1/2x+1/3y=7
1/4x+2/3y=6
4
What is the solution of the system shown?
6,12

1/6,14

10 2/3, 5

Answers

Answer 1

The solution to the system of linear equation is:

x = 10 2/3, y = 5

The correct option is the last option   10 2/3, 5

Solving system of linear equations

From the question, we are to solve the given system of linear equation.

The given system of linear equations is

1/2x + 1/3y = 7

1/4x + 2/3y = 6

Multiply the first equation by 2

1/2x + 1/3y = 7      × 2

x + 2/3y = 14

Subtract the second equation from the resulting equation

     x + 2/3y = 14

- 1/4x + 2/3y = 6

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

3/4x = 8

Multiply both sides of the equation by 4/3

4/3 × 3/4x = 8 × 4/3

x = 32/3

x = 10 2/3

Substitute the value of x into

x + 2/3y = 14

To determine y

(10 2/3) + 2/3y = 14

32/3 + 2/3y = 14

Multiply through by 3

32 + 2y = 42

Subtract 32 from both sides

32 - 32 + 2y = 42 - 32

2y = 10

Divide both sides by 2

2y / 2 = 10 / 2

y = 5

Hence, the solution is:

x = 10 2/3, y = 5

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Related Questions

Math, some system by elimination

Answers

The elimination method is a technique used to solve linear equations that comprise a system. The fundamental principle behind this methodology involves nullifying one of the variables.

What is the elimination method about?

It should be noted that to implement the elimination approach successfully, we must exclude either x or y, which can be accomplished by multiplying the second equation by an amount necessary to make the coefficient of y consistent in both the equations:

With x's value now discerned, we can insert it into any of the original equations to calculate y. This explains the method.

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i need answer for this +explanation i don't get it​

Answers

Answer: 95 ft²

Step-by-step explanation:

      To solve for the surface area, we will find the area of all the sides and then add them together. We see that we have a square as the base and 4 congruent triangles.

For the square:

      A = LW

      A = (5 ft)(5 ft)

      A = 25 ft²

For one triangle:

      A = [tex]\frac{BH}{2}[/tex]

      A = [tex]\frac{(5\;ft)(7\;ft)}{2}[/tex]

      A = 17.5 ft²

For all four triangles:

      A = 17.5 ft² * 4 = 70 ft²

Total surface area by adding the triangles and square together:

       70 ft² + 25 ft² = 95 ft²

A spinner was spun 900 times using Spin Spinner on the TI-84
calculator, with 1 representing blue, 2 representing purple, 3
representing green, and 4 representing red as shown

what was the experimental
probability of landing on green?
a 23.80%
b 26.80%
C 22.80%
d 24.80%

Answers

The experimental probability of the spinner landing on green is calculated as follows:

p = Number of times that the number 3 was generated/900 x 100%.

How to calculate a probability?

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

A green result is obtained when the number on the calculator is of 3, hence the experimental probability of the spinner landing on green is calculated as follows:

p = Number of times that the number 3 was generated/900 x 100%.

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Calculator What is the surface area of this rectangular prism? O 110 in² O 180 in² O200 in² O220 in² 10 in. 5 in.

Answers

The surface area of the rectangular prism is 220 square inches

What is the surface area of the rectangular prism?

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

5 in by 10 in by 4 in

The surface area of the rectangular prism is calculated as

Area = 2 * (5 * 10 + 5 * 4 + 10 * 4)

Evaluate

Area = 220

Hence, teh area is 220 square inches

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The graph to the right is the uniform probability density function for a friend who is x minutes late:

​(a) Find the probability that the friend is between 10 and 30 minutes late.

​(b) It is 10 A.M. and there is a 20​% probability the friend will arrive within how many​ minutes?

Answers

Answer for (a): 2/3

Explanation:
In a uniform distribution, all probabilities are equal. In this case, the probability for being ‘x’ minutes late is each 1/30. Therefore, the probability that the friend is between 10 and 30 minutes late is 20/30 because we exclude the first 10 minutes. That can be simplified down to 2/3.

Answer for (b): 6 minutes

Explanation:
The answer is simply 20% of 30. Since 30x0.2 is 6, the friend will arrive within 6 minutes.

The 6-inch segment of tape stores 4608 bits of data and it is a portion of a tape reel that is 1200 feet long. How much data can be stored on the entire reel?

Answers

The answer is explain the animal link and it is 600

The data can be stored on the entire reel is 66,355,200 bits.

What is Unit Conversion?

Conversion could appear difficult, but this tip will make it simple for you to convert any unit. The fundamental rule is to multiply when converting from a larger unit to a smaller unit. Divide if you need to go from a smaller to a larger unit.

