If a woodchuck could chuck 2
pieces of wood every hour, how big is a beavers dam?

The length of the field is greater than the width by the expression \((14x - 3x^2 + 2y) - (5x - 7x^2 + 7y).\)

1. The length of the field is represented by the expression \(14x - 3x^2 + 2y.\)

2. The width of the field is represented by the expression \(5x - 7x^2 + 7y\).

3. To find the difference between the length and width, we subtract the width from the length: (\(14x - 3x^2 + 2y) - (5x - 7x^2 + 7y\)).

4. Simplifying the expression, we remove the parentheses: \(14x - 3x^2 + 2y - 5x + 7x^2 - 7y.\)

5. Combining like terms, we group the \(x^2\) terms together and the x terms together: \(-3x^2 + 7x^2 + 14x - 5x + 2y - 7y.\)

6. Simplifying further, we add the coefficients of like terms:\((7x^2 - 3x^2) + (14x - 5x) + (2y - 7y).\)

7. The simplified expression becomes: \(4x^2 + 9x - 5y.\)

8. Therefore, the length of the field is greater than the width by the expression \(4x^2 + 9x - 5y.\)

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Answer:

\(x=33\)

Step-by-step explanation:

Since all three angles marked form one side of a line, they must add up to 180 degrees. Therefore, we have the following equation:

\(90+(x+1)+(3x-43)=180,\\x+1+3x-43=90,\\4x-42=90,\\4x=132,\\x=\boxed{33}\)

Answer:

x=33

Step-by-step explanation:

The three angles form a straight line, which is 180 degrees

90+ x+1 + 3x-43 = 180

Combine like terms

4x+48 = 180

Subtract 48 from each side

4x+48-48 = 180-48

4x = 132

Divide by 4

4x/4 = 132/4

x=33

Answer:

2 only

Step-by-step explanation:

Only even PRIME number is 2.

Why do we need EVEN PRIME numbers?

Say we do 11*5 we get 55 but when we add one we get 56

Meaning: An odd number multiplied by an odd number plus an odd number equals EVEN number which isn't PRIME. 2 being the ONLY even prime is therefore the only number we can choose.

Answer:

12

Step-by-step explanation:

Because 44 divided by 6(the number of rolls you can get) rounds to 12

The total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.

To determine the number of possible outcomes, we need to consider the number of outcomes for each event and then multiply them together.

1. Picking a marble: Let's assume there are n marbles to choose from. If there are n marbles, then the number of outcomes for this event is n.

2. Rolling a die: A standard die has 6 sides numbered 1 to 6. Therefore, the number of outcomes for this event is 6.

3. Picking a card: A standard deck of cards has 52 cards. Hence, the number of outcomes for this event is 52.

To find the total number of possible outcomes, we multiply the number of outcomes for each event together:

Total number of outcomes = (number of outcomes for picking a marble) × (number of outcomes for rolling a die) × (number of outcomes for picking a card)

Total number of outcomes = n × 6 × 52

Therefore, the total number of possible outcomes is given by the expression 6n × 52, where n represents the number of marbles to choose from.

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Answer:

There are 6 children in the group and 4 adults

Step-by-step explanation:

Because the adult ticket cost $8, so there are 4 adults and a total of $32 for adults.

Then I took 62-32=$30

$30 (total for children price) / $5 (the children's tickets) = 6 children

Answer:

The company charged $500 for its services,and Mia gives the movers a 16% tip. Now, we can add the tip amount to the cost of the service to find the total amount Mia paid: Total amount = Cost of service + Tip amount = $500 + $80 = $580

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

Here we have a dilation of scale factor 2.

We can see that bot figures we have the same slope, so we just have a dilation of scale factor K to go from figure A to figure B.

To find the value of K, notice that for some side length L in figure A, the correspondent length L' in figure B must be:

L' = K*L

Here if we use the left sides, we will get:

for figure A; L= 2

for figure B: L = 4

4 = K*2

4/2 = K

2 = K

So this is a dilation of scale factor k = 2.

