Function A is represented by the equation y= 6x-1.
Function B is a linear function that goes through the points shown in the
table.
x 13 4 6
y 0 10 15 25
Which statement correctly compares the rates of change of the two
functions?
A. The rate of change of function A is 6.
The rate of change of function B is 5.
B. The rate of change of function A is 6.
The rate of change of function B is 10.
C. The rate of change of function A is
-1.
The rate of change of function B is 5.
D. The rate of change of function A is
-1.
The rate of change of function B is 10.

The net cash flow from operating activities would be $100,800.

Change in accounts receivable:

= $20,900 - $20,000

= $900

Change in inventory:

= $61,800 - $62,500

= -$700

Change in accounts payable:

= $19,700 - $18,600

= $1,100

Change in dividends payable:

= $24,000 - $22,000

= $2,000

Change in operating assets and liabilities:

= Change in accounts receivable + Change in inventory - Change in accounts payable - Change in dividends payable

= $900 + (-$700) + $1,100 + $2,000

= $2,300

Net cash flow from operating activities:

= Net income + Change in operating assets and liabilities

= $98,500 + $2,300

= $100,800.

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The expression you provided appears to be an integral with multiple terms involving logarithmic and trigonometric functions. To solve it, we need to break it down and evaluate each term separately.

Let's examine each term in the given expression:The integral of 1 with respect to x is simply x.The integral of 1/x is ln|x|.

The integral of tan(x) can be evaluated using a substitution or integration by parts technique, depending on the specific limits of integration or any additional context provided.

Without specific limits or further instructions, it's challenging to provide a precise solution or simplify the expression further. However, if you provide more information or clarify the problem statement, I can help you with a more detailed solution.

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The length of the shortest path ABCD is 7 units.

To find the length of the shortest path ABCD, we need to determine the coordinates of points B and C and then calculate the distances between these points.

Given that B has a y-coordinate of 2, it lies on a horizontal line. Therefore, the y-coordinate of B is 2, and the x-coordinate is the same as the x-coordinate of point A, which is 7. So, B is the point (7, 2).

Similarly, C lies on a vertical line, and its x-coordinate is the same as the x-coordinate of point D, which is -5. So, C is the point (-5, 0).

Now, we can calculate the distances between the points. The distance between A and B can be found using the distance formula:

AB = √[tex]((x2 - x1)^2 + (y2 - y1)^2[/tex])

Substituting the coordinates of A and B, we have:

AB = √[tex]((7 - 7)^2 + (2 - 4)^2) = √(0^2 + (-2)^2[/tex]) = √4 = 2

The distance between B and C is simply the difference in their y-coordinates:

BC = |y2 - y1| = |2 - 0| = 2

Finally, the distance between C and D can be calculated using the distance formula:

CD = √[tex]((-5 - (-5))^2 + (0 - (-3))^2)[/tex] = √[tex](0^2 + 3^2)[/tex] = √9 = 3

Therefore, the length of the shortest path ABCD is the sum of the distances AB, BC, and CD:

Shortest path ABCD = AB + BC + CD = 2 + 2 + 3 = 7

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It will take approximately 5.33 minutes for Jeff to catch up to Roger. Both Jeff and Roger will have run a distance of 1 mile.

Let's calculate the time it takes for Jeff to catch up to Roger and the distance each will have run.

First, we need to determine how much distance Roger covers during the 1-minute head start. Since Roger runs one mile in 9 minutes, in 1 minute, he would cover 1/9 of a mile.

Now, let's set up an equation to represent the time it takes for Jeff to catch up to Roger:

Distance covered by Jeff = Distance covered by Roger + Distance covered during the head start

Let's denote the time it takes for Jeff to catch up as t minutes. During this time, Jeff runs a distance of 1 mile, while Roger runs a distance of 1/9 of a mile (from the head start).

Distance covered by Jeff = Distance covered by Roger + Distance covered during the head start

1 mile = (1/9) mile + (6 minutes) × t × (1 mile/6 minutes)

Now, let's solve this equation to find the time it takes for Jeff to catch up:

1 = (1/9) + (1/6)t

Multiplying the equation by the least common multiple (LCM) of 9 and 6, which is 18, to clear the fractions:

18 = 2 + 3t

Subtracting 2 from both sides:

16 = 3t

Dividing by 3:

t = 16/3 = 5.33 minutes (rounded to two decimal places)

Therefore, it will take approximately 5.33 minutes for Jeff to catch up to Roger. Both Jeff and Roger will have run a distance of 1 mile.

