Part II: Find a Pattern.
Use the terms from Part I to answer each question.
• What is a proof? (1 point)
.
• You want to prove a theorem in a two-column proof. You start with your given statement and
list deductions in the left-hand column. What are the three main types of reasoning you will use
for reasons in the right-hand column? (3 points; 1 point each)
1.
2.

Answer:

Angle L

Step-by-step explanation:

Angle L is the obtuse angle, as it is the only angle with a measure greater than 90 degrees.

The restaurant chef made 4 2/3 pints of mushroom soup and each bowl can hold 2/3 of a pint.

To determine how many bowls of soup the chef will be able to fill, we need to find the quotient of the total amount of soup divided by the amount in each bowl.

First, let's convert the mixed number 4 2/3 to an improper fraction. Multiplying the whole number (4) by the denominator (3) and adding the numerator (2) gives us 14/3.

Now, we can divide the total amount of soup (14/3 pints) by the amount in each bowl (2/3 pint).

We divide a fraction by another fraction, we invert the second fraction and multiply.

We have:

(14/3) ÷ (2/3) = (14/3) × (3/2)

Canceling out the common factor of 3 in the numerators and denominators, we get:

(14/1) × (1/2) = 14/2

= 7

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The value of x in the triangle is 20 units.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

Using triangle proportional theorem, If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

Hence,

11 / 121 = 10 / 5x + 10

cross multiply

11(5x + 10) = 1210

55x + 110 = 1210

55x = 1210 - 110

55x = 1100

divide both sides of the equation by 55

x = 1100 / 55

x = 20

Therefore,

x = 20

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The coterminal angle of 31π/6 is angle of 210 degrees.

To find a coterminal angle, we can add or subtract a full revolution (2π) or any multiple of it.

Let's calculate the coterminal angle:

31π/6 = (30π/6) + (π/6) = 5π + π/6

To simplify the angle, we can express it in terms of a common denominator:

5π + π/6 -2π

3π+ π/6

19π/6

570 degrees.

The other coterminal angle is 210 degrees which lies in the third quadrant.

Therefore, the coterminal angle of 31π/6 is  210 degrees.

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The scale factor that is used to perform the dilation is 3/2

Dilation is a transformation, which is used to resize the object.

Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape.

Scale factor is the ratio of the dimension of the new imaged formed to the dimensions of old dimension.

The base of the original triangle is 4 units

The base of the new length = 6 units

Scale factor = 6/4

= 3/2

Therefore the scale factor in the dilation is 3/2.

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A number repeated as a term three times can be expressed as a sequence or as a repeated multiplication.

A number repeated as a term three times means that the same number is used three times in a row. It can be expressed as a sequence or as a repeated multiplication.

For example, if the number is 5, the expression "5, 5, 5" represents the number 5 repeated three times in a sequence. It indicates that the number 5 is repeated consecutively as three separate terms.

Alternatively, the repeated multiplication of the number can also represent the concept. In this case, "5 x 5 x 5" would be equal to 125, which means that the number 5 is multiplied by itself three times.

In both cases, the idea is that the number is used three times in succession, either as a sequence or through multiplication, resulting in a repeated representation of the number.

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The inequality graphed on the number line can be written as:

-3 ≤ x < 2

Here we can see an inequality graphed on a number line, we can see that we start with a closed circle at x = -3

A closed circle means that x = -3 is a solution.

And we can see that it ends with an open circle at x = 2, the open circle means that the point is not a solution.

Then the inequality thati is shown in the number line is written as:

-3 ≤ x < 2

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To find the endpoint coordinates for the midsegment of ABCD that is parallel to BC, we need to determine the midpoints of the corresponding sides.

Let's start by finding the midpoint of BC. The coordinates of B are (-5, 4) and the coordinates of C are (2, 3). To find the midpoint, we average the x-coordinates and the y-coordinates separately:

Midpoint of BC:

x-coordinate: (-5 + 2) / 2 = -3/2 = -1.5

y-coordinate: (4 + 3) / 2 = 7/2 = 3.5

So, the midpoint of BC is (-1.5, 3.5).

Now let's find the midpoint of AD. The coordinates of A are (-4, 6) and the coordinates of D are (8, 9).

