This is an algebraic equation.

-12x^2/2x^2

The lateral surface area is 84 square centimeters and the total surface area is 96 square centimeters. The solution has been obtained by using the triangular prism.

What is a triangular prism?

A pentahedron with nine different nets, the triangular prism. Through their three rectangular sides, the bases' vertices and edges are connected. The rectangular sides of the triangular prism are joined side by side to one another. A triangle is represented by any cross-section that is parallel to the base faces.

We know that lateral surface area of prism is given by

A = (a + b + c) * h

Here, we are given

a = 4

b = 3

c = 5

h = 7

On substituting this, we get

⇒ A = (4 + 3 + 5) * 7

⇒ A = (12) * 7

⇒ A = 84 square centimeters

The formula for total surface area is

A = 2 * (area of base) + lateral surface area

Area of base = 0.5 * 3 * 4

Area of base = 6 square centimeters

So, we get

⇒ Total surface area = 2 * 6 + 84

⇒ Total surface area = 12 + 84

⇒ Total surface area = 96 square centimeters

Hence, the lateral and total surface area of the prism are obtained.

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Example of The Transitivity Property that follows

Premise:  If x = 3 and y = x + 2, then y = 5.

Premise: If y = 5 and z = y - 1, then z = 4.

Conclusion: If x = 3, then z = 4.

The transitivity property is a logical property that states that if a=b and b=c, then a=c. This property is commonly used in mathematics to make deductions and draw conclusions.

Example:

Premise: If x = 3 and y = x + 2, then y = 5.

Premise: If y = 5 and z = y - 1, then z = 4.

Conclusion: If x = 3, then z = 4.

Explanation: By the transitivity property, we can substitute the value of y in the second premise with the value of x + 2 from the first premise to get z = (x + 2) - 1, which simplifies to z = x + 1. Then, we can substitute x = 3 to get z = 4.

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The required answers are a) 6.5 m, b) Dimensions 8 m, 5 m c) square has the greater area.

(a) Let s be the length of a side of the square. The perimeter of a square is given by 4s. Since the piece of wire used to make the square has length 26 m, we have:

[tex]$\begin{align*}4s &= 26 \s &= \frac{26}{4} = 6.5 \text{ m}\end{align*}[/tex]

Therefore, the length of a side of the square is 6.5 m.

(b) Let l be the length of the rectangle. Then the width of the rectangle is l-3. The perimeter of a rectangle is given by 2(l+w). Since the piece of wire used to make the rectangle has length 26 m, we have:

[tex]$\begin{align*}2(l + (l-3)) &= 26 \2(2l-3) &= 26 \4l - 6 &= 26 \4l &= 32 \l &= 8 \text{ m}\end{align*}[/tex]

Therefore, the length of the rectangle is 8 m and its width is 8-3=5 m.

(c) The area of the square is given by [tex]$s^2$[/tex], which in this case is [tex]$6.5^2 = 42.25$[/tex] square meters. The area of the rectangle is given by lw, which in this case is [tex]$8\times5 = 40$[/tex] square meters. Therefore, the square has the greater area.

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Complete question;

A workman has two pieces of worse, each of length 26 m. One piece is to be bent into a square. The other piece is to be bent into a rectangle whose width is 3 m shorter than its length.

(a) What is the length of a side of the square?

(b) What are the dimensions of the rectangle?

(c) Which shape has the greater area?

Answer: 2252.25 - 1018.50 = P58.75

Step-by-step explanation:

Histogram would be the best for the data representation of the girls by dietitian.

Histogram, it is an approximate representation of the distribution of numerical data. The most popular graph for showing frequency distributions is a histogram. Though it also closely resembles a bar chart, there are significant differences. One of the seven basic quality tools is this useful gathering and analysing information tool.

Variable = the height of 13-year-olds in the state of Texas.

Where the height of each bar represents the frequency of observations.

[tex](2 - 2.5) feet\\\\(2.6 - 3) feet\\(3.1 - 3.5) feet\\(4.1 - 4.5) feet[/tex]

So, The best graphical representation of the dietitian's data would be a histogram.

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Answer:

Step-by-step explanation:

To fill in the table, we can use the following steps:

Calculate the interest for each month, which is the prior balance multiplied by the monthly interest rate (1.75%).

Subtract the monthly interest from the prior balance to get the new balance before the monthly payment.

Subtract the monthly payment from the new balance to get the ending balance.

Month Prior Balance 1.75% Interest on Prior Balance Monthly Payment Ending Balance

1 $5000 $87.50 $325 $4762.50

2 $4762.50 $83.39 $325 $4520.84

3 $4520.84 $79.06 $325 $4276.90

4 $4276.90 $74.50 $325 $4029.23

5 $4029.23 $69.69 $325 $3777.87

Therefore, after 5 months of making $325 payments, the remaining balance on the loan is $3777.87.