We have,

The 6-inch segment of tape stores 4608 bits of data.

Now, length of of reel = 1200 feet

= 1200 x 12

= 14,400 inch

So, the data that can be stored in reel

= 14,400 x 4608

= 66,355,200 bits

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folue the √(x-3) ³ - 64 equation √(ac-3)solve the equation​

Answers

Solving the equation​ √(x - 3)³ - 64 = 0 for the variable x gives x = 19

Solving the equation​ for x

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

√(x - 3)³ - 64

Express as an equation

So, we have

√(x - 3)³ - 64 = 0

Add 64 to both sides of the equation

√(x - 3)³ = 64

Take the cube roots of both sides

So, we have

√(x - 3) = 4

Square both sides of the equation

This gives

x - 3 = 16

Add 3 to the equation

x = 19

Hence, the solution is x = 19

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3. A 35 kg child on a 4.2 kg sled is sliding at 5.0 m/s, with negligible friction, along an icy, horizontal surface. As the sled passes underneath a tree, a 6.2 kg mass of snow falls vertically and lands on the moving sled. Calculate the final velocity of the sled. Calculate the final velocity of the sled. Show your work.
Answer:

Answers

The final velocity of the sled is 4.317 m/s.

Before the snow,

Total mass of sled = 35 + 4.2 = 39.2 kg

Initial velocity of the sled = 5 m/s

Momentum = Mass × Velocity

                   = 39.2 × 5

                   = 196 kg m/s

After the snow,

Total mass = 35 + 4.2 + 6.2 = 45.4 kg

Let v be the final velocity.

By the law of conservation of momentum,

Momentum before snow = momentum after snow

196 = 45.4 v

v = 4.317 m/s

Hence the final velocity is 4.317 m/s.

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Triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). Determine the line of reflection if X′(4, 5).

y-axis
x-axis
y = 1
x = −4

Answers

The line of reflection is x-axis.

Given that, the triangle XYZ is drawn with vertices X(4, −5), Y(6, −1), Z(10, −8). we need to determine the line of the reflection if the X′(4, 5).

We know that the rule of the reflection over x-axis is

(x, y) → (x, -y)

Here, the y-intercept is changing its sign so we can say that the line of reflection is x-axis.

Hence, the line of reflection is x-axis.

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I am faster than the speed of
sound. I weigh nothing, but I
can fill a room. What am I?

Answers

Answer: I think it’s light

[tex]4√3[/tex]what is equivalent to 4 sqrt 3

Answers

The equivalent expression to  4√3 is  √48 or 6.928.

What is the equivalent expression?

An equivalent expression is an expression that has equal value to the original given expression.

From the given expression, we can determine its equivalent expression as follows;

The given expression = 4√3

We can square 4 and multiply it by 3 and enclose all with the square root.

4√3 = √(4² x 3 )

= √ ( 16 x 3 )

= √ ( 48 )

= 6.928

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Help solving

5/8 + 11/12 =

Answers

Answer:

37/24

Step-by-step explanation:

You have to find the common denominator.

Fill in the missing values to make the equations true.

Answers

The missing terms in the logarithmic equation are solved

Given data ,

Let the logarithmic equation be represented as A

Now , the value of A is

a)

log₄ 11 + log₄ 5 = log₄ ( a )

Now , the value of a is

From the logarithmic properties , we get

log A + log B = log AB

So , a = 11 + 5 = 16

b)

log₅ 3 - log₅ ( a ) = log₅( 3/5 )

From the logarithmic properties , we get

log A − log B = log A/B

So , a = 5

c)

log₇ 8 = 3 log₇ ( a )

From the logarithmic properties , we get

log Aⁿ = n log A

8 = 2³

So , a = 3

Hence , the logarithmic equation is solved

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En una correctera tiene una longitud 65 millas
¿cuántos metros mide
esa carretera?

Answers

If the length of the road in miles is 65, then in meters is approximately 104607.1 meters.

To convert miles to meters, we need to use a conversion factor. There are 1609.34 meters in one mile. So, to convert 65 miles to meters, we can multiply 65 by 1609.34.

65 miles * 1609.34 meters/mile = 104607.1 meters

The units when making conversions. Miles and meters are units of length, but they are not the same. To convert from one unit to another, we need to use a conversion factor that relates the two units. In this case, we used the conversion factor of 1609.34 meters per mile to convert from miles to meters.