Midpoint of AD:

x-coordinate: (-4 + 8) / 2 = 4 / 2 = 2

y-coordinate: (6 + 9) / 2 = 15 / 2 = 7.5

So, the midpoint of AD is (2, 7.5).

Therefore, the endpoints of the midsegment of ABCD that is parallel to BC are (-1.5, 3.5) and (2, 7.5).

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The volume of the man when using a cylinder to approximate the mans shape is  1222110 cm³.

A 188 cm tall man has a waistline of 91cm. Therefore, the measure that best  approximates the volume of the man when using a cylinder to approximate the man's shape can be calculated as follows:

Modelling the mans shape to a cylinder,

volume of the cylinder = πr²h

where

r = 91 / 2 = 45.5 cm

h = 188 cm

Therefore,

volume of the cylinder = 3.14 × 45.5² × 188

volume of the cylinder = 3.14 × 2070.25 × 188

volume of the cylinder = 1222109.98

volume of the cylinder = 1222110 cm³

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The expression [tex]\frac{x^2 - 2x - 24}{x^2 + 7x + 12} * \frac{x^2 - 1}{x-6}[/tex] when simplified is [tex]\frac{x^2 - 1}{x + 3}[/tex]

From the question, we have the following expression

[tex]\frac{x^2 - 2x - 24}{x^2 + 7x + 12} * \frac{x^2 - 1}{x-6}[/tex]

When the factors of the expression are factorized, we have

[tex]\frac{(x + 4)(x - 6)}{(x + 4)(x + 3)} * \frac{(x - 1)(x + 1)}{x-6}[/tex]

Cancel out the common factors

So, we have

[tex]\frac{1}{(x + 3)} * \frac{(x - 1)(x + 1)}{1}[/tex]

Evaluate the products

[tex]\frac{x^2 - 1}{x + 3}[/tex]

Hence, the expression when simplified is [tex]\frac{x^2 - 1}{x + 3}[/tex]

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The Factorization of the given expression gives:

(1/27) (9x - 7)³  

Factorization is the process of finding factors which when multiplied together results in the original number or expression.

We have:

27x³ - 63x² + 49x - 343/27

Step 1:

Factor out (1/27)  from the expression

= (1/27) { 27 · 27 x³ - 27· 63x² + 27· 49x - 343)

= (1/27) { 729 x³ - 1701x² + 1323x - 343)

Step 2:

Rewrite terms in the expression

= (1/27) { 9³ x³ - 3·7·9²x² + 3·7²·9x - 7³ }

= (1/27) { (9x)³ - 3(9x)²7 + 3(9x)7² - 7³}

Step 3:

Use (a - b)³ = a³ - 3a²b + 3ab² - b³   where a = 9x , b = 7

= (1/27) { 9³ x³ - 3.7.9²x² + 3.7².9x - 7³ }

= (1/27)   (9x - 7)³  

Thus,

27x³ - 63x² + 49x - 343/27 = (1/27)   (9x - 7)³  

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Recording the required adjusting entries related to the balances and events of the select accounts is as sfollows:

Debit Supplies Expense $3,340

Credit Supplies $3,340

(To record supplies expense for the period.)

Debit Rent Expense $40

Credit Prepaid Rent $40

(To record rent expense for the period.)

Debit Uneared Service Revenue $4,100

Credit Service Revenue $4,100

(To record earned service revenue.)

Adjusting entries are period-end records in the general journal that recognize income and expenses for the period that do not have cash effects.

Some of the adjusting entries include accrued revenues, accrued expenses, unearned revenues, prepaid expenses, and depreciation expenses.

Supplies Expense $3,340 Supplies $3,340 ($4,300 - $960)

Rent Expense $40 Prepaid Rent $40

Uneared Service Revenue $4,100 Service Revenue $4,100

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No, The given question ''How many pounds are in one kilogram?'' is not a statistical question.

We have to given that,

The question is,

''How many pounds are in one kilogram?''

Since, We know that,

The given question is a straightforward conversion that can be answered with a simple fact or formula.

And, A statistical question is one that seeks to collect and analyze data in order to make inferences and conclusions about a population or sample.

Hence, The given question is not a statistical question.

