What is the solution to the system of equations?
y = A system of equations. y equals StartFraction one-half EndFraction x minus 6. x equals negative 4.x – 6
x = –4

The value of (f - g)(x) is as follows:

(f - g)(x)  =  4x³ + 6x² - 7x - 1

f(x) = 4x³ + 6x² - 3x - 4

g(x) = 4x - 3

Let's find the function:

(f - g)(x)

Therefore,

(f - g)(x)  = 4x³ + 6x² - 3x - 4 - ( 4x - 3)

Hence, let's open the bracket

(f - g)(x)  = 4x³ + 6x² - 3x - 4 - 4x + 3

Let's combine like terms

(f - g)(x)  =  4x³ + 6x²  - 3x - 4x - 4 + 3

Therefore,

(f - g)(x)  =  4x³ + 6x² - 7x - 1

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The solutions to the equations are x = 7/3 and y = 24/7

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

4x + 10 = -2x + 4

y - 4(2y - 5) = -4

Considering the first equation

4x + 10 = -2x + 4

Collect the like terms

4x + 2x = 10 + 4

Evaluate the like terms, by adding them

6x = 14

Divide both sides of the equation by 6

x = 7/3

Considering the second equation

y - 4(2y - 5) = -4

Expand the bracket in the above equation

y - 8y + 20 = -4

Collect the like terms

y - 8y = -20 -4

Evaluate the like terms, by adding them

-7y = -24

Divide both sides of the equation by -7

y = 24/7

Hence, the solutions to the equations are x = 7/3 and y = 24/7

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Answer:

-9

Step-by-step explanation:

The missing number will be labeled as x.

-15*x*8*(-4)=-4320

480x=-4320

x=-9

Answer:

120

Step-by-step explanation:

My choices are: 1, 3, 5, 7, 9.  I cannot repeat any of the numbers.

The first spot, I have 5 choices.  The second spot, I have 4 choices, the third spot, I have 3 choices and the final spot has only 2 choices.

5x4x3x2 = 60

360° ÷ 10 ÷ 2 = 18°

So the length of the decagon side is:

10 × tan18° × 2 = 20 × tan18°

The area is: ½ × 20 × tan18° × 10 × 10 = 1000 × tan18°

≈ 324.9

.: 324.9 is the final answer.

I hope this helps.

The value of x for the given equation is 0.632 and -0.632.

According to the statement

We have given that the equation and we have to a find the value of the x.

So, The given quadratic equation are:

Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power solve for x in the quadratic equation

The given terms are

[tex]6x^2 + 4(x^2 - 1) = 0[/tex]

Solving the equation the the outcome equation is

[tex]6x^2 + 4x^2 - 4 = 0\\10x^2 - 4 = 0\\10x^2 = 4\\x^2 = 4/10[/tex]

The value of x is 0.632 and -0.632.

So, The value of x for the given equation is 0.632 and -0.632.

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Answer:

20%

Step-by-step explanation:

We can start by finding out how much the price of the television was reduced by.

250 - 200 = 50

Now, we need to know what percent of 250 is 50? Let x represent the percent of 250 that is 50. Using this, we can set up an equation:

[tex]x\%\times 250=50[/tex]

Notice that a percentage can also be written as that number over 100.

[tex]\frac{x}{100}\times250=50[/tex]

[tex]\frac{250x}{100}=50[/tex]

Reduce the fraction (250 and 100 have a common factor of 10)

[tex]\frac{25x}{10}=50[/tex]

Reduce the fraction again (25 and 10 have a common factor of 5)

[tex]\frac{5x}{2}=50[/tex]

Multiply both sides by two

[tex]5x=100[/tex]

Divide both sides by 5

[tex]x=20[/tex]

Therefore the price of the television was reduced by 20%.

