylon C =  [tex]\sqrt{845^2 + 567^2}[/tex]

                                                        = 1017.60 m

Thus, The distance between pylon B and pylon C is 1017.60 m, using the Pythagorean theorem.

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The formula using the pronumerasl we get

For 'e' the formula stands as 2f = g+1

For 'f' the formula stands as c = 3s + 1

For 'g' the formula stands as a = 4d-3

For 'h' the formula stands as g = 5g-4

For 'i' the formula stands as e = 11f- 20

For 'j' the formula stands as q = 20p + 4

For 'k' the formula stands as t = 4b

For 'l' the formula stands as p = 3u - 1

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. We have LHS = RHS (left hand side = right hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. The statement is not an equation if there is no "equal to" sign in it.

One of the significant forms used to express a straight line algebraically is the two point form. Each point on the line fulfills the equation for the line, which means that the equation for the line represents every single point on the line. When two points on a line, (x 1, y 1) and (x 2, y 2), are known, the two-point form of a line is used to get the equation of the line.

For 'e' the formula stands as 2f = g+1

For 'f' the formula stands as c = 3s + 1

For 'g' the formula stands as a = 4d-3

For 'h' the formula stands as g = 5g-4

For 'i' the formula stands as e = 11f- 20

For 'j' the formula stands as q = 20p + 4

For 'k' the formula stands as t = 4b

For 'l' the formula stands as p = 3u - 1

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The number of possible ways in which Juan can pick exactly one purple counter from Box A and Box B is 3.

Given,

      We know that,   Box A contains only green and purple counters.

       We also know that,   Box B contains only green, purple, and orange counters.

According to question ,

Juan picked one counter from Box A and one counter from Box B

Possible ways to pick exactly one purple counter :

Box A                                       Box B

one purple counter       one orange counter

one purple counter       one green counter

one green counter        one purple counter

Hence, there are 3 ways in which Juan can pick exactly one purple counter.

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