What is the solution to the system?.

Answer: The domain of g(x) = √(x - 3) is (3, ∞) because the square root function is defined for non-negative numbers, x - 3 must be greater than or equal to 0, which means x must be greater than 3.

The range of g(x) = √(x - 3) is (0, ∞) because the square root function can only output non-negative numbers, and as x increases, the value of √(x - 3) will also increase.

So the correct answer is: D: (3, ∞) and R: (0, ∞)

Step-by-step explanation:

The domain of the given function is Domain: [3,∞),{x|x≥3} and the range is Range: [0,∞),{y|y≥0}. Therefore, the option A is the correct answer.

The given function is g(x)=√(x-3).

We know that, the domain is set of all x-values and the range is set of all y-values.

Substitute x=1, 2, 3, 4,.....in the given function, we get

g(1)=√(1-3) = i√2

g(7)=√(7-3) = 2

g(19)=√(19-3) = 4

So,

Domain: [3,∞),{x|x≥3}

Range: [0,∞),{y|y≥0}

Therefore, the option A is the correct answer.

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Answer:

I = 17deg, II = 73deg

Step-by-step explanation:

Let's say first angle is x, and then respectively, the second angle is 4*x + 5.

Their sum is 90 degrees, so:

x + (4*x+5) = 90

5x + 5 = 90

5x = 85 | :5

x = 17 degrees ==> first angle

4*x+5 = 73 degrees ==> second angle

the mid point of the side AB is (0,-1).

What is triangle?

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle containing the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane. A triangle's area is the region that each of its sides touches. A triangle's area varies from one triangle to another depending on the size of its sides and internal angles. Triangle area is measured in square units like m2, cm2, and in2.

A = (2,-3)

B = (-2,1)

Mid point will be 1+3/2, -2-2/2

Mid point is (0,-1)

Hence the midpoint of the side AB is (0,-10).

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Plot the lines and shade in the regions on the same x-y plane to find the solution to the system of inequalities 4x+6y ≤ 24 and x + 5y ≤ 10 fall under the mixed shaded region in the graph.

What is the linear inequalities?

Linear inequalities are mathematical expressions that describe a relationship between two variables that is linear in nature. The most common form of a linear inequality is of the form ax + by < c, where a, b, and c are constants and x and y are variables.

Yes, this system of two linear inequalities can be represented graphically on the x-y plane by plotting the solutions to each inequality. The steps are as follows:

        4x + 6y <= 24

        => -6y <= -4x + 24

        => y >= (4/6)x + 4

        => y = (4/6)x + 4

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Answer:

  see attached

Step-by-step explanation:

You want to graph the piecewise defined function ...

  f(x) = 2x+9 for x < -3; 2x-2 for x > 4

You normally graph a line by finding (at least) two points on the line and drawing a line through them to make the graph. Often, it is convenient to start with the y-intercept. Here, it is convenient to start with the end point of the domain on which the line is defined. Additional points can be found by making use of the slope: rise 2 for each run of 1 to the right.

For x < -3, the value of y at x=-3 is ...

  y = 2(-3) +9 = 3

So, the point (-3, 3) will appear on the graph. This point is not actually in the domain, which is x < -3, so will be graphed as an open circle. The line goes down and to the left from there with a slope of 2.

For x > 4, the value of y at x=4 is ...

  y = 2(4) -2 = 6

So, the point (4, 6) will appear on the graph as an open circle, because x=4 is not actually in the domain of the function. The line will go up to the right from there with a slope of 2.

See the attachment for a finished graph.

The Mean for June 2006 and 2005 is  $345,909 and $335,977 respectively. The median for June 2006 and 2005 is $254,000 and $139,000 respectively, there's no mode in this question.

In statistics, the mean, mode, and median are three measures of central tendency that describe a set of numerical data.

The mean is the average of a set of numbers, calculated by adding up all the values and dividing by the number of values. For example, if a set of data contains the values {1, 2, 3, 4, 5}, the mean is (1 + 2 + 3 + 4 + 5) / 5 = 3.

The mode is the value that appears most frequently in a set of data. For example, if a set of data contains the values {1, 2, 2, 3, 4, 4, 4, 5}, the mode is 4, because it appears three times, which is more than any other value.

The median is the middle value in a set of data when it is ordered in ascending or descending order. For example, if a set of data contains the values {1, 2, 3, 4, 5}, the median is 3, because it is the middle value. If there is an even number of values, then the median is the average of the two middle values.