Answer:

Exact Form:

61/12

Decimal Form:

5.083 with 3 repeating

Mixed Number Form:

5   1/12

Step-by-Step Explanation:

-5/3×3/8 = -5/8

-5/8+3/8= -1/4

-1/4+6/9=5/12

5/12+14/3=61/12

Answer:

x = -1

y = 1

Step-by-step explanation:

Given expressions

1) 2x + 3y - 1 = 0

2) 5x + 2y + 3 = 0

Add 1 on both sides of the 1) equation:

2x + 3y - 1 + 1 = 0 + 1

2x + 3y = 1

Subtract 3 on both sides of the 2) equation:

5x + 2y + 3 - 3 = 0 - 3

5x + 2y = -3

Current System

1) 2x + 3y = 1

2) 5x + 2y = -3

Multiply 2.5 on both sides of the 1) equation

(2.5) 2x + (2.5) 3y = (2.5) 1

5x + 7.5y = 2.5

Current System

1) 5x + 7.5y = 2.5

2) 5x + 2y = -3

Subtract 2) equation from 1) equation

(5x + 7.5y) - (5x + 2y) = 2.5 - (-3)

Get rid of the parenthesis

5x + 7.5y - 5x - 2y = 2.5 + 3

Combine like terms

5x - 5x + 7.5y - 2y = 5.5

0 + 5.5y = 5.5

5.5y = 5.5

Divide 5.5 on both sides

5.5y / 5.5 = 5.5 / 5.5

[tex]\boxed{y=1}[/tex]

Substitute the y-value back to one of the equations to find the x-value

2x + 3y - 1 = 0

2x + 3(1) - 1 = 0

Combine like terms

2x + 3 - 1 = 0

2x + 2 = 0

Subtract 2 on both sides

2x + 2 - 2 = 0 - 2

2x = -2

Divide 2 on both sides

2x / 2 = -2 / 2

[tex]\boxed{x=-1}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The range of possible values should be (7,34), i.e 7 < x < 34.

The answer must be more noteworthy than 7, else the two sides are less than or rise to to the third. That triangle is outlandish. The reply must moreover be less than 34, since at that point the two other sides would rise to the third, making an impossible triangle.

By the property of triangle, Sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

To prove above propert, let us assume a  ΔABC

extend AB to D in such a way that AD=AC.

In ΔDBC, as the angles opposite to equal sides are always equal, so,

∠ADC=∠ACD

so,

∠BCD>∠BDC

As the sides opposite to the greater angle is longer, so,

BD>BC

AB+AD>BC

Since AD=AC, then,

AB+AC>BC

Hence, sum of two sides of a triangle is always greater than the third side.

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Answer:

7 < x < 34

Step-by-step explanation:

When followers' needs for security and certainty, belonging, and feeling chosen or special are strong, it makes them vulnerable to the dictates of abusive leaders.

The epistemic attribute of beliefs that one cannot rationally reject is certainty, often known as epistemic certainty or objective certainty. Epistemic certainty is commonly defined as a belief being certain if and only if the person holding it could not be wrong in holding it.

In both public and private markets, securities are fungible, tradeable financial instruments used to raise capital.

The three main categories of securities are: equity, which gives holders ownership rights; debt, which is effectively a loan returned with recurring payments; and hybrids, which include features of both debt and equity.

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The the biggest 5 digit number based on the computation will be 87,978.

The difference between the sum of the odd-numbered digits (1st, 3rd, 5th...) and the sum of the even-numbered digits (2nd, 4th...) is divisible by 11.

An example is that 34871903 is divisible by 11

3+8+1+0=12

4+7+9+3=23

23-12=11

Here, we want (b + b) - (a + c + a) to be divisible by 11.

2b - (2a + c) to be divisible by 11

ab,cba (using 7 and 8 and 9 since they biggest)

78 987 --> 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO

87 978 --> 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES

79 897 --> 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO

97 879 --> 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO

89 798 --> 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO

98 789 --> 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO

Therefore, the biggest 5 digit number is 87,978.

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Answer:

(2, - 1 )

Step-by-step explanation:

3x - y = 7 → (1)

2x + 3y -= 1 → (2)

multiplying ( 1) by 3 and adding to (2) will eliminate y

9x - 3y = 21 → (30

add (2) and (3) to eliminate y

11x = 22 (divide both sides by 2 )

x = 2

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

substituting into (2)

2(2) + 3y = 1

4 + 3y = 1 (subtract 4 from both sides )

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

y = - 1

solution = (2, - 1 )

Answer:

$329.00

Step-by-step explanation:

Let the original price be $x, then

x - 0.30x - 0.10(x - 0.30x) =  207.27

x - 0.30x - 0.10x + 0.03x = 207.27

0.63x = 207.27

x = 329.00.