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The graph of given quadratic function is plotted below.

Graph the parabola using its properties and the selected points.

Direction: Opens Down

Vertex: (2.80612244,46.38418367)

Focus: (2.80612244,46.33316326)

Axis of Symmetry: x=2.80612244

Directrix: y=46.43520408

Use the formula x=−b/2a to find the maximum and minimum.(2.80612244,46.38418367)

Therefore, the graph of given quadratic function is plotted below.

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In the 3 group Venn Diagram with Roman numeral labeled regions

A ∪ B ∪ C = V: Items in A, B, and C. Region

The union of sets refers to the operation of combining or merging two or more sets to create a new  set that contains all the distinct elements from the original sets.

It is denoted by the symbol "∪"

when you take the union of two sets A and B and C, the resulting set, denoted as A ∪ B ∪ C, consists of all the elements that are present in either set A or set B or set C, or in the three sets.

hence the right choice is V: Items in A, B, and C. Region

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The area of the circle created by the paint is given by the expression 4πt².

The area of the circle is 100π, which is approximately 314.16 in².

The circle will be at least 300 in² in 5 minutes. Yes.

To find the area of the canvas, we multiply the lengths of its sides:

Area = (3x + 5) × (2x + 1)

Expanding the expression:

Area = 6x² + 3x + 10x + 5

Combining like terms:

Area = 6x² + 13x + 5

The area of the canvas is given by the expression 6x² + 13x + 5.

Now, let's find the area of the circle created by the paint.

The area of a circle is given by the formula A = πr², where r represents the radius.

The radius is given by the spreading of paint, which is r(t) = 2t.

Substituting the value of r(t) into the formula, we have:

A[r(t)] = π(2t)²

Simplifying:

A[r(t)] = π(4t²)

A[r(t)] = 4πt²

Now, let's determine if the area of the circle will be at least 300 in² in 5 minutes.

Substitute t = 5 into the area formula:

A[r(5)] = 4π(5)²

A[r(5)] = 4π(25)

A[r(5)] = 100π

Since 314.16 in² is larger than 300 in², the circle created by the paint will be larger than 300 in² in 5 minutes.

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The algebraic expression for "the quotient of 42 and x" is 42/x.

The algebraic expression for "the quotient of 42 and x" can be represented as 42 divided by x, which is written as 42/x.

In this expression, 42 represents the dividend, which is the number being divided, and x represents the divisor, which is the number by which the dividend is divided.

The division symbol (/) is often used to represent the quotient or the result of the division operation.

So, the algebraic expression for "the quotient of 42 and x" is 42/x.

It's important to note that this expression assumes that x is not equal to zero, as division by zero is undefined.

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Mrs. Tilmos should be used 8.5 cups of fertilizer.

Now, we can use the formula:

Area = (base x height) / 2

Since, We have to given that,

One side of the garden measures 13 feet and is perpendicular to a second side which is twice as long, we can use the Pythagorean theorem to find the length of the third side,

a² + b² = c²

13² + (2b)² = c²

169 + 4b² = c²

Simplifying:

4b² = c² - 169

The length of the third side is therefore:

c = √(4b² + 169)

Since the second side is twice as long as the first, we can write:

b = 2(13)

b = 26

Now we can substitute:

c = √(4(26²) + 169)

c = √(4(676) + 169)

c = √(2705)

c ≈ 52.0 feet

So the base of the triangle-shaped garden is 26 feet, and the height can be found using the formula:

Area = (base x height) / 2

Area = (26 x height) / 2

Area = 13 x height

So, the height of the garden is 13 feet.

The area of the garden is,

Area = (base x height) / 2

Area = (26 x 13) / 2

Area = 169 square feet

Now, the cups of fertilizer needed,

Cups of fertilizer = Area / 20

Cups of fertilizer = 169 / 20

Cups of fertilizer ≈ 8.4

Hence, Mrs. Tilmos should be used 8.5 cups of fertilizer.

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Answer:5y-3x

Step-by-step explanation: distributive

The given data represents a direct variation, as when x increases, y increases.

A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.

The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:

y = kx.

The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.

The constant for this problem is given as follows:

k = 8/5 = 1.6.

Hence the equation is given as follows:

y = 1.6x.