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The table of values for the equation y = 3/x can be completed as follows:

x | y

1 | 3/1 = 3

2 | 3/2 = 1.5

3 | 3/3 = 1

4 | 3/4 = 0.75

5 | 3/5 = 0.6

To complete the table of values for the equation y = 3/x, we substitute different values of x into the equation and calculate the corresponding values of y.

When x = 1:

Substitute x = 1 into the equation: y = 3/1 = 3

So, when x = 1, y = 3.

When x = 2:

Substitute x = 2 into the equation: y = 3/2 = 1.5

So, when x = 2, y = 1.5.

When x = 3:

Substitute x = 3 into the equation: y = 3/3 = 1

So, when x = 3, y = 1.

When x = 4:

Substitute x = 4 into the equation: y = 3/4 = 0.75

So, when x = 4, y = 0.75.

When x = 5:

Substitute x = 5 into the equation: y = 3/5 = 0.6

So, when x = 5, y = 0.6.

By substituting different values of x into the equation y = 3/x, we can complete the table of values as shown above.

Hence, the completed table of values for y = 3/x is:

x | y

1 | 3

2 | 1.5

3 | 1

4 | 0.75

5 | 0.6

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Answer:

9

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

the diagonal AC divides the rectangle into 2 right triangles.

Consider the right triangle ABC with legs AB , BC and hypotenuse AC

using Pythagoras' identity in right triangle ABC

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

AB² + BC² = AC² ( substitute values )

x² + (x + 2)² = (x + 4)² ← expand factors using FOIL

x² + x² + 4x + 4 = x² + 8x + 16

2x² + 4x + 4 = x² + 8x + 16 ( subtract x² + 8x + 16 from both sides )

x² - 4x - 12 = 0 ← in standard form

(x - 6)(x + 2) = 0 ← in factored form

equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 2 = 0 ⇒ x = - 2

however , x > 0 , then x = 6

The given statement proposition is a that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.

The given statement is a logical proposition involving the concept of induction. Let's break it down and analyze its components.

"If x is inductive..."

This implies that x is a concept or object that possesses the property of being inductive. In mathematics, the term "inductive" typically refers to the property of being a natural number or belonging to the set of natural numbers.

"...then so is (x ∈ X : x = Ф or x = y ∪ {y} for some y)"

Here, we have a set X that consists of elements satisfying a certain condition. The condition states that an element x in X can either be equal to the empty set (Ф) or the union of a set y with itself ({y}). This construction represents a recursive definition, where each element in X is defined in terms of a base case (Ф) and a recursive step ({y}).

"...hence each n ≠ 0 is m + 1 for some m."

This conclusion states that for every natural number n that is not equal to 0, there exists another natural number m such that n can be expressed as m + 1. In other words, any non-zero natural number is the successor of some other natural number.

Overall, the given statement is a proposition that suggests that if x is an inductive element, defined in terms of the set X as described, then it follows that every non-zero natural number can be expressed as the successor of some other natural number.

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The calculated value o x in the circle is 7

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

The circle

The value of x can be calculated using teh equation of the intersection of chords

So, we have

122 = 1/2(6x + 8 + 194)

Evaluate

244 = 6x + 202

So, we have

6x = 42

Divide by 6

x = 7

Hence, the solution for x is 7

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The system B is gotten from system A by operation (d)

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

x + y = 8

4x - 6y = 2

Also, we have the solution to be (5, 3)

Recall that

x + y = 8

4x - 6y = 2

Multiply the first equation by 6

So, we have

6x + 6y = 48

4x - 6y = 2

Add the equations

10x = 50

This means that the system B from system A is (d)

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The function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

To complete the square for the function g(x) = 4x² - 28x + 49, we follow these steps:

Step 1: Divide the coefficient of x by 2 and square the result.

  (Coefficient of x) / 2 = -28/2 = -14

  (-14)² = 196

Step 2: Add and subtract the value obtained in Step 1 inside the parentheses.

  g(x) = 4x² - 28x + 49

  = 4x² - 28x + 196 - 196 + 49

Step 3: Rearrange the terms and factor the perfect square trinomial.

  g(x) = (4x² - 28x + 196) - 196 + 49

  = 4(x² - 7x + 49) - 147

  = 4(x² - 7x + 49) - 147

Step 4: Write the perfect square trinomial as the square of a binomial.

  g(x) = 4(x - 7/2)² - 147

Therefore, the function g(x) = 4x² - 28x + 49 can be rewritten as g(x) = 4(x - 7/2)² - 147 after completing the square.

