Solve for x
.............

The surface area of hexagonal prism A is 9√3x² cm². We are given that hexagonal prism B is the image of hexagonal prism A after dilation by a scale factor of 2.

Therefore, all corresponding sides of prism A and prism B are in the ratio of 1:2. Let the side length of the base of hexagonal prism A be 'x'. Then, the side length of the base of hexagonal prism B is '2x'.

We know that the surface area of hexagonal prism B is 172 cm². Using the formula for the surface area of a hexagonal prism, we can write:

172 = 2(3√3)(2x)^2 + 6(2x)h

where h is the height of hexagonal prism B.

Simplifying this equation, we get:

172 = 24√3x² + 12xh

Dividing both sides by 12, we get:

14.33 = 2√3x² + h

Now, since hexagonal prism B is a dilation of hexagonal prism A by a scale factor of 2, the height of hexagonal prism A is half the height of hexagonal prism B. So, the height of hexagonal prism A is h/2.

Using the formula for the surface area of a hexagonal prism, we can write:

SA(A) = 2(3√3)x² + 6x(h/2)

Substituting h/2 for the height of hexagonal prism A, we get:

SA(A) = 2(3√3)x² + 3xh

Substituting 2√3x² + h/2 for h, we get:

SA(A) = 2(3√3)x² + 3x(2√3x² + h/2)

SA(A) = 6√3x² + 3√3x² + (3/2)xh

Substituting 2√3x² for h in the above equation, we get:

SA(A) = 6√3x² + 3√3x² + (3/2)x(2√3x²)

SA(A) = 9√3x²

Therefore, the surface area of hexagonal prism A is 9√3x² cm².

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The product of a non-zero rational and an irrational number is always irrational number.

To prove this statement:

Let x be a rational number and y be an irrational number.

Let xy=a.

Let us assume that a is rational.

Since, a is rational it can be expressed as  p/q , where p and q are integers.

Let x= m/n , where m and n are integers.

Now, xy=a

[tex]\frac{my}{n} = \frac{p}{q}[/tex]

On cross multiplying we get,

y = pn/qm​

Now, pn and qm are integers.

Hence, pn/qm is a rational number.

However, y is irrational.

Hence, our assumption is incorrect.

Hence, the product of a non-zero rational and an irrational number is always an Irrational number.

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The correct options are sample more families, sample families having children who are not in seventh grade.

Sample families that do not have children. Sample families living in every third house in neighborhood.

To increase the validity of the results of Kai's survey, he could make the following improvements to his sample:

Sample more families: Increasing the sample size would make the results more representative of the neighborhood as a whole, reducing the impact of random variation and making the estimates more precise.

Sample families that have children who are not in seventh grade: This would make the sample more diverse and representative of families with children of different ages.

Sample families that do not have children: Including families without children would make the sample more diverse and representative of the entire neighborhood.

Sample families living in every third house in the neighborhood: This would help to ensure that the sample is geographically representative of the neighborhood, reducing the chance of

sampling bias.

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Answer:

9

Step-by-step explanation:

set up a ratio

20 is to 3x-2   as    ( 20 + 28) is to 7x -3

20 / ( 3x-2) = ( 20 + 28) / (7x-3 )           cross multiply to get

140x - 60 = 144x - 96

          36 = 4x

              x = 9

Answer:

In order in which the boxes appear

[tex]\boxed{cubic}\\\\\boxed{3}\\\\\boxed{8}\\\\\boxed{x^3}\\\\\boxed{1}[/tex]

Step-by-step explanation:

Do not know the answer choices look like but this should fit

The polynomial has degree 3, therefore it is a cubic polynomial

There are 3 terms

The constant term is 8

The leading term is x³

and the leading coefficient is 1

Answer:

Cubic,3,8,x^3,1

Step-by-step explanation:

The polynomial is :

-x/10+x^3+8

The above polynomial, it contains 3 terms i.e, -x/10,x^3,8. The leading term is x^3 since it has power 3 so it is a cubic polynomial and its leading coefficient is 1.

The expression represents a cubic polynomial with 3 terms. The constant term is 8, the leading term is x^3, and the leading coefficient is 1.