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K
In 2019, 2 out of every 5 members of an army reserve were female. There were 188,667 army reserve personnel that year. Estimate the number of
female members of the army reserve in 2019.
The approximate number of female members of the army reserve in 2019 was.
(Do not round until the final answer. Then round to the nearest whole number as needed.)
ew an example Get more help.
Clear all
Skill builder
Check answer

Answers

The approximate number of female members of the army reserve in 2019 was 75,467.

What is the number of female members in 2019?

If 2 out of every 5 members of the army reserve were female, then the proportion of female army reserve personnel can be represented as:

=  2/5

= 0.4.

Now, we can multiply the proportion to total number of army reserve to get the number of female members which is:

= 0.4 x 188,667

= 75,466.80

= 75,467

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Given the triangle ABC at points A = ( 2, 2 ) B = ( 4, 5 ) C = ( 6, 3 ), and if the triangle is first reflected over the y axis, and then over the x axis, find the new point A''.

Answers

To reflect a point over the y-axis, we negate the x-coordinate of the point. To reflect the resulting point over the x-axis, we negate the y-coordinate of the point. So, to find the new point A'', we can perform these operations on the original point A:

1. Reflect A over the y-axis to get A': (-2, 2)

2. Reflect A' over the x-axis to get A'': (-2, -2)

Therefore, the new point A'' is (-2, -2).

The tree diagram shows the sample space for tossing a coin three times. Which of these shows all outcomes with exactly 2 heads?

Answers

The probability of tossing exactly 2 tails is 0.375.

We have,

A coin is tossed three times.

So, the outcomes can either be a head or a tail.

The possible outcomes when a coin is tossed three times are:

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Now, the Pr(tossing exactly 2 tails)

= 3/8

= 0.375

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what is the radius of this shape?

Answers

Answer 7/12

Step-by-step explanation:

Answer:

Step-by-step explanation:

The radius is the length from the center dot to the circle.

They gave you the radius

r=6 1/4 in

Find the values of x and y.
E
25
24
20
D
G

Answers

The value of x and y are 32.02 and 13.3 respectively.

What is Pythagoras theorem?

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

If a and b are the legs of the triangle and c is the hypotenuse, then,

c² = a²+b²

Triangle EFG is a right angled triangle so also triangle DEG

Therefore,

x² = 25²+20²

x² = 625 + 400

x² = 1025

x = √1025

x = 32.02

Also,

y² = 24² - 20²

y² = 576 - 400

y² = 176

y = √176

y = 13.3

Therefore the value of x and y is 32.02 and 13.3 respectively.

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David's gasoline station offers 4 cents off per gallon if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period, 15 customers buy gasoline at this station. What is the probability that more than 8 and less than 12 customers pay in cash?

Answers

The probability that more than 8 and less than 12 customers pay in cash is 0.376 or 37.6%.

What is the probability?

The probability that more than 8 and less than 12 customers pay in cash is calculated using the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where:

n is the number of trials = 15

x = customers who pay in cash

p = paying in cash, which is 0.4 according to the problem

The probability that more than 8 and less than 12 customers pay in cash. is the sum of the probabilities of 9, 10, and 11 customers paying in cash.

Using the binomial probability formula:

P(x) = (15Cx) * 0.4 * (1 - 0.4)¹⁵⁻ˣ

P(9) = 15C₉ * 0.4⁹ * 0.6⁶

P(9) = 0.212

P(10) = 15C₁₀ * 0.4¹⁰ * 0.6⁵

P(10) = 0.121

P(11) = 15C₁₁* 0.4¹¹ * 0.6⁴

P(11)= 0.043

Hence;

P(9 or 10 or 11) = 0.212 + 0.121 + 0.043

P(9 or 10 or 11) = 0.376

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HELP PLEASEE

Find the value of x to the nearest tenth of a unit.

Answers

Check the picture below.

[tex]\tan(18^o )=\cfrac{\stackrel{opposite}{x}}{\underset{adjacent}{18}} \implies 18\tan(18^o)=x \implies 5.8\approx x[/tex]

Make sure your calculator is in Degree mode.

If A is the set of numbers that are multiples of 8, B is the set of multiples of 4, and C is the set of multiples of 2, which of the following is the set of integers that will be in A but not B and C?

Answers

The set of integers that will be in A but not B and C will be 24, 32, 40,

How to explain the integer

The multiples of 8 comprise a set of {8, 16, 24, 32, 40, ...}, while the multiples of 4 correspond to {4, 8, 12, 16, 20, ...} and  those of 2 are documented as {2, 4, 6, 8, 10, …}. The intersection of these two sets, B and C (B ∩ C = {4, 8, 12, 16, 20, ...}) remains unchanged.