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Answer:

E

Step-by-step explanation:

using the Sine rule in Δ ABC

\(\frac{a}{sinA}\) = \(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

where a is the side opposite ∠ A , b opposite ∠ B , c opposite ∠ C

we require to calculate ∠ C

∠ C = 180° - (64 + 85)° = 180° - 149° = 31°

then to find a , using

\(\frac{a}{sinA}\) = \(\frac{c}{sinC}\)

\(\frac{a}{sin64}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

a × sin31° = 9.3 × sin64° ( divide both sides by sin31° )

a = \(\frac{9.3sin64}{sin31}\) ≈ 16.23 ( to 2 decimal places )

then to find b , using

\(\frac{b}{sinB}\) = \(\frac{c}{sinC}\)

\(\frac{b}{sin85}\) = \(\frac{9.3}{sin31}\) ( cross- multiply )

b × sin31° = 9.3 × sin85° ( divide both sides by sin31° )

b = \(\frac{9.3sin85}{sin31}\) ≈ 17.99 ( to 2 decimal places )

Answer:

\(x ^{2} + 6x + 9 \\ \: = x ^{2} + (3 + 3)x \: + 9 \\ = x {}^{2} + 3x + 3x \: + 9 \\ \: \: \: \: = x(x + 3) + 3(x + 3) \\ = (x + 3) \: \: \: \: \: (x + 3)\)

So, the Answer is (x + 3) (x + 3)

The linear function that relates y to x is given as follows:

y = -0.5x + 57.

The slope indicates that the height decays 0.5 feet per minute. The y-intercept indicates that the descent starts at a cruising altitude of 57 feet.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

The coefficients m and b represent the slope and the intercept, respectively, and are explained as follows:

From the table, when x = 0, y = 57, hence the intercept b is given as follows:

b = 57.

When x increases by 10, y decays by 5, hence the slope m is given as follows:

m = -5/10

m = -0.5.

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Answer:

\(\rm( {a}^{2} - 2ab + {b}^{2} ) \: by \: ( - {a}^{2} b)\)

\( \displaystyle \rm( {a}^{2} \times - {a}^{2} b) - (2ab \times - {a}^{2} b) + ( {b}^{2} \times - {a}^{2} b)\)

\( \rm{ - {a}^{4} b} + {2a}^{3} {b}^{2} - {a}^{2} {b}^{3} \)

The circumference of a circle with one-third the curvature of a circle of radius 1 is 18.85 units

What is circumference ?

The perimeter of a circle is known as its circumference. It is the length of the circle's whole perimeter. The diameter of a circle and the constant are multiplied to get the circumference of the circle. This measurement of a circle's circumference is necessary for someone to cross a circular park or for a circle-shaped table to have a border. The units of the circumference are the same as the units of length and it is a linear value.

If a circle has a radius of 1,

the curvature is inversely proportional to this

So, the curvature= 1

A circle with a curvature of 1/3 :

radius=3

Thus, the circumference of the circle  =  2 *π * radius

                                                               =  2*π * 3

                                                               =  6π

                                                               ≈ 18.85 units

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The value of f(x) when x is 3 is 15

A Function in mathematics is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

For example, if f(x) = x² +2x +5 , the value of f(x) when x is 2 is calculated as;

f(x) = 2² + 2(2) + 5

f(x) = 4 +4+5

= 13

This done by substituting the given value of x into the expression.

Similarly , if f(x) = 5x, the value of f(x) when x is 3 is calculated as;

f(x) = 5(3)

f(x) = 15

therefore the value of f(x) when x is 3 is 15

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Answer:

See image

Step-by-step explanation:

Twice means times by 2.

Half means cut in half, in math it means times by 1/2.

See image

Factories produce a total of 21550 gallons in a calendar year.

The gallon is used as a unit of volume in both imperial and US customary measurements.

Eight pints make up a gallon, which is a unit of measurement for liquids. It is equivalent to roughly 4.546 litres in Britain. It is roughly equivalent to 3.785 litres in America.

Lemonade, it has been stated, equals 11,650 gallons.

Lemonade = 4,950 fewer than ice tea.

Ice tea: 3,500 fewer than Root beer.