The measure of other sides of a triangle are 15.11 units and 10.76 units.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

In the given triangle, ∠B=45°, ∠C=52° and AB=12 units.

By using angle sum property of a triangle,

∠A+∠B+∠C=180°

∠A+45°+52°=180°

∠A+97°=180°

∠A=83°

Now, by using sine rule, we get

sin83°/a=sin45°/b=sin52°/12

0.9925/a=0.7071/b=0.788/12

0.9925/a=0.788/12 and 0.7071/b=0.788/12

0.788a=11.91 and 0.788b=8.4852

a=11.91/0.788 and b=8.4852/0.788

a=15.11 units and b=10.76 units

Therefore, the measure of other sides of a triangle are 15.11 units and 10.76 units.

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The amount of money that would be paid for rent each year for the spa would be = $37,800

The area of the potential space for the opening of your first spa = 1,800 square feet.

The price for each square feet per year = $21

That is; = 1800× 21 = $37,800

Therefore, annual rent fees for the space which will be used for spa = $37,800.

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a. There were 126 people who voted for Goron.

b. There were 144 people who voted for Fishman.

The percentage is defined as a ratio expressed as a fraction of 100.

The given circle graph shows the results.

There were 360 people who voted in the election.

According to the question, the required solution would be as:

number of people who voted for Goron = 35% of 360

15%  is expressed as 15/100 in fractional form

number of people who voted for Goron = (35/100) × 360

number of people who voted for Goron = 126

number of people who voted for Fishman = 40% of 360

number of people who voted for Fishman = (40/100) × 360

number of people who voted for Fishman = 144

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The missing figure has been attached below

[tex]\lim_{p \to \(-8}[/tex]  = -59

What is a Limit?

Limit is the values that a function approaches the output for the given input values.

How to calculate this

[tex]\lim_{p \to \(-8}[/tex] ( -[tex]p^{2}[/tex] - p -3)

when p = -8

By inserting the value of p

[tex]\lim_{p \to \(-8}[/tex] = {-(-8)^2 - (-8) - 3 }

open the bracket

[tex]\lim_{p \to \(-8}[/tex] = (-64 + 8 - 3 )

[tex]\lim_{p \to \(-8}[/tex] = ( - 59 )

So, [tex]\lim_{p \to \(-8}[/tex]  =-59

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Answer:

Below

Step-by-step explanation:

1.4 m = .42     divide both sides of the equation by   1.4 to get

 m = .3     Done.

The difference in cost between a one-line ad and a four-line ad is 0

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

c(x) = 40 x ≤ 5

c(x) = 40 + 7(x-4), x>5)

For one line add, we make use of the function

c(x) = 40 x ≤ 5

This is so because 1 is in the domain of x ≤ 5

For four line add, we make use of the function

c(x) = 40 x ≤ 5

This is so because 4 is in the domain of x ≤ 5

So, we have

C(1) = 40 and C(4) = 40

The difference, it

Difference = 40 - 40

Evaluate

Difference = 0

Hence, the difference is 0

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Answer:

D

Step-by-step explanation:

3x² - 10x - 8

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 8 = - 24 and sum = - 10

the factors are - 12 and + 2

use these factors to split the x- term

3x² - 12x + 2x - 8 ( factor the first/second and third/fourth terms )

= 3x(x - 4) + 2(x - 4) ← factor out (x - 4) from each term

= (x - 4)(3x + 2)

Answer:

5.15%

Step-by-step explanation:

Difference between estimated throw and actual throw

= estimated - actual

= 22.52 - 21.36

= 1.16 m

As a fraction of estimated throw:
1.16/22.52

As a percentage:
1.16/22.52  x 100 =  5.15%

Answer:

Below

Step-by-step explanation:

One leg would be    hyp * cos 30   and one would be  hyp cos 60

                   hyp cos 30 : hyp cos 60

                           cos 30 : cos 60

                      =   ratio     sqrt (3) /2  :  1/2     or     sqrt 3  : 1

To volume to fill the rectangular garden is 8.99 cubic yard

To determine the volume of amount of sand required to fill the garden, we can simply convert the dimensions from inches and feet into yard.

inch to yard

6 inch = 0.17 yard

Feet to yard

28 feet = 9.33 yard

17 feet = 5.67 yard

The volume of the rectangular garden is given as;

v = l * w * h

Substituting the values;

V = 0.17 * 9.33 * 5.67

v = 8.99 cubic yard

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Answer:

Let's call the number of students at the college "x". Then, the number of faculty/staff is 3 times that number, or 3x. The total number of people at the college is the sum of the students and faculty/staff, which is x + 3x = 4x.