It should be noted that to obtain the number of integers found in the multples of 8 that aren’t multiples either of 4 or 2, the intersection needs to be excluded from set A. This will yield {24, 32, 40, ...} - thus it is concluded that the integer set of multiples of 8, but not of 4 or 2, is {24, 32, 40, ...}

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Need help looking for the area.

Answers

The area under the curve (since the function of the parabolic expression is y = x - x²) is 1/6 square units.

What is a parabolic expression?

A parabolic function has an expression represented as f(x) = ax² + bx + c, which allows solving for x using either the factorization method or applying the quadratic formula. By zeroing out this expression, it becomes possible to determine its roots as with any quadratic equation.

In the case of the above function:

To find the area under the curve, above the x-axis, we need to integrate the parabolic expression from 0-1

that is:

∫[0,1](x-x²)dx

This is evaluated using the power rule

∫[0,1](x-x²)dx = [1/2x² - 1/3x³) fro x= 0 to x = 1

inserting the limits of the integration, we have:
[1/2 (1) ² - 1/3 ( 1) ³] - [1/2 (0)² - 1/3 (0) ³]

Simplified, and we have :

Area  = 1/2 - 1/3

Thus, Area under the curve = 1/6

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I need help with this please

Answers

The answer is C because if you add 2, 1 3/4 and 1 1/2 it equals 4 1/2

Correct answer gets brainliest!! So please help!!

Answers

Answer:

b

Step-by-step explanation:just do it heh

Answer:

The Correct answer is D

the lower whiskers from 10 to 28

M<2
Answers please the ask is in the picture

Answers

I did and got that once answer

URGENT!! ILL GIVE BRAINLIEST! ALONG WITH 100 POINTS!!!!!!!!

Match the given information with the equation for the line
-5x + 3y = -12
y = 3/2 x - 8
2y-x = -4
Y= -3/4x-2

Answers

Answer:

1. y = 3/2 x - 8

2. 2y-x = -4

3. y = -3/4x-2

4. -5x + 3y = -12

A company produces two products: A and B. The relative market values at the split-off point are not available. For every $300,000 of joint costs, Product A produces 10,000 pounds, and Product B produces 40,000 pounds. The amount of joint costs allocated to Product B using the physical quantities method is $

Answers

The joint costs allocated to Product B is $240,000.

What is amount of joint costs allocated to Product B?

We must allocate joint costs based on the relative physical quantities produced by each product.

The total physical quantity produced by both products is:

= Quantity of A + Quantity of B

= 10,000 + 40,000

= 50,000 pounds

We will calculate the proportion of physical quantity produced by product A:

= Quantity of B / Total physical quantity

= 40,000 / 50,000

= 0.8

The amount of joint costs allocated to Product B is will be

= Total joint costs x Proportion of

= $300,000 x 0.8

= $240,000.

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consider the following two claims about whether the government should do more to help the poor and middle class
. A adjusted for inflation, income has risen significantly over recent decades with average households income in the us rising nearly 30% over the time period.
claim 2. a adjusted for inflation, income has been relatively stagnant for more than three decades, with average household income in the us rising less that 10%over that time period

Answers

Therefore, it is clear that the government should do more to help the poor and middle class, as their incomes have been relatively stagnant for an extended period of time.

Both claims are true, depending on the time period being considered. If we look at the time period over the last few decades, then Claim 1 is accurate, as average household income has risen nearly 30% over the time period, adjusted for inflation.

However, if we look at the past three decades, then Claim 2 is more accurate, as average household income has only risen less than 10%, adjusted for inflation.

Therefore, it is clear that the government should do more to help the poor and middle class, as their incomes have been relatively stagnant for an extended period of time.

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A rectangular field is four times as long as it is wideIf the perimeter of the field is 300yards, what are the field's dimensions?

Answers

Answer:

Length = 120 yards, width = 30 yards.

Step-by-step explanation:

Lets use [tex]l[/tex] for length and [tex]w[/tex] for width.

The perimeter of a rectangular field is [tex]2l + 2w[/tex]. We can construct the following equations:

[tex]4w = l[/tex].

[tex]2l + 2w = 300.[/tex]

If we plug [tex]4w[/tex] in for [tex]l[/tex] into the second equation, we get:

[tex]2w + 2(4w) = 300.[/tex]

[tex]2w+8w = 300.[/tex]

[tex]10w = 300.[/tex]

[tex]w= 30.[/tex]

Plug 30 in for [tex]w[/tex] into the first equation.

[tex]l = 4*30 = 120.[/tex]

Length = 120 yards, width = 30 yards.

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