It is important to note that different sets of data may have different measures of central tendency, and sometimes none of these measures may be appropriate.

Measures of central tendency are used to summarize and describe a set of data. The most common measures of central tendency are the mean, median, and mode.

1. Mean:

• Mean for June 2006: (508+435+538+913+367+033+254+240+137+022+160+548+260+458+358+035+222+879+136+371+127+586+201+316)/22 = $345,909

• Mean for June 2005: (422+843+469+588+245+803+199+409+132+054+139+728+254+725+345+065+210+740+134+334+125+455+184+853)/22 = $335,977

2. Median:

• Median for June 2006: Median of ordered data is the value in the middle of the data set, It is the 11th value in order set. we can see that it is $254,000

• Median for June 2005: Median of ordered data is the value in the middle of the data set, It is the 11th value in order set. we can see that it is $139,000

3. Mode:

• Mode for June 2006: There is no mode, because no value is repeated.

• Mode for June 2005: There is no mode, because no value is repeated.

Conclusions:

• The mean housing price in June 2006 is higher than the mean housing price in June

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The gradient of the line is 0.

A line's slope is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by the symbols y and x, respectively. where "m" represents the slope of a line. So, tan is the slope of a line.

According to the question

Given the equation of a line is y = -10.

The general equation of the line is y = mx + c

This is a horizontal line because, regardless of the value of x, the value of y is always less than 10. A horizontal line by definition has a slope of:

m = 0

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Answer :

HU length = 24

If UVW is Isosceles triangle then UGH is Isosceles

UV=UW = 132

Then,

HU = UG = 24

The product of equation (4y-3)(2y²+3y-5) is 8y³+6y²-29y+15.

According to the question,

The equation is  = (4y-3)(2y²+3y-5)

First, let us start with "4y"

4y×2y² = 8y³

4y×3y =  12y²

4y×(-5 )= -20y

Next, let us multiply by "-3"

(-3)×(2y²) = -6y²

(-3)×3y = -9y

(-3)×(-5) = 15

Now, let us combine all of our values.

The product is = 8y³+12y²-6y²-20y-9y+15

                        = 8y³+6y²-29y+15 (apply BODMAS rule)

So, the product is 8y³+6y²-29y+15.

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Answer:

The average marks = 31

Step-by-step explanation:

We know that the average can be measured using mean

Mean = Sum of observations /  no of observations

In the given data no of observations = sum of frequencies

                                                                 = 3+6+10+7+4

                                                                  =30

Sum of observations = No of marks * frequency 1 + No of marks * frequency 2+...

             =  10*3 +20*6+30*10+40*7+50*4

              = 930

Mean = 930/30

          = 31

The main difference between a mixture and a compound is that a mixture is a physical combination of substances while a compound is a chemical combination of elements.

In chemistry, a mixture is a combination of two or more substances that are not chemically combined and can be easily separated by physical means. The properties of a mixture depend on the properties of the individual substances that make it up, and the substances retain their original properties. Examples of mixtures include air, salt water, and a bowl of fruit.

A compound, on the other hand, is a substance that is made up of two or more elements chemically combined in a fixed ratio. The properties of a compound are different from those of the individual elements that make it up. The atoms in a compound are chemically bonded together and cannot be easily separated by physical means. Examples of compounds include water (H₂O), table salt (NaCl) and sugar (C₁₁H₂₂O₁₁).

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The set of -values that are appropriate in the given situation is known as the practical domain. Solution: F (x) = 2 x is the function's formula.

You are not accounting for or measuring any rainfall that occurred prior to the storm's onset, thus there is a total of 0 inches of precipitation at that time. Six and a half hours are spent in the storm.

Example :

Miami, Florida, experiences heavy rainfall due to a powerful hurricane. A 2 inch per hour downpour is occurring. In 6 and a half hours, the storm is over. The total amount of rain that has fallen throughout time should be modeled mathematically. The function is plotted. For this situation, identify the practical domain. The set of -values that are appropriate in the given situation is known as the practical domain.

Solution: Since there was no rain measured or included before the storm began, the function is as follows:

f(x)= 2x

There was 0 inches of rain at the moment the storm began. Six and a half hours are spent in the storm. f(6.5) = 2(6.5) = 13 inches of rain had been recorded at 6.5 hours, or so. It follows in words what the domain and range are:

Domain :

All real numbers between and including 0 and 6.5 hours.

Range :

All real numbers between and including 0 and 1.3 inches.