Answer: 98

Step-by-step explanation:

Area of four walls = Curved surface area

                             = perimeter × height

                              =    28          ×   3.5

                              = 98 m square  

Given a triangle ABC at points A = (-6, 3) B=(-4,7) C = (-2, 3), and a first transformation of up 2 and right 3, and a second transformation of down 1 and left 6, the final point B" is located at (-7, 8), which is option (a).

In mathematics, a transformation refers to a change or mapping of one set of values to another set. In geometry, a transformation involves changing the position, size, or orientation of a geometric object.

To find the location of the final point B", we need to apply the two transformations given to the initial point B (-4, 7).

First transformation: up 2 and right 3

This means we add 2 to the y-coordinate (to move the point up) and add 3 to the x-coordinate (to move the point right).

So, the new location of B after the first transformation is: (-4 + 3, 7 + 2) = (-1, 9)

Second transformation: down 1 and left 6

This means we subtract 1 from the y-coordinate (to move the point down) and subtract 6 from the x-coordinate (to move the point left).

So, the new location of B" after the second transformation is: (-1 - 6, 9 - 1) = (-7, 8)

Therefore, the final point B" is located at (-7, 8), the correct option is a.

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The mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.

A cylinder is a surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.

larger-sized candle = 2(smaller-sized candle)

= 2(240 cubic centimeters)

= 480 cubic centimeters

Therefore, the mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.

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Answer:

A cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold.

Hope this helps!

Step-by-step explanation:

The number of complete packages the store have for sale is  x / 12

The donuts sells packages of 12 donuts. This means the each package has 12 donuts.

The store has made x donuts. This means the store made x number of donut. The donuts are not in packages.

Therefore, the number of complete packages the store have for sale is as follows:

12 donuts = 1 package

x donuts = ?

cross multiply

number of packages for sale = x / 12

Therefore, the number of complete packages the store have for sale is  x / 12

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The value of x is 25 degrees if XY is parallel to the BC option (b) 25 degrees is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

It is given that:

A circle is given:

XY ║ BC

x = angle XYB

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

Angle BAX = Angle XYB

In triangle AXY, Angle XAY = 90 degrees

Angle BAX = 90 - Angle BAY

x = Angle BAX = 90 - 65

x = 25 degrees

Thus, the value of x is 25 degrees if XY is parallel to the BC option (b) 25 degrees is correct.

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The maximum possible side length of the base of the building is; C: 71 feet.

The given parameters of the new building in the shape of a square pyramid that is to be constructed are as follows:

Base is expressed as b

Slant height (l) is expressed as 5b

The lateral surface area of the square pyramid is calculated from the formula given as;

LSA = 2bl

Thus, the lateral surface area is expressed as;

L = 2 * b * 5b

L = 10b²

The total surface area is calculated using the formula:

T = L + b²

Thus, plugging in the value of 10b² for L gives the total surface area as;

T = 10b² + b²

T = 11b²

The maximum surface area is 50,000 square feet and so we can find b from the following expression;

11b² = 50000

Divide both sides of the equation by 11 to get;

b² = 50000/11

b = √(50000/11)

b =  71 feet to the nearest foot.

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Voluntary sampling is one type of sampling method that is not probability based this means that the survey's findings cannot be reliably extrapolated or generalized.

What is voluntary sampling?

A sample made up of people who freely decided to take part in the sample group is known as a voluntary sampling. Those who want to participate in a voluntary sampling typically do so because they are passionate about the topic of the survey. According to definitions, a sample with self-selected individuals is one that includes voluntary responses.

Researchers who wanted to be able to generalize their findings to the entire community would not choose volunteer sampling because it does not produce a representative sample.

A convenience sample is one that the researcher can use at their discretion, such as voluntary sampling.

However, because only those who have strong opinions about the poll will typically agree to participate, voluntary sampling can result in bias.