As a result, 0.85 or 85% of vacationers are likely to visit either the Magic Kingdom or Epcot Center.

The measurement and study of random events are the focus of the mathematic branch known as probability. It is a means to express how likely an event or series of events are to occur. Probability is stated as a number between 0 and 1, where 0 denotes the impossibility of an event and 1 denotes its certainty. An occurrence that has a probability of 0.5 (or 50%) is equally likely to occur or not. In a variety of disciplines, including statistics, economics, engineering, and science, probability is used to evaluate and forecast the possibility of specific events in light of the information and presumptions at hand.

given

The formula for the union of two events must be used to determine the likelihood that a visitor will go to either the Magic Kingdom or Epcot Center:

P(A or B) equals P(A) + P(B) - P (A and B)

P(A) represents the likelihood that event A will occur, P(B) represents the likelihood that event B will occur, and P(A and B) represents the likelihood that both events will occur at the same time.

Let's describe event A in this scenario as a trip to the Magic Kingdom, and event B as a trip to the Epcot Center. We are aware of:

P(A) = 0.60 (the Magic Kingdom is visited by 60% of tourists)

P(B) = 0.50 (50 percent of tourists go to the Epcot Center)

P(A and B) = 0.25 (25% of tourists go to both places).

The result of the formula is:

P(A or B) is equal to P(A) + P(B) - P(A and B), which is 0.60 + 0.50 - 0.25 = 0.85.

As a result, 0.85 or 85% of vacationers are likely to visit either the Magic Kingdom or Epcot Center.

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Answer:

10 miles

the first option

Work Shown:

[tex]17600 \text{ yards} = 17600 \text{ yards}\times\frac{3 \text{ feet}}{1 \text{ yard}}\times\frac{1 \text{ mile}}{5280 \text{ feet}}\\\\= \frac{17600 \times 3\times 1}{1 \times 5280\times 1} \text{ miles}\\\\= \frac{52800}{5280} \text{ miles}\\\\= 10 \text{ miles}\\\\[/tex]

Take notice in the jump from the 1st to 2nd lines, we have the "yards" and "feet" units cancel out.

Answer:33.34

Step-by-step explanation:

we'll use sinuses theorem for this which is,

[tex]\frac{x}{sina}=\frac{y}{sinb}\\\frac{27}{sin39} =\frac{x}{sin(90-39)} \\\frac{27}{sin39} =\frac{x}{sin51} \\x=\frac{sin51*27}{sin39}\\x=33.34[/tex]

Answer: We are given a right triangle where the two legs have lengths 2 and 4, and we need to find the length of the hypotenuse (which is denoted by x in the question). We can use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. That is,

hypotenuse^2 = leg1^2 + leg2^2

Plugging in the values we know, we get:

x^2 = 2^2 + 4^2

Simplifying the right-hand side, we get:

x^2 = 4 + 16

x^2 = 20

Taking the square root of both sides (and noting that x must be positive since it is a length), we get:

x = sqrt(20) = 2sqrt(5)

Therefore, the length of the hypotenuse is 2sqrt(5).

Step-by-step explanation:

Answer:

17,500

Step-by-step explanation:

Answer:

Let's first recall the Pythagorean identity:

sin²θ + cos²θ = 1

We can use this identity to find the value of sinθ, given that cosθ = 1/7 and θ is in the first quadrant. Since θ is in the first quadrant, both sinθ and cosθ are positive.

cosθ = 1/7

cos²θ = (1/7)² = 1/49

sin²θ + cos²θ = 1

sin²θ + 1/49 = 1

sin²θ = 1 - 1/49 = 48/49

sinθ = √(48/49) = (4/7)√3

Now we can use the definition of cotangent to find cotθ:

cotθ = cosθ/sinθ

Substituting the values we found for cosθ and sinθ, we get:

cotθ = (1/7)/[(4/7)√3] = √3/4

Therefore, cotθ = √3/4 when cosθ = 1/7 and θ is in the first quadrant.

The polynomial equation with the roots is P(x) = x^2 - 15x + 56

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

Roots: x = 8 and x = 7

Using the above as a guide, we have the following:

The equation can be represented as

P(x) = (x - root)

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

P(x) = (x - 8)(x - 7)

Evaluate the product

P(x) = x^2 - 8x - 7x + 56

This gives

P(x) = x^2 - 15x + 56

Hence, the equation is P(x) = x^2 - 15x + 56

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Answer:

  -5

Step-by-step explanation:

You want the minimum value of f(x) = x² +6x +4.

