the satellite is in the shape of a rectangular prism. which polynomial represents the volume of the satellite? a rectangular prism with length 4 x minus 3 feet, a width of x plus 1 feet, and a height of x plus 2 feet.

The correct statements are:

The length of the other leg is 6√2 feet.

The length of the hypotenuse is 12 feet.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given:

One leg of an isosceles triangle is 6√2 feet.

As, we know isosceles triangle two of its sides equal in length then the other side can be  6√2 feet.

Now, using Pythagoras theorem

H² = P² + B²

H² = (6√2)² + (6√2)²

H² = 72 + 72

H² = 144

H= 12 units

The statements that applies here are:

The length of the other leg is 6√2 feet.

The length of the hypotenuse is 12 feet.

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Answer:

The answer is B and D

Step-by-step explanation:

I took the test.

let me know if you would like an explanation down in the comments!

The probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

The number of possible subcommittees that contain only undergraduate students can be calculated by choosing 3 members from the 4 undergraduate students. This can be done in (4 choose 3) = 4 ways.

The total number of possible subcommittees of three students that can be formed from the 6 members of the committee can be calculated by choosing 3 members from the 6 students. This can be done in (6 choose 3) = 20 ways.

Therefore, the probability that there will be no graduate students on the subcommittee is:

Number of subcommittees with only undergraduate students / Total number of possible subcommittees

= 4 / 20

= 1/5

= 0.2

So, the probability of choosing a subcommittee of 3 members with no graduate students is 0.2, or 20%.

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Answer:

yes its 106

Step-by-step explanation:

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In a sample of 20 men, the mean height was 178 cm and a sample of 30 women, the mean height was 164 cm, then the mean height for both groups combined is approximately 172.4 cm.

To find the mean height for both groups combined, we need to calculate the weighted average of the means of each group, where the weight of each group is proportional to its sample size.

We can begin by finding the total height of all the individuals in both groups combined. The total height for the men's group would be 20 multiplied by the mean height of 178 cm, which is 3560 cm.

Similarly, the total height for the women's group would be 30 multiplied by the mean height of 164 cm, which is 4920 cm. Adding these two values gives a total height of 8480 cm for both groups combined.

Next, we need to find the total sample size, which is the sum of the sample sizes of the two groups. The total sample size is 20 + 30 = 50.

Finally, we can calculate the weighted average of the means of each group using the formula:

Weighted average = (weight of group 1 * mean of group 1 + weight of group 2 * mean of group 2) / (weight of group 1 + weight of group 2)

In this case, the weights of each group are proportional to their sample sizes. Therefore, the weighted average can be calculated as:

Weighted average = (20/50 * 178 cm) + (30/50 * 164 cm) = 172.4 cm

In summary, to find the mean height for both groups combined, we need to calculate the weighted average of the means of each group, where the weight of each group is proportional to its sample size. This is done by multiplying the sample size of each group by its mean height, adding the values, and then dividing by the total sample size.

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Answer:

1. SAS

2. Not congruent

Step-by-step explanation:

1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.

If you rotate the first triangle, you'll see that it is the same as the second.

4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.

The solution is,

1. SAS

2. AAS

3. SAS

4. Not congruent.

Two triangles are congruent if all three pairs of corresponding sides are equal. Two pairs of corresponding sides and the corresponding angles between them are equal.

here, we have,

we know that,

To identify which triangles are congruent measure the angles and sides of each of the triangles and compare them.

Meaning of congruent:

In mathematics, the word congruent is used if two figures have the same size and shape, although their orientation can be different.

Two triangles are congruent:

In the case of triangles two factors should be considered:

1) Lengths of each side are equal.

2) Angles are equal.

This means that to determine if the triangles are congruent, we must measure each side and angle and make sure these are the same in each triangle.

now, we have,

1. These two triangles have a pair of congruent sides with a congruent angle between them. Therefore, they are congruent by SAS.

If you rotate the first triangle, you'll see that it is the same as the second and, similar for 2 & 3 by AAS & SAS.

4. These two triangles have a pair of congruent angles. We can also show that the third angles are also congruent. However, we don't have any congruent sides. Therefore, these triangles are similar, but not necessary congruent.

Hence, 1. SAS

2. AAS

3. SAS

4. Not congruent.

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The measure of each angle is given below:

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively.

Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The measure of angles {contd.} is:

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The value of x is given as follows:

x = 131º.

An interior angle is supplementary with it's exterior angle, meaning that the sum of their measures is of 180º.

Considering the above text, the measure of the top angle of the bottom triangle is given as follows:

a = 180 - 98

a = 82.

The base angles of the bottom triangle have the same measure, as the triangle is isosceles, hence:

2b + 82 = 180

2b = 98

b = 49.