The survey's findings cannot be confidently extrapolated or generalized because of the possibility of bias.

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the correct inequality is"any rational number less than 9"

x < 9

Remember that when we have a number line, an open circle means that we can use the symbols > or <.

While a closed circle uses the symbols ≤ or ≥.

Here we know that we have an open circle at 9, ant everything to the left of the circle is shaded.

To the left of 9 there are the numbers smaller than 9, then the inequality would be:

x < 9

Then the correct option is "any rational number less than 9"

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Answer: x<9

any rational number less than 9"

Step-by-step explanation:

The z-score to the normal distribution table is 1.625

The standard score is the number of standard deviations by which the value of a raw score is above or below the mean value of what is being observed or measured.

The formula for calculating the z-score is expressed as;

z = x-μ/σ

where

μ is the mean of the data

σ is the standard deviation

x is the value

Given the parameters

μ = 25.1

σ = 2.4

x = 29

Substitute the given parameters

z = 29-25.1/2.4

z = 3.9/2.4

z = 1.625

Hence the z-score to the normal distribution table is 1.625

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The first scatter plot is the only one that does not have a zero correlation.

In this problem, the last three graphs do not have the format of a line, that is, they have zero correlation, and the first scatter plot is the only one that does not have a zero correlation, as the points are in the format of a line.

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The expected value of the random variable is 7

The probability distribution is given as:

x=2,3,4,5,6,7,8,9,10,11,12

Probability =1/36,1/18,1/12,1/9,5/36,1/6,5/36,1/9,1/12,1/18,1/36

The expected value of the random variable is calculated using

E(X) = ∑xP(x)

Using the above formula, we have

E(x) = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9+ 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18+ 12 * 1/36

Evaluate the sum of products

E(x) = 7

Hence, the expected value of the random variable is 7

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Step-by-step explanation:

y = a(b^x)

a = initial value

If b > 0 and b < 1, then 1 - b is the decay factor.

If b > 1, then b is the growth factor.

what function has a growth factor of 3

Function 3

what function has an initial value of 2

Function 2

what function has an initial value of 0.2

Function 4 since 1/5 = 0.2

what function has an initial value of 1

Function 3

what function has a decay factor of 0.2

None. In Function 2, the decay factor is 1 - 1/5 = 0.8, not 0.2.

what functions are increasing across real numbers?

Functions 3, 4

what functions are decreasing across all real numbers?

Functions 1, 2

The total cost of electricity when the business operates for 4 hours is correct.

The slope of a line is also known as rate of change, The formula for calculating the slope of a line is expressed as:

Slope = y2-y1/x2-x1

If the proportional relationship between the number of hours a business operates and its total cost of electricity is shown in the following graph.

Using the coordinate points (1, 20) and (2, 40)

Slope = 40-20/2-1
Slope = 20/1

Slope = 20

This shows that the total cost of electricity is $20 when operating business for 1 hour.

According to the coordinate point A (4, 120), this shows that the y-coordinate of point A is represents the total cost of electricity when the business operates for 4 hours.

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[tex]\huge\boxed{18\ \text{points}}[/tex]

We'll represent Louise's, Tammy's, Delores's, and Sheryl's point values with [tex]x[/tex], [tex]x+1[/tex], [tex]x+2[/tex], and [tex]x+3[/tex] respectively since each one is 1 point more than the last.

Add all of these values up and set it all equal to [tex]78[/tex].

[tex]x+x+1+x+2+x+3=78[/tex]

Now, simplify.

[tex]4x+6=78[/tex]

Subtract [tex]6[/tex] on both sides.

[tex]\begin{aligned}4x+6-6&=78-6\\4x&=72\end{aligned}[/tex]

Divide both sides by [tex]4[/tex].

[tex]\begin{aligned}\frac{4x}{4}&=\frac{72}{4}\\x&=\boxed{18}\end{aligned}[/tex]

Since Louise's score is [tex]x[/tex], the answer is [tex]18[/tex].

To verify our answer, add the point totals [tex]18[/tex], [tex]19[/tex], [tex]20[/tex], and [tex]21[/tex].

This equals [tex]78[/tex], so we can be sure the answer is correct.