Which is a direct proportional relationship, as when x increases, y also increases.

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can you send a photo please

The equation's close approximation [tex]2^x = 3^{(x+1)[/tex]is x ≈ -2.713.

To solve the equation [tex]2^x = 3^{(x+1)[/tex]  for x, we can use logarithms.

If we take the logarithm of both sides of the equation (base 2), we get:

[tex]log2(2^x) = log2(3^{(x+1)})[/tex]

Using the properties of logarithms, we can simplify this equation as:

[tex]x = (x+1) \times log2(3)[/tex]

Expanding further:

[tex]x = x log2(3) + log2(3)[/tex]

Now, we can isolate the x terms on one side of the equation:

[tex]x - x \times log2(3) = log2(3)[/tex]

Factoring out x from the left side:

x(1 - log2(3)) = log2(3)

Dividing both sides by (1 - log2(3)), we find:

x = log2(3) / (1 - log2(3))

This gives us the exact solution for x.

We can change log2(3) = 1.585 into the equation to get an approximation of the answer:

x ≈ 1.585 / (1 - 1.585)

Simplifying further:

x ≈ 1.585 / (-0.585)

x ≈ -2.713

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The statement is true for the data sets is B. The mean study time of students in Class B is less than students in Class A.

For Class A, the mean is 5.3 hours. For Class B, the mean is 5.7 hours. Therefore, OB. The mean study time of students in Class B is less than students in Class A is the correct answer.

For Class A, the median is 5 hours. For Class B, the median is 5 hours. Therefore, OC.

The range is the difference between the largest and smallest values in the set. For Class A, the range is 8 hours. For Class B, the range is 21 hours.

The correct option is B.

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The ratio of the areas of the figures is 25/64

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

The ratio of the sides of two figures is 5/8,

The ratio of their areas is calculated as

Ratio = Side ratio²

substitute the known values in the above equation, so, we have the following representation

Ratio = (5/8)²

Evaluate

Ratio = 25/64

Hence, the ratio of their areas is 25/64

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The probability that a randomly chosen member of the population owns a cat or a dog is 33%.

Given information:

Percentage of population owning dogs (D): 19%

Percentage of population owning cats (C): 14%

Percentage of population owning both a cat and a dog (C ∩ D): 6%

To find the probability of owning a cat or a dog (C ∪ D), we use the principle of inclusion-exclusion:

P(C ∪ D) = P(C) + P(D) - P(C ∩ D)

Plugging in the given percentages:

P(C ∪ D) = 14% + 19% - 6%

P(C ∪ D) = 33%

Therefore, the probability that a randomly chosen member of the population owns a cat or a dog is 33%.

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the answer lyes in the cave at the end of a island

The best estimate of the number of students in the 1st and 2nd grade is approximately 39 students in the 1st grade and 29 students in the 2nd grade.

The best estimate of the number of students in 1st and 2nd grade, we need to calculate the percentages based on the total number of students, which is 205.

1st grade:

19% of 205 students.

To find the number of students in the 1st grade, we multiply the total number of students by the percentage:

19% of 205 = (19/100) × 205

= 0.19 × 205

= 38.95

≈ 39 students.

2nd grade: 14% of 205 students.

Similarly, we calculate the number of students in the 2nd grade:

14% of 205 = (14/100) × 205

= 0.14 × 205

= 28.7

≈ 29 students.

The percentages given represent the distribution of students across the grades accurately.

It is important to keep in mind that actual class sizes and grade distributions may vary.

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The Dividend per Shareholder in 2017 is $20.

As, Dividend per Shareholder = Profit / Number of Shareholders

Since the number of shareholders is assumed to have remained unchanged during the period 2017-2020, we can calculate the dividend per shareholder in 2017 using the profit value for that year.

Based on the given table, the profit for 2017 is $7,000.

Dividend per Shareholder in 2017

7000/x = 15500 / 44.29

7000/x = 349.966

x = 7000/349.966

x= 20.01

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Answer:

Step-by-step explanation:

given m=-6

(x1,y1)=5,-20

equation of line is given by

y-y1=m(x-x1)

substituting

y-(-20)=-6(x-5)

y+20=-6x+30

6x-y+10=0 is equation of line