Using the formula Ice tea = 11,650 - 4,950

6700 gallons of iced tea

Root beer = 6700 - 3,500

3200 gallons equals root beer.

Total manufacturing output for a year is equal to 11,650 + 6700 + 3200

Thus, 21550 gallons are produced in total by factories each year.

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Answer:

<5=39

Step-by-step explanation:

<2=48

<3=93

<2 and <4 are equal to each other because they are alternate interior angles

93+48=141

180-141=39

Answer:

∠5 = 39º

Step-by-step explanation:

∠1 + ∠2 + ∠3 = 180

∠1 + 48 + 93 = 180

∠1 = 180 - 48 - 93

∠1 = 39

Corresponding angles are congruent

∠5 = ∠1

∠5 = 39º

FIFO - March cost of goods sold = $13,050. March 31 inventory = $7,350. LIFO - March cost of goods sold = $14,600. March 31 inventory = $5,800.

To calculate March cost of goods sold we need to add the given data for FIFO =

March cost of goods sold

= (2,800 + 3,700 + 6,550)

= 13,050

To calculate March cost of goods sold we need to add the given data for LIFO =

March cost of goods sold

= (3,400 + 4,400 + 6,800)

= 5,800

Sales data refers to the information collected and recorded about the transactions that occur when a business sells products or services to customers. This data typically includes details such as the date and time of the sale, the products or services sold, the quantity sold, the price paid, and the customer's information. Sales data is crucial for businesses as it helps them understand their sales performance, identify trends and patterns and make informed decisions about their pricing, marketing and inventory management strategies.

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Answer:

AC = 7.29 in

AB = 11.58 in

Step-by-step explanation:

tan 51 = 9/AC

1.2349 = 9/AC

AC = 7.29 in

sin 51 = 9/AB

0.7771 = 9/AB

AB = 11.58 in

Answer:

x + 2y = 6

2y = -x -6

y = - 1/2 x - 3

From the equation, the y intercept is -3

Put y = 0,

-1/2 x -3 = 0

-1/2 x = 3

x = -6

Therefore, x intercept = -6

The new coordinates of the reflected point will be (2, 2).

In mathematics, reflection is a transformation that "flips" an object over a line or plane. Reflection is a type of symmetry, where an object appears exactly the same after being reflected as it did before.  

When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same.  

Here we have

The point (-2, 2) is reflected across the y-axis

When a point is reflected across the y-axis, its x-coordinate changes sign while its y-coordinate remains the same.

The new coordinate of the point = (-(-2), 2) = (2, 2)

Therefore,

The new coordinates of the reflected point will be (2, 2).

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The obtained answers for the given line segments are as follows:

9. The value of the line segment \(\overline {DE}\) = 43; Where \(\overline { DF}\) = 61 and \(\overline {EF}\)

10. The value of x is 6; Where \(\overline {DE}\) = 4x - 1, \(\overline {EF}\) = 9, and \(\overline { DF}\) = 9x - 22

11. The value of line segment \(\overline {EF}\) = 32; Where  \(\overline { DF}\) = 78, \(\overline {DE}\) = 5x - 9, and \(\overline {EF}\) = 2x + 10

12. The value of line segment \(\overline { DF}\) = 57; Where \(\overline {DE}\)  = 4x + 10 \(\overline {EF}\) = 2x - 1, and \(\overline { DF}\) = 9x - 15.

The calculation for the required values is as follows:

9. Finding \(\overline{DE}\):

It is given that,

\(\overline{DF}\) = 61; \(\overline{EF}\) = 18

From the figure, we can write

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting the given values,

61 = \(\overline{DE}\) + 18

⇒ \(\overline{DE}\) = 61 - 18

∴ \(\overline{DE}\) = 43

10. Finding x:

It is given that,

\(\overline {DE}\) = 4x - 1, \(\overline {EF}\) = 9, and \(\overline { DF}\) = 9x - 22

From the figure we have

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting,

(9x - 22) = (4x - 1) + 9

⇒ 9x - 22 = 4x - 1 + 9

⇒ 9x - 4x = 8 + 22

⇒ 5x = 30

∴ x = 6

11. Finding \(\overline{EF}\):

It is given that,

\(\overline { DF}\) = 78, \(\overline {DE}\) = 5x - 9, and \(\overline {EF}\) = 2x + 10

