If a linear function has the points (6,3) and (4,8) on its graph, what is the rate of change of the function?

Answer:

A.

What were the sixth grade student scores of the final exam?

If the length of the garden is 8 feet and width is 12 feet then the area of the garden be 96 \(feet^{2}\), if the length of garden is 12 and the area of the garden is 96 \(feet^{2}\),then the width be 8 feet, if the length of garden is 16 feet and the area is 64 \(feet^{2}\), then the width of garden be 4 feet and the length and breadth which produce largest area are 8 feet and 12 feet and they can be interchanged.

Given a table of various combinations of length and breadth of garden.

We are required to fill the blanks and find the length and widths which produce largest area.

Length           Width                 Area

4                       16                      64

8                       12                      96  

10                          

12                     8                       96

14                                          

16                      4                       64

The bold values were the blanks. The blanks which is not filled cannot be filled because we need atleast two values whether they will be length and breadth , breadth and area or length and area. The largest area is 96 \(feet^{2}\). The length and breadth are 8 feet and 12 feet. They can be interchanged because we have two such combinations.

Hence if the length of the garden is 8 feet and width is 12 feet then the area of the garden be 96 \(feet^{2}\), if the length of garden is 12 and the area of the garden is 96 \(feet^{2}\),then the width be 8 feet, if the length of garden is 16 feet and the area is 64 \(feet^{2}\), then the width of garden be 4 feet and the length and breadth which produce largest area are 8 feet and 12 feet and they can be interchanged.

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

The correct answer is - 768.

Step-by-step explanation:

The given question is based on a specific pattern present in between the numbers in the given series -

Series = 25 50 99 196 388

to find - next number in series

let us find the relation between the initial two number:

25 - 50, here number 50 is two times of 25 or (x*2-0)

relation between 2nd and 3rd number:

50 - 99, here 99 is two times of 50 minus 1 or (x*2-1)

relation between 3rd and 4th number:

99 - 196, here 196 is two times of 99 minus 2 or (x*2-2)

relation between 4th and 5th number:

196 - 388, here 388 is the two times of 196 minus 4 or (x*2-4)

So on this pattern, the next number would be = x*2-8

388*2-8

= 768

The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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By analyzing the graph and evaluating the objective function at each vertex of the feasible region, we can find the optimal solution, which is the vertex that maximizes the objective function z = 3x + y.

To find the optimal solution of the given problem using the graphical method, we need to plot the feasible region determined by the given constraints and then identify the point within that region that maximizes the objective function.

Let's start by graphing the constraints:

1. Plot the line 2x - y = 5. To do this, find two points on the line by setting x = 0 and solving for y, and setting y = 0 and solving for x. Connect the two points to draw the line.

2. Plot the line -x + 3y = 6 using a similar process.

3. The x-axis and y-axis represent the constraints x ≥ 0 and y ≥ 0, respectively.

Next, identify the feasible region, which is the region where all the constraints are satisfied. This region will be the intersection of the shaded regions determined by each constraint.

Finally, we need to identify the point within the feasible region that maximizes the objective function z = 3x + y. The optimal solution will be the vertex of the feasible region that gives the highest value for the objective function. This can be determined by evaluating the objective function at each vertex and comparing the values.

Note: Without a specific graph or additional information, it is not possible to provide the precise coordinates of the optimal solution in this case.

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The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Answer:

$ 5x

Step-by-step explanation:

Answer: 6/7 The required option is (3) 6/7

Step-by-step explanation: Explanation : A term is combination of variables and numerals by means of multiplication and division.

Answer:

y = 2/3x+1/3

Step-by-step explanation:

2x−3y+1 = 0

Solve for y

Add 3y to each side

2x−3y+1 +3y= 0+3y

2x +1 = 3y

Divide by 3

2/3 x + 1/3 =3y/3

2/3x +1/3 = y

The slope is 2/3 and the y intercept is 1/3

y = 2/3x+1/3

The x- and y-intercepts of the graph of x +6y= 10 is 10 and 5/3.

In the given question we have to find the x- and y-intercepts of the graph of x +6y= 10.

The given equation is x +6y= 10.

To find the x intercept we have to put y=o and to find the y intercept we have to put x=0.

Firstly finding the x intercept by putting y=0 in the equation.

x +6×0= 10

x+0=10

x=10

Now finding the y intercept by putting x=0 in the equation.

0 +6y= 10

6y = 10

Divide by 6 on both side

6/6 y =10/6

y=5/3

Hence, the x- and y-intercepts of the graph of x +6y= 10 is 10 and 5/3.

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Answer:

\(\frac{1}{50}\) or 0.02

Step-by-step explanation:

2% x 1 to give the answer

or

reduce it to faction like

Answer:b

Step-by-step explanation:

The simplified form of -20/2(7 2/3) is -230/3.

To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.

First, let's convert the mixed number 7 2/3 to an improper fraction.

7 2/3 = (7 * 3 + 2) / 3 = 23/3

Now, let's substitute the value back into the expression:

-20/2 * (23/3)

Next, we simplify the multiplication:

-10 * (23/3)

To multiply a fraction by a whole number, we multiply the numerator by the whole number:

-10 * 23 / 3

Now, we perform the multiplication:

-230 / 3

Therefore, the simplified form of -20/2(7 2/3) is -230/3.