The line of symmetry of a quadratic function f(x) = ax² +bx +c is given by ...

  x = -b/(2a)

The line of symmetry passes through the extreme point. When a > 0, that extreme point is the minimum.

Here, we have a=1, b=6, so the line of symmetry is ...

  x = -6/(2·1) = -3

The extreme point (minimum) is ...

  f(-3) = (-3)² +6(-3) +4 = (-3 +6)(-3) +4 = -9 +4

  f(-3) = -5

The minimum value of f(x) is -5.

The equation of the axis of symmetry is [tex]x = 1/2.[/tex]

The definition of the an equation in algebra is a logical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical equation, such as 6 × 4 = 12 x 2, states that two quantities or values are equal. A noun that counts. When two or more components must be taken into account together in order to comprehend or describe the whole situation, this is known as an equations.

To find the equation of the axis of symmetry for the parabola[tex]y = x^2 - x - 6,[/tex]  we first need to find the x-coordinate of the vertex.

We can use the formula [tex]x = -b/2a[/tex] to find the x-coordinate of the vertex. In this case, a = 1 and b = -1, so:

[tex]x = -(-1) / 2(1) = 1/2[/tex]

So the x-coordinate of the vertex is [tex]1/2[/tex].

To find the y-coordinate of the vertex,

x = 1/2

[tex]y = (1/2)^2 - (1/2) - 6 = -25/4[/tex]

So the coordinates of the vertex are [tex](1/2, -25/4).[/tex]

[tex]x = 1/2[/tex]

Therefore, the equation of the axis of symmetry is [tex]x = 1/2.[/tex]

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Answer:

x = -14

Step-by-step explanation:

(x+1)² + 120 = (x-3)²

expand each binomial:

x² + 2x + 1 + 120 = x² -6x + 9

combine 'like terms' to simplify:

8x = -112

x = -14

Answer: 48.3

Step-by-step explanation:

Answer:

48.3

Step-by-step explanation:

The angles measures are m∠1 is 103, m∠2  is 38, m∠3 is 77.

In geometry, an angle is a measure of the amount of turn between two lines or line segments that meet at a common endpoint, called the vertex of the angle. Angles are measured in degrees or radians.

A degree is a unit of measure for angles, where one full circle contains 360 degrees. A right angle, which forms a quarter of a circle, is 90 degrees. Angles that are smaller than a right angle are called acute angles, while angles that are larger than a right angle are called obtuse angles. Angles that add up to a straight line, which forms half of a circle, are called supplementary angles, while angles that add up to a full circle are called explementary angles.

A radian is another unit of measure for angles, where one full circle contains 2π radians. A right angle, which forms a quarter of a circle, is π/2 radians.

Here, m∠5 + m∠2 = 180   [ Supplementary Angles ]

142 + m∠2 = 180

m∠2 = 180 - 142 = 38

Now, m∠2 + m∠3 + m∠4 = 180   [ Angles in a Triangle ]

38 + m∠3 + 65 = 180

m∠3 = 180 - 103

m∠3 = 77

Again, m∠3 + m∠1 = 180   [ Supplementary Angles ]

m∠1 + 77 = 180

m∠1 = 180 - 77 = 103

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The complete question is:

The correct option is (d) i.e. by grouping x²(x + 11) -3(x +11).

What are Factors?

Factors are numbers or algebraic expressions that can be multiplied together to obtain a given product.

In algebra, factors are often used to factorize polynomials or other expressions, which involves expressing them as a product of simpler expressions.

One way to determine the factors of x³ + 11x² - 3x - 33 by grouping is:

x²(x + 11) - 3(x + 11)

We can see that the two terms have a common factor of (x + 11), so we can factor it out as follows:

 = x³ + 11x² - 3x - 33

 =x²(x + 11) -3(x +11)

 = (x² - 3) (x+11).

The quadratic factor can be factored further using the difference of squares formula:

(x + 11)(x - √3)(x + √3)

So the factors of x³ + 11x² - 3x - 33 are (x + 11)(x - √3)(x + √3).

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The radian measure for 315° is (7/4)π radians.

What exactly is a radian measure?

Radian measure is a unit of measurement for angles, where one radian is defined as the central angle subtended by an arc of a circle with a length equal to the radius of the circle. Therefore, to convert degrees to radians, we need to multiply the degree measure by pi/180.

Now,

To convert 315 degrees to radians, we can use the formula:

radians = degrees x π/180

So, we have:

radians = 315 x π/180

Simplifying this expression, we get:

radians = (7/4) x π

Therefore,

             315 degrees is equal to (7/4) π radians.