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The probable question may be:

Rewrite the function by completing the square.

g(x)=4x²-28x +49

g(x)= ____  (x+___ )²+____.

To find the volume of the given cylinder, we need to use the formula of volume of a cylinder which is given by V = πr²h, where V is the volume of the cylinder, r is the radius of the cylinder and h is the height of the cylinder. So, the volume is 1078.1 cubic units.

Given, Length = 14 units, Height = 11 units. Now, we know that the formula for the volume of a cylinder is given as; V = πr²h.

Here, the radius of the cylinder is half the length of the cylinder, which is; Radius = Length/2

Radius = 14/2

Radius = 7 units

Substituting the value of the radius and height, we have; V = π(7)²(11)

V = 1078.1 cubic units. Therefore, the volume of the cylinder is 1078.1 cubic units. Rounded off to one decimal place, the volume is 1078.1 cubic units.

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Answer:

A requested task is subject to be reported when it has been completed according to the instructions provided.

To demonstrate this with chain of thought reasoning:

1. The task requested will have details outlining what needs to be done.

2. To fulfill the request of the task, the instructions outlined must be followed.

3. Once all instructions are met, the task is complete.

4. Completion of the task means it is subject to be reported.

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

(|7 − 3 x 5| ÷ 4)³ + √64

(|7 − 3 x 5| ÷ 4)³ + √64

(|7 − 15| ÷ 4)³ + √64

(|7 − 15| ÷ 4)³ + √64

(8 ÷ 4)³ + √64

(8 ÷ 4)³ + √64

2³ + √64

8 + 8

16

Answer:

16

Step-by-step explanation:

To solve, use PEMDAS as it applies to the expression.

First, you must carry out what is in the parenthesis.

Multiply (3*5 = 15), then subtract (7 - 15 = -8). The two little vertical lines surrounding (7 - 3 x 5) mean absolute value. This means that you will write -8 as +8.

Continuing on in the parenthesis, carry out (8 ÷ 4 = 2).

Next, we must do exponents.

We see that everything in the parenthesis is being raised to the power of three (cubed). Since we've solved what was in the parenthesis, we simply need to carry out ([tex]2^{3}[/tex] = 8).

Now, we need to quickly carry out [tex]\sqrt{64}[/tex]. Square roots are just whatever number can be multiplied by itself to get, in this case, 64.

[tex]\sqrt{64} = 8[/tex].

Finally, we must add what remains.

8 + 8 = 16.

So, (|7 - 3 x 5) | ÷ [tex]4)^{3}[/tex] + [tex]\sqrt{64}[/tex] = 16.

The correct solutions to the quadratic equation are:

c. -8

e. 2

To determine the solutions to the quadratic equation 2x^2 + 6x - 10 = x^2 + 6, we need to solve for x.

First, let's simplify the equation by combining like terms:

2x^2 + 6x - 10 - x^2 - 6 = 0

x^2 + 6x - 16 = 0

Now, we can solve this quadratic equation by factoring or by using the quadratic formula.

By factoring:

(x + 8)(x - 2) = 0

Setting each factor equal to zero, we get:

x + 8 = 0 --> x = -8

x - 2 = 0 --> x = 2

So, the solutions to the quadratic equation are x = -8 and x = 2.

Now, let's check the given options:

a. -2: This value is not a solution to the equation.

b. 1/3: This value is not a solution to the equation.

c. -8: This value is a solution to the equation.

d. -1/2: This value is not a solution to the equation.

e. 2: This value is a solution to the equation.

f. 8: This value is not a solution to the equation.

The following are the proper answers to the quadratic equation: c. -8 e.2

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Answer:

718000

Step-by-step explanation:

718000 is already in standard form

The statement that is correct about the dot plots is that:

A) The distribution for Class M is approximately symmetric

A symmetric distribution in dot plots is defined as a distribution with a vertical line of symmetry in the center of the graphical representation, so that the mean is equal to the median.

A symmetric distribution is one that occurs when the values ​​of a variable occur at regular frequencies, and often the mean, median, and mode all occur at the same point. If we draw a line through the middle of the chart, we can see that the two planes mirror each other.  