According to the problem, the ratio of faculty/staff to students is 3 to 13, so we can write an equation:

3x / x = 3 / 13

To find the number of students, we can solve for x:

4x = 4000

x = 1000

So, there are 1000 students at the college.

From the given figure we can say that , Evan's used the given shape correctly to represent the unit fraction .

What is a unit fraction ?

A unit fraction is a fraction whose numerator (top number) is equal to 1. For example, 1/2, 1/3, 1/4, and so on are all unit fractions. Unit fractions are commonly used to represent parts of a whole, and they can also be used to perform certain mathematical operations such as addition and multiplication.

Given ,

Evan and Yong used the given shape representing the unit fraction, to draw 1 whole.

so,

from the given figure ,

in the evan diagram we can say it was mentioned correct, as we need to write down that in 1/3 where as in the Yong's case we can say that it does not come to 1/3 as a final resultant.

Therefore, From the given figure we can say that , Evan's used the given shape correctly to represent the unit fraction .

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Answer:

[tex]90 \ in^{3}[/tex]

Step-by-step explanation:

The volume of a cone is ¹/₃ the volume of the cylinder of a given radius and perpendicular height

[tex]V_{C} = volume \ of \ cylinder \\\\ V_{c} = volume \ of \ cone\\\\ r = radius \\\\ h = perpendicular \ height[/tex]

[tex]V_{C} = \pi r^{2}h \\\\ V_{c} = \frac{1}{3}\pi r^{2}h[/tex]   →   [tex]3V_{c} = \pi r^{2}h = V_{C}[/tex]

So if r and h are the same, then:

[tex]V_{C} = 3V_{c}[/tex]

Therefore:

[tex]V_{C} = 3(30) \\\\ V_{C} = 90[/tex]

The area of the equilateral triangle with side length 10 cm is 25 cm².

What is triangle ?

Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.

To find the area of an equilateral triangle, we need to find the height first. The height of an equilateral triangle is equal to the length of the perpendicular line from the center of the triangle to one of its sides.

To find the height, we can divide the equilateral triangle into two 30-60-90 triangles. The height is equal to half of the hypotenuse of one of these triangles, which can be calculated as:

10 cm / 2 = 5 cm

Now that we have the height, we can find the area of the equilateral triangle as follows:

Area = ½ * base * height

Area = ½ * 10 cm * 5 cm

Area = 25 cm²

Hence, The area of the equilateral triangle with side length 10 cm is 25 cm².

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The equation that describes this situation is, 3 + 15n = 153

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

Given that,

Three more than product of 15,

And a number n is 153.

More than = + (addition)

Product = x (multiplication)

Product of 15 and n = 15 x n = 15n

Therefore, the equation is 3 + 15n = 153.

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The term that best describes the point W in the triangle is given by the following option:

B. Orthocenter.

The orthocenter is the point where all three altitudes of a triangle will intersect.

An altitude is a line which passing through one of the three vertices of the triangle and is perpendicular to the opposite side relative to this vertex.

Hence point W is the orthocenter of triangle XYZ.

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The solution is;

 a. (2, 10) is not a solution to y < 12- x.

 b. (3, 13) is a solution to y ≤ 15 - x

 c. (4, 19) is a solution to y > 19 - x

 d. (5, 13) is not a solution to y ≥ 12 - x

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality.

A Set of such values is called a solution set to the considered equation or inequality.

Substitute the values where the variables are, and simplify to the point where you can tell whether the statement is true.