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Answer:

d ≈ 4.5

Step-by-step explanation:

calculate AB using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = A (1, 0 ) and (x₂, y₂ ) = B (5, 2 )

d = [tex]\sqrt{(5-1)^2+(2-0)^2}[/tex]

  = [tex]\sqrt{4^2+2^2}[/tex]

  = [tex]\sqrt{16+4}[/tex]

  = [tex]\sqrt{20}[/tex]

  ≈ 4.5 ( to the nearest tenth )

Answer:

A, B, and D

Step-by-step explanation:

The inequality n + 15 less-than 22 can be simplified by subtracting 15 from both sides:

n + 15 - 15 < 22 - 15

This simplifies to:

n < 7

So, any inequality of the form n < 7 is equivalent to n + 15 less-than 22.

Out of the given options:

A: n + 15 minus 15 less-than 22 minus 15

This simplifies to n < 7, which is equivalent to the original inequality.

B: n + 15 less-than 22 minus 15

This simplifies to n < 7, which is equivalent to the original inequality.

C: n + 15 minus 22 less-than 22 minus 22

This simplifies to n - 7 < 0, which is not equivalent to the original inequality.

D: n + 15 + 6 less-than 22 + 6

This simplifies to n + 21 less-than 28, which simplifies further to n < 7, which is equivalent to the original inequality.

E: n + 15 minus 22 less-than 22

This simplifies to n - 7 less-than 0, which is not equivalent to the original inequality.

Therefore, options A, B, and D are equivalent to the inequality n + 15 less-than 22.

Answer:

its A C D

Step-by-step explanation:i took the test the answer i used was wrong

Answer:

To find the total interest paid by Brian, we can use the simple interest formula:

I = P * r * t

where I is the interest, P is the principal (the amount borrowed), r is the annual interest rate as a decimal, and t is the time period in years.

For Brian's loan, we have:

I = 1800 * 0.12 * 4 = $864

So Brian paid a total of $864 in interest over the 4-year term.

For Andy's loan, we can use the same formula:

I = 4200 * 0.10 * 2 = $840

So Andy paid a total of $840 in interest over the 2-year term.

To find the difference in interest paid, we subtract the smaller amount from the larger amount:

864 - 840 = $24

Therefore, Brian paid $24 more in interest than Andy. The answer is option D.

Answer: the answer is C. Brian paid $24 more in interest than Andy.

Step-by-step explanation: To find out how much interest each person paid, we can use the formula:

Interest = Principal x Rate x Time

where Principal is the amount borrowed, Rate is the annual interest rate (as a decimal), and Time is the length of the loan (in years).

For Brian's loan:

Principal = $1,800

Rate = 0.12

Time = 4 years

Interest = $1,800 x 0.12 x 4 = $864

For Andy's loan:

Principal = $4,200

Rate = 0.10

Time = 2 years

Interest = $4,200 x 0.10 x 2 = $840

So Andy paid $840 in interest, while Brian paid $864 in interest. To find out how much more Brian paid than Andy, we can subtract:

$864 - $840 = $24

Answer:

C: 54-x^2

Step-by-step explanation:

54(decreased=minus)-number^2

Answer:

Therefore, the depth of Challenger Deep to the nearest fathom is 6,466 fathoms, and it is greater than 7 miles.

Step-by-step explanation:

One fathom is equal to 6 feet. To convert 38,797 ft. to fathoms, we divide by 6:

38,797 ft. / 6 = 6,466.17 fathoms

Rounding this to the nearest fathom gives us 6,466 fathoms.

One mile is equal to 5,280 feet. Seven miles would be:

7 mi. x 5,280 ft/mi = 36,960 ft.

Since 38,797 ft. is greater than 36,960 ft., we can conclude that Challenger Deep's depth is greater than 7 miles.

Therefore, the depth of Challenger Deep to the nearest fathom is 6,466 fathoms, and it is greater than 7 miles.

The statement that is most likely true is: "The data in Sample B is clustered around the center where Sample A is more spread out."

A dataset is a collection of information, often represented in a tabular form, that contains one or more variables or pieces of data for a particular set of individuals or observations. Each individual or observation in the dataset is typically represented by a row in the table, while the variables are represented by columns. Datasets can be used to study a wide variety of phenomena, from social and economic trends to scientific experiments and medical studies. They can be collected through a variety of methods, including surveys, experiments, observations, and automated data collection systems, and can be analyzed using statistical methods to gain insights into the underlying patterns and relationships in the data.

Here,

This is because Sample A has a larger range than Sample B, indicating that the data points in Sample A are more spread out across the number line. Additionally, the median for both samples is the same (5), but the mean for Sample A is higher than the mean for Sample B, which could suggest that there are some larger values pulling the mean upward in Sample A. Taken together, these characteristics suggest that Sample A has more variability in its data points, while Sample B is more clustered around the center.

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