Now, from the given two dot plots of class M and Class N, it is very clear that class M is very close to being symmetric about the data value 3.

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Answer:

Step-by-step explanation:

x-intercept is where the line cuts the x-axis. That is, when y=0.

Substitute y=0 and we get:

       [tex]0=\frac{1}{3} x-1[/tex]

       [tex]1=\frac{1}{3} x[/tex]

       [tex]x=3[/tex]

So x-intercept is the point (3,0).

The probability that the dial stops on yellow is 2/5 or 0.4 (or 40%).

Therefore, there is a 40% chance that the spinner will stop on yellow.

To find the probability that the spinner stops on yellow, we need to determine the number of favorable outcomes (yellow) and the total number of possible outcomes.

The spinner has 10 equally sized slices, with 4 yellow, 4 red, and 2 blue.

The number of favorable outcomes (yellow) is 4 because there are 4 yellow slices.

The total number of possible outcomes is 10 because there are 10 slices in total.

Therefore, the probability of the spinner stopping on yellow can be calculated as:

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = 4 / 10

Simplifying this fraction, we get:

Probability = 2 / 5

So, the probability that the dial stops on yellow is 2/5 or 0.4 (or 40%).

Therefore, there is a 40% chance that the spinner will stop on yellow.

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Answer:

A= 220.5ft

B= $2425.5

Step-by-step explanation:

A= 220.5ft

B= $2425.5

Answer:

A

Step-by-step explanation:

For a table of values to be a function, all inputs must have one unique output. The only table that doesn't violate this is table A.

Notice that while two different inputs (-4 and 1) have the same output of 7, it is still a function because both outputs of 7 are associated with two different inputs.

The corresponding sides and angles of the similar and congruent triangles indicates that we get the following approximate and exact values;

Page 1;

5. [tex]\overleftrightarrow{AC}[/tex] = 4.3. 6. [tex]\overline{BP}[/tex] ≈ 7.5 7. [tex]\overline{YV}[/tex] ≈ 8

Page 2

5. [tex]\overline{DF}[/tex] = [tex]11\frac{1}{4}[/tex], 6. [tex]\overline{ED}[/tex] = 5, 7. [tex]\overline{BC}[/tex] = 22, 8. [tex]\overline{EF}[/tex] = 8

Page 3;

8. m∠ABC = 30°, 9. m∠XYP = 44°, 10. [tex]\overline{AC}[/tex] = 14

Congruent triangles are triangles that have all three corresponding sides of the same length and all three angles of the same measure.

First Page

5. The distance from the vertex B to the line segment [tex]\overleftrightarrow{AC}[/tex] in the triangle ΔABC is the altitude of the triangle, which is 4.3

6. The distance from the vertex B to [tex]\overleftrightarrow{AC}[/tex] = [tex]\overline{BP}[/tex]

Pythagorean theorem indicates that the length of the segment [tex]\overline{BP}[/tex] can be found as follows;

[tex]\overline{BP}[/tex] = √(13.5² - 11.2²) ≈ 7.5

7. The distance from Y to  [tex]\overleftrightarrow{XZ}[/tex] is the altitude of the triangle ΔXYZ, which indicates;

The distance from Y to  [tex]\overleftrightarrow{XZ}[/tex] = [tex]\overline{YV}[/tex]

The Pythagorean theorem indicates that we get;

[tex]\overline{YV}[/tex] = √(13.34² - 10.67²) ≈ 8

Second page;

5. The scale factor from ΔABC to ΔDEF = 3/4

Therefore, the length of [tex]\overline{DF}[/tex] = (3/4) × 15 = 45/4 = [tex]11\frac{1}{4}[/tex]

6. The scale factor of (1/3) indicates that we get;

[tex]\overline{ED}[/tex] = (1/2) × 10 = 5

7. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 18/9 = 10/5 = 2

The corresponding side to [tex]\overline{BC}[/tex] is [tex]\overline{EF}[/tex]

[tex]\overline{EF}[/tex] = 11, therefore, the length of [tex]\overline{BC}[/tex] = 2 × 11 = 22

8. The ratio of the corresponding sides by length which is the scale factor is; S.F. = 4/6 = 10/15 = 2/3

The corresponding side to [tex]\overline{EF}[/tex] is [tex]\overline{BC}[/tex]