Domain and range can be expressed more easily with the help of some helpful notation, such as the following:

Domain { x∈R,0≤ x ≤ 6.5} [0,6.5]

Range { x∈R,0≤ x ≤ 6.13 [0,13].

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To write 149600000000 in standard form, we need to move the decimal point to the left or right so that there is only one non-zero digit to the left of the decimal point. 149600000000 in standard form would be written as 1.496 x 10^11.

To arrive at this form, we move the decimal point 11 places to the left (since there are 11 zeros in 149600000000) and add the power of 10 notation, indicating that we moved the decimal point 11 places to the left. The number 1.496 is the coefficient and 11 is the exponent. This way, we get 1.496 x 10^11 which is the standard form of 149600000000.

Standard form, also known as scientific notation, is a way of expressing a number in a compact and efficient manner. It is typically used for very large or very small numbers. To write a number in standard form, the decimal point is moved so that there is only one non-zero digit to the left of the decimal point. The number of places the decimal point is moved is indicated by a power of 10

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Samantha is willing to pay up to $72,000 for the 1963 Chevrolet Corvette, which is $17,000 more than Ivan's asking price of $55,000.

It means to receive something from a parent or ancestor through genetic transmission. It also means to receive something as a devise or legacy from an ancestor. inherit an enzyme that is flawed.

Ivan inherited the car and valued it at $45,000, therefore he would make a profit of $17,000 if he sells the car to Samantha.

It's important to note that the final price will depend on the negotiation and agreement between Ivan and Samantha.

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The rounded number to the nearest tenth is 7.1

How to round to the nearest tenth?

Examine the hundredth number to determine the decimal number's nearest tenth. Add one to the tenth value if the number is more than 5. The tenth place value should remain unchanged if it is less than 5, but all subsequent numbers should be eliminated.

√50 = 7.071

hundredth number is 7 greater than 5

Add one to the tenth value if the number is more than 5

all subsequent numbers should be eliminated.

Thus, the rounded number to the nearest tenth is 7.1

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Answer:

3.2

Step-by-step explanation:

......................

Carl has 2 5/36 yard cable, more than 1 yard, not specified left.

What is yard ?

A yard is a unit of length measurement in the U.S. customary system and the imperial system. It is equal to 3 feet or 36 inches. The symbol for yard is "yd". It is mostly used in the United States and the United Kingdom for measuring small lengths, such as in construction, textiles, and landscaping.

Carl has three lengths of cable, 5/6 yard long, 1/4 yard long and 2/3 yard long. The total length of the cable that Carl has is:

5/6 + 1/4 + 2/3 = (30 + 15 + 40) / 36 = 85 / 36 = 2 5/36 yard

To check whether he has at least one yard of cable or not, we need to compare the total length of the cable he has (2 5/36 yard) with 1 yard. Since 2 5/36 is greater than 1, it means he has more than 1 yard of cable. So, he will have at least 1 yard of cable left after using some of it.

Carl has 2 5/36 yard cable, more than 1 yard, not specified left.

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Carl has three lengths of wire, each measuring 5/6 yards, 1/4 yards, and 2/3 yards. The wire that Carl has measures a total of:

5/6 + 1/4 + 2/3 = (30 + 15 + 40) / 36 = 85 / 36 = 2 5/36 yard

We need to compare the entire length of the cable he has (2 5/36 yard) with 1 yard to see if he has at least one yard of cable or not. He has more than one yard of cable since 2 5/36 is larger than 1, which is greater than 1. After using some of the wire, he will still have at least 1 yard of it.

The slope of the line 5y = -3x + 10 is -3/5.

To find the slope of the line represented by the equation 5y = -3x + 10, we can first put the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

In this case, we can start by dividing both sides of the equation by 5:

y = (-3/5)x + 2

where (-3/5) is the slope of the line, and 2 is the y-intercept. Therefore, the slope of the line 5y = -3x + 10 is -3/5.

Alternatively, you could have directly found the slope by looking at the x and y coefficients, in this case the slope is -3/5

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The study comes to the additional conclusion that both interventions—traditional methods of instruction and the use of graphing calculators—improve students' abilities to compute mathematically.

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The ratios of the sides of a right triangle are called trigonometric ratios. Three common trigonometric ratios are the sine (sin), cosine (cos), and tangent (tan).