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Answer:

x= - 16

Step-by-step explanation:

substitute y=0 then multuply both sides move the variable to the left and change the sign.

Answer:

taco = 1

burrito = 1.79

Step-by-step explanation:

Answer: The function h because the graphs of f and h are symmetrical about the line y=x.

Answer:

\(\huge\boxed{\sf 18^{-3}}\)

Step-by-step explanation:

\(\displaystyle \frac{18^4}{18^7}\)

So, the expression becomes:

= \(18 ^{4-7}\)

= \(18^{-3}\)

\(\rule[225]{225}{2}\)

Answer:

I think the answer is -3≤x≤∞

Step-by-step explanation:

For the given geometric sequence, we have that:

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

\(a_n = a_1q^{n-1}\)

In which \(a_1\) is the first term.

For the series given by:

8, 12, 18, 27, ...

We have that:

When a geometric series is infinite and has a common ratio greater than 1, it diverges.

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Answer:

this is pretty easy we just replace the x with -1 so

(-1)^2+(-1)9+10

-1*-1=1

-1*9=-9

1+-9=-8

-8+10=2

f(-1)=2

Hope This Helps!!!

Answer:

1: 50

2: 2.5

3: 5

1: multiply 10 by 100 and then divide the total by 5

as follows:

(10 x 100) / 5multiply 10 by 100 and then divide the total by 5 as follows:

(10 x 100) ÷5

equals 200

2: 90 is 250% of 36

3: 4: 20*100 =

(4*100): 20 =

400: 20 = 20

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

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The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

It is difficult to make a general statement about whether tennis coaches generally get paid more than football coaches in Jacksonville or elsewhere, as the salaries of coaches are influenced by a Wide range of factors

As an AI language model, I do not have access to up-to-date information about salaries of coaches in Jacksonville. However, in general, the salaries of coaches vary widely depending on a number of factors, such as the type of sport, the level of competition, the location, the success of the team, and the budget of the institution.

In terms of tennis and football, football is generally considered to be a more popular and high-profile sport than tennis in the United States, which could result in higher salaries for football coaches at the collegiate level. Football also typically generates more revenue and has larger budgets for athletic programs, which could also influence the salaries of coaches.

However, there are also factors that could affect the salaries of tennis coaches. For example, if a tennis program has a particularly successful season or has produced successful players, the coach may negotiate a higher salary. Additionally, some colleges may place a greater emphasis on tennis or have larger budgets for tennis programs, which could also impact the salaries of coaches.

Overall, it is difficult to make a general statement about whether tennis coaches generally get paid more than football coaches in Jacksonville or elsewhere, as the salaries of coaches are influenced by a wide range of factors. It is also important to note that salaries can vary widely between individual institutions, even within the same sport, and that negotiations between coaches and their institutions can play a significant role in determining salaries.

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We have

The vertical angles have equal measure, therefore:

then solve for x

So, angle A is:

Answer:

Answer:

48 pieces are cut.

Step-by-step explanation:

1/12 of an inch means that one inch would be 12 pieces. Since there are 4 pieces it would be 12x4= 48 pieces.

The option that is extraneous solution of

√-3x-2=x+2 is A. -6.

From the information given, taking square both sides

-3x - 2 = (x + 3)²

On applying identity   = a² + b² + 2ab

Then ,

-3x -2 =  x² + 2² + 2 * 2 *x

-3x -2 =  x² + 4 + 4x.

On adding both sides by 3x

-2 =  x² + 4 + 4x + 3x

-2 =  x² + 4 + 7x

On adding both sides by 2

0 =  x² + 4 + 7x + 2

On switching sides

x² +7x + 6 = 0

On Factoring

x² +6x + x + 6 = 0

x ( x+ 6 ) +1 (x +6 ) = 0

On grouping

( x +1) ( x +6) = 0

x = -1, -6.

An extraneous solution is a root of a transformed equation that is not a root of the original equation. Therefore, -6 is the extraneous solution.

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Complete question

Which of the following is an extraneous solution of sqrt(-3x-2)=x+2 a.-6 b.-1 c.1 d.6

\(\: u_{1} - u_{0}= u_{2} - u_{1} \\ - 514 + 514 = - 514 + 514 \\ 0 = 0 \\ true \: so \: u_{n} \: arithmetic \: \: (d = 0)\)

\( \frac{u_{1}}{u_{0}} = \frac{u_{2}}{u_{1}} \\ \frac{ - 514}{ - 514} = \frac{ - 514}{ - 514} \\ 1 = 1 \\ true \: so \: u_{n} \: geometric \: (r =1 )\)

\(conclusion = \\ u_{n} \: is \: both \: arithmetic \: and \: geometric\)

The tangent line at that point is:

y = (-3/25)*x + 6/5

so m = -3/25, and b = 6/5

To find the slope at that point, we need to evaluate the derivative at that point.

y = 3/x

The derivative is:

y' = -3/x²

When x = 5, we have:

y' = -3/5² = -3/25

So that is the slope, m.

Now let's find the line.

The line must pass trhough the point (5, 3/5), then:

3/5 = (-3/25)*5 + b

3/5 = -3/5 + b

3/5 + 3/5 = b

6/5 = b

The equation of the line is:

y = (-3/25)*x + 6/5

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