From the figure we have

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting,

78 = (5x - 9) + (2x + 10)

⇒ 78 = 5x - 9 + 2x + 10

⇒ 7x + 1 = 78

⇒ 7x = 78 - 1

⇒ 7x = 77

∴ x = 11

On substituting x = 11 in \(\overline {EF}\) = 2x + 10; we get

\(\overline {EF}\) = 2(11) + 10

      = 22 + 10

      = 32

Therefore, the value of the line segment \(\overline {EF}\) is 32.

12. Finding \(\overline {DF}\):

It is given that,

\(\overline {DE}\)  = 4x + 10 \(\overline {EF}\) = 2x - 1, and \(\overline { DF}\) = 9x - 15

From the figure we have

\(\overline{DF} = \overline{DE} + \overline{EF}\)

On substituting,

(9x - 15) = (4x + 10) + (2x - 1)

⇒ 9x - 15 = 4x + 10 + 2x - 1

⇒ 9x - 15 = 6x + 9

⇒ 9x - 6x = 9 + 15

⇒ 3x = 24

∴ x = 8

On substituting x = 8 in \(\overline { DF}\) = 9x - 15; we get

\(\overline { DF}\) = 9(8) - 15

      = 72 - 15

      = 57

Therefore, the value of the line segment \(\overline { DF}\) is 57.

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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:

\(x > 1\)

if you graph

\(f(x) = x + 1\)

you'll see that it's that part of graph from x=1 to right and x=1 on this graph is not ncluded so it's x>1

Angle ∠EBD is congruent to angle ∠DBA. Option D is the true statement.

An angle bisector is the line segment that bisects the angle into two equal halves.

Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.

Here,

Ray BE is a bisector of angle CBA,

∠CBE = ∠EBA = 60°

∠EBD = ∠EBA - ∠DBA

∠EBD = 60 - 30 = 30

So,

∠EBD = ∠DBA [DB becomes angle bisector of angle EBA]

Thus, ∠EBD is congruent with ∠DBA is the only correct answer among the option.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Which of the following statements is true if ray BE is a bisector of angle CBA?

A. Ray BD is a bisector of angle CBA.

B. ∠EBD is congruent to ∠CBE.

C. Ray BE is a bisector of angle ABE.

D. ∠EBD is congruent to ∠DBA.

Answer:

f(x) = 1/x

Step-by-step explanation:

h(x) = f(g(x)) = f(x-6) = 1/x-6

1/x-6 could only be accomplished if f(x) = 1/x

Assuming f(x) = 1/x and g(x) = x-6, f(g(x)) = f(x-6) = 1/x-6

Since f(g(x)) = 1/x-6 = h(x), we've proven that f(x) = 1/x.

The given functions are illustrations of a composite function, where the function f(x) is:

\(f(x) = \frac{1}{x}\)

Given that:

\(h(x) = \frac{1}{x - 6}\)

\(g(x) = x - 6\)

f o g can be written as f(g(x))

So, we have:

\(h(x) = f(g(x))\)

Rewrite as:

\(f(g(x)) = \frac{1 }{x - 6}\)

Substitute g(x) for x - 6

\(f(g(x)) = \frac{1 }{g(x)}\)

Replace g(x) with x

\(f(x) = \frac{1}{x}\)

Hence, the function f(x) is: \(f(x) = \frac{1}{x}\)

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Answer:

B,

Step-by-step explanation:

y - 7 = 3(x - 5)

y - 7 = 3x - 15

y = 3x - 8

answer is B

Answer:

y = 4x -13

y = 4x -13Step-by-step explanation:

y= mx + b

y= mx + b m is the Slope

y= mx + b m is the Slopem = 4

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = b

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = bThe line in slope intercept form is

y= mx + b m is the Slopem = 4Now just plug in the coordinates (5, 7) from above to solve for b7 = 4(5) + b7 = 20 + bSubtract 20 from both sides of the equation7- 20 = b-13 = bThe line in slope intercept form isy = 4x -13