Each ordered pair is (x, y), thus the first value gets substituted for x; the second value gets substituted for y.

a. (2, 10)

 11 < 13 -2 = 11

no

b.(3, 13)

 8 ≤ 16 -3 = 13

yes

c. (4, 19)

 20 > 18 -4 = 14

yes

d. (5, 13)

 9 ≥ 15 -5 = 10

no

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Answer:

17

Step-by-step explanation:

5 x 3 = 15

15 - (-2) = 17

Sarah goes first, James goes second, and Matthew goes third.

Answer:

= -1+12h.

Step-by-step explanation:

I guess my answer is correct

The antiderivative of the given expression can be found using the substitution method. We'll make the substitution u = 4 - 9x^2, so du/dx = -18x.

Substituting these into the original expression, we get:

∫{√(4-9x²)/x}dx = ∫{√u/x}du = 2√u * ln|x| + C, where C is an arbitrary constant of integration.

Substituting back for u, we get:

∫{√(4-9x²)/x}dx = 2√(4 - 9x^2) * ln|x| + C.

To verify this result, we can differentiate the antiderivative and see if it matches the original expression. Taking the derivative of the antiderivative with respect to x, we get:

d/dx [2√(4 - 9x^2) * ln|x| + C] = -18x√(4 - 9x^2)/x + 2 * (-9x) / (2√(4 - 9x^2)) = (√(4-9x²)/x)

Thus, the antiderivative found is indeed correct.

Answer:

Step-by-step explanation:

To solve for the value of "a", we can isolate "a" in one of the equations and then substitute the result into the other equation. Here's how we can do that:

Starting with the first equation:

5a - 26 = -10

5a = -10 + 26

5a = 16

a = 16 / 5

a = 3.2

Now that we know the value of "a", we can substitute it into the second equation:

6a + 46 = 36

6 * 3.2 + 46 = 36

19.2 + 46 = 36

65.2 = 36

This means that the system of equations has no solution, as the values of "a" and "b" can't both satisfy both equations at the same time.

Answer:

the speed of the plane in still air is 540 miles per hour and the speed of the wind is 280 miles per hour.

Step-by-step explanation:

Step 1: Define the variables

Let's call the speed of the plane in still air "V". Let's call the speed of the wind "W".

Step 2: Write an equation for the distance traveled with the wind

The distance traveled by the plane with the wind in 6.5 hours can be represented by the equation:

D1 = (V + W) * t

where D1 is the distance traveled, t is the time (6.5 hours), and V and W are the speeds of the plane and the wind, respectively.

Substitute the known values into the equation:

3900 = (V + W) * 6.5

Step 3: Write an equation for the distance traveled against the wind

The distance traveled by the plane against the wind in 6.5 hours can be represented by the equation:

D2 = (V - W) * t

where D2 is the distance traveled, t is the time (6.5 hours), and V and W are the speeds of the plane and the wind, respectively.

Substitute the known values into the equation:

3120 = (V - W) * 6.5

Step 4: Solve for the speed of the wind

We can now use the two equations from Steps 2 and 3 to solve for the speed of the wind.

First, let's rearrange the equation from Step 2 to isolate "W":

W = (3900 / 6.5) - V

Next, substitute this expression for "W" into the equation from Step 3:

3120 = (V - ((3900 / 6.5) - V)) * 6.5

Expand the right side of the equation:

3120 = (V - 3900 / 6.5 + V) * 6.5

Simplify the equation:

3120 = 2V * 6.5 - 3900

Divide both sides of the equation by 2:

1560 = V * 6.5 - 1950

Multiply both sides of the equation by 2:

3120 = V * 13 - 3900

Add 3900 to both sides of the equation:

7020 = V * 13

Divide both sides of the equation by 13:

V = 540

Step 5: Solve for the speed of the wind

Now that we know the speed of the plane in still air, we can use the equation from Step 2 to find the speed of the wind:

W = (3900 / 6.5) - V

Substitute the value of "V" that we found in Step 4 into the equation:

W = (3900 / 6.5) - 540

Simplify the equation:

W = 280

Step 6: Conclusion

Therefore, the speed of the plane in still air is 540 miles per hour and the speed of the wind is 280 miles per hour.