[tex]\overline{BC}[/tex] = 12, therefore [tex]\overline{EF}[/tex] = (2/3) × 12 = 8

Third page;

8. The triangles ΔABV and ΔCVB are congruent triangles by the Leg Hypotenuse congruence theorem.

The angles ∠ABV and ∠CBV are corresponding triangles, therefore;

∠ABV ≅ ∠CBV

m∠CVB = m∠ABV = 15° (Definition of congruent triangles and symmetric and substitution property)

∠ABC = ∠ABV + ∠CBV

Therefore; m∠ABC = 15° + 15° = 30°

9. The angles ∠YXP and ∠YZP are right triangles, therefore;

m∠YXP = m∠YZP = 90°

The right triangles  ΔYXP and ΔYZP are congruent by the LH congruence theorem

∠XYP ≅ ∠ZYP (Corresponding Parts of Congruent Triangles are Congruent, CPCTC)

m∠XYP = m∠ZYP (Definition of congruent triangles)

m∠XYZ = m∠XYP + m∠ZYP (Angle addition property)

m∠XYZ = 2 × m∠XYP

2 × m∠XYP = m∠XYZ = 88°

m∠XYP = 88°/2 = 44°

10. The angles ∠ACP and ∠ABP are right angles, according to the indicated markings, therefore;

∠ACP ≅ ∠ABP (All right angles are congruent)

ΔACP ≅ ΔABP by SAA congruence theorem

[tex]\overline{AC}[/tex] ≅ [tex]\overline{AB}[/tex] (CPCTC)

[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] (Definition of congruent segments)

[tex]\overline{AC}[/tex] = [tex]\overline{AB}[/tex] = 14

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Answer:

[tex]y = |x - 2| + 3[/tex]

The correct answer is C.

Answer:

a

Step-by-step explanation:

Answer:

f(2.5) = 100

Step-by-step explanation:

to evaluate f(2.5) substitute x = 2.5 into f(x)

f(2.5) = 16(2.5)² = 16 × 6.25 = 100

The solution to the system is (a) a = 4/5, b = 5, c = -4 and d =-4

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

The augmented matrix

Where, we have

[tex]\left[\begin{array}{cccc|c}1&0&0&0&4/5\\0&1&0&0&5\\0&0&1&0&-4\\0&0&0&1&-4\end{array}\right][/tex]

From the above, we have the diagonals to be 1

And other elements to be 0

This means that the equation has been solved

So, we have

a = 4/5, b = 5, c = -4 and d =-4

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The correct answer is:  A. Yes; each input pairs with only one output.

To determine whether the given mapping diagram represents a function, we need to analyze the relationship between the input values (x) and the corresponding output values (y).

Looking at the mapping diagram, we can see that the input value -5 is paired with the output value 8. This implies that when x = -5, the corresponding y value is 8. Similarly, when x = 9, the corresponding y value is -8.

Since each input value has a unique and specific output value, we can conclude that the mapping diagram represents a function. In other words, for every input value, there is only one output value associated with it.

This is consistent with the definition of a function, where each input has a single and distinct output. Therefore, the mapping diagram satisfies the criteria for a function, and the correct answer is:

A. Yes; each input pairs with only one output.

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The mapping diagram does not represent a function that reflects this is: No; each output value pairs with two input values. D.

To determine whether the mapping diagram represents a function, we need to assess whether each input value pairs with only one output value.

Looking at the given mapping diagram:

-5 -> 8

9 -> y

-8 -> y

We can see that the input value -5 maps to the output value 8.

There are two different input values, 9 and -8, that map to the same output value, y.

In a function, each input should correspond to exactly one output, but in this case, the output value y is associated with two different input values.

In this case, y, the output value, pairs with both 9 and -8, indicating that the diagram does not meet the criteria for a function.

We must examine if each input value couples with only one output value in order to evaluate whether the mapping diagram reflects a function.

Observing the provided mapping diagram:

-5 -> 8 9 -> y -8 -> y

As can be seen, the input value of -5 corresponds to the output value of 8.

The identical output value, y, is mapped to two distinct input values, 9 and -8.

A function should have only one output for each input, however in this situation, the output value y is connected to two separate input values.

This figure does not fit the definition of a function because the output value, y, couples with both 9 and -8.

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Answer:

The correct answer is a.

Step-by-step explanation:

The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.