In arithmetic, the trigonometric functions (also known as circular features, perspective features, or goniometric functions) are actual features that relate an angle of a proper-angled triangle to ratios of side lengths. they may be extensively utilized in all sciences which might be associated with geometry, such as navigation, strong mechanics, celestial mechanics, geodesy, and lots of others. they are a few of the handiest periodic features, and as such are also extensively used for analyzing periodic phenomena through Fourier analysis.

The trigonometric functions most extensively used in cutting-edge mathematics are the sine, the cosine, and the tangent. Their reciprocals are respectively the cosecant, the secant, and the cotangent, which are less used. each of these six trigonometric capabilities has a corresponding inverse function and an analog most of the hyperbolic features.

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The balance at the end of five years is $552.04.

The equation that that represents the balance in the account is $500 x (1.02)^5

The amount of money in the bank account would grow at an exponential rate.

The formula for calculating future value:

FV = P (1 + r)^nm

Where:

$500 x (1 + 2/100)^5

$500 x (1.02)^5 = $552.04

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There are 21 states landlocked and 27 states do not border an ocean.

A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

Since there are 48 states in the continental United States, some of which are on the border of an ocean and some of which are not.

According to the question,

The ratio of the states having the border to the ocean and not having the border to the ocean = 7 : 9

Let the states having the border to the ocean = 7x

The states do not have a border to the ocean = 9x

Thus, 7x + 9x = 48

⇒ 16x = 48

⇒ x = 3

So, the states do not have a border to the ocean = 7 × 3 = 21

And, the states do not have a border to the ocean = 9 × 3 = 27

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The y-intercept for the graph of this line 3x-5y=6 is -6/5.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

To determine the intercept of the equation, it would be helpful to write it in its slope-intercept form which is expressed as:

y = mx + b

where m is the slope and b is the y-intercept. Therefore, the value of b would be the correct answer here.

3x-5y=6

5y=3x - 6

y = 3x/5 - 6/5

Thus, the y-intercept is -6/5.

Thus, the y-intercept for the graph of this line 3x-5y=6 is -6/5.

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The recursive formula represents the total amount of money in Victoria’s account at the end of the nth year

Generally, The recursive formula representing the total amount of money in Victoria's account at the end of the nth year is:

A(n) = A(n-1) + 15 + 0.02 * A(n-1)

where

To get the first value of A(n) we can use the initial condition

A(1) = 200 + 15 + 0.02 * 200

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The equation which is the best model for a line of best fit for the data is y = ½ x – 1. (Option B)

A line of best fit refers to a straight line which minimizes the distance between it and some data. It expresses a relationship in a scatter plot of different data points. It is an educated guess about where a linear equation which may fall in a set of data plotted on a scatter plot. It is an output of regression analysis and is used as a prediction tool.

The equation of the line can be determined using slope intercept form of the line which is y = mx + b where m is the slope and b is the y intercept. From the given graph, two points which lie on the line of best fit can be used to determine the slope. Let consider two points (2, 0) and (0, -1). Hence

m = (-1 – 0)/(0 – 2) = -1/-2 = ½

The value of y intercept is -1 (when x = 0)

Hence, the equation is:

y = ½ x - 1

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Answer: 1/6

Step-by-step explanation: 2/3 = 4/6

1/2 = 3/6

4/6 - 3/6  = 1/6

Answer:

Mini golf costs: $10.00 per round.

Batting cages cost: $2.50 each turn.

Step-by-step explanation:

Let g= rounds of golf

Let b = batting cage

Sylvester

5g+4b = 60

Lin

3g +6b = 45

We have two equations and two unknowns

5g+4b = 60

3g +6b = 45

Divide the second equation by 3

3/3g +6/3b = 45/3

q+2b = 15

Multiply this equation by -2

-2q -4b= -30

Add this to the first equation

5g+4b = 60

-2q -4b = -30

3q = 30

Divide by 3

3g/3 = 30/3

g = 10

A game of mingolf is 10 dollars

Now we need to find b

q+2b = 15

10 +26 =15

Subtract 10

10-10+2b =15-10

26=5

Divide by 2

2b/2 =5/2

b=25

A turn in the batting cage is 2.50

The probability that a student picked from this group at random is using a pen or pencil is 19/21

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.

Given that, in a group of 42 students, 17 use pens for writing and 21 use pencils for writing.

P(A or B) = P(A) + P(B)

P(A) = 17 / 42

P(B) = 21 / 42

P(A or B) = 17 / 42 + 21 / 42

P(A or B) = 38 / 42

P(A or B) = 19/21

Hence, the probability that a student picked from this group at random is using a pen or pencil is 19/21

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