(the sum of the measures of the internal angles of a triangle is of 180º).

Considering the vertical angles, the base angles of the top triangle are given as follows:

b = 49.

Hence the value of x is given as follows:

x = 180 - 49

x = 131º.

(as the top triangle is also isosceles, and the angle measure x is the exterior angle of an interior angle with measure of 49º).

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The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.  

We can solve the given function by adding or subtracting the same integer on both sides. Here adding or subtracting the same number on both sides doesn't change the condition of the function. In end-use trial and error mothed to find the value of the variable 'x'

Here we have

f(x) = - 6x + 14  and g(x) = - 2ˣ + 6  

The solution of - 6x + 14 = - 2ˣ + 6 can be calculated as follows

=> - 6x + 14 =  - 2ˣ + 6    

=> - 6x + 8 = - 2ˣ    

=> - 6x + 8 = - 2ˣ

=> - 6x + 2ˣ = - 8          

By using the trial and error method

At x = 2

=> - 6(2) + 2² = -8

=> - 12 + 4 = -8

Therefore,

The solution of the function - 6x + 14 = - 2ˣ + 6 is 2. The required graphs are given below.  

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Answer: £122.45

Step-by-step explanation: 7.90*15.5

Answer: 109?

Step-by-step explanation:

On a coordinate plane, locations of the points (2 , -1) and (2 , 1) related by reflection across the x-axis.

It is given that the locations of the two points are (2 , -1) and (2 , 1).

We have to find the relation between two points.

From the given points (2 , -1) and (2 , 1), it is clear that the y-coordinates are same but the sign of x-coordinates are opposite.

If a figure is reflected across the y-axis, then we change the sign of y-coordinate and the x-coordinates remain same,

So, it is reflection across the x-axis.

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The percentage increase in the population of the town is 12%.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Increase in population =  90,000 - 80,000  = 10,000

          Percentage increase = 10,000/80,000 * 100 = 100/8 = 12.5%

Hence the percentage increase in the population of the town is 12%.

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Answer:

Step-by-step explanation:

4 = d

5=1/5

3 the first one is 4x1/12 and 2x3/12

Answer:

7 and 7x

Step-by-step explanation:

We distributing these factors are the only that can make sense

The ordered pairs from the graph of quadratic and linear equations are (-2, 7) and (2, -1)

A graph of a quadratic equation is a parabolic curve that opens up or down, depending on the sign of the coefficient of the squared term. A general form of a quadratic equation is given by:

y = ax^2 + bx + c,

where a, b, and c are constants. The graph of this equation can be plotted by choosing a range of values for x and calculating the corresponding values of y.

A graph of a linear equation is a straight line. A general form of a linear equation is given by:

y = mx + b,

where m is the slope of the line and b is the y-intercept.

In this problem, the ordered-pairs will be the point in which they intersect with each other.

Looking carefully at the graph, the ordered pair will be at points

A = (-2, 7)

B = (2, -1)

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The length of the third side of a triangle with perimeter 9x + 6 and measures of other two sides of the triangle is equal to option a. x + 13.

Perimeter of the triangle is equal to

= 9x + 6

First side of the triangle = 5x

Second side of the triangle = 3x - 7

Let 'n' be the third side of the triangle

perimeter of the triangle = 9x + 6

⇒ 5x + 3x - 7 + n = 9x + 6

⇒ n + 8x - 7 = 9x + 6

⇒ n = 9x -8x + 6 + 7

⇒ n = x + 13

Therefore, the third side of the triangle with given perimeter of the triangle is equal to option a. x + 13.

The above question is incomplete , the complete question is :

A triangle has a perimeter of 9x + 6. the first side of the triangle has a length of 5x, and the second side has a length of 3x − 7. what is the length of the third side of the triangle?

a. x + 13       b. x − 1            c. 8x − 7         d. 17x − 1

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The roots of the quadratic equation are -

{x} = 4 ± i(√2/2)

The  general form of a quadratic equation is -

y = f(x) = ax² + bx + c

Given is the quadratic equation as -

f(x) = x² - 8x + 17

We can write the roots of the equation as -

x = {- b ± √(b² - 4ac)}/2a

x = {8 ± √(64 - 68)}/2

x = {8 ± i√2}/2

x = 4 ± i(√2/2)

Therefore, the roots of the quadratic equation are -

{x} = 4 ± i(√2/2).

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Answer:

Any line except a vertical line represents a linear function.

Step-by-step explanation:

Any "diagonal" line is a linear function. Even a horizontal line represents a linear function. Only a vertical line does NOT represent a linear function.

Answer:

it will be £960

Step-by-step explanation:

first £800×20/100

simplify £8×20

£160= VAT

Total cost=VAT+ normal cost

£160+£800

=£960

Answer:

The statement "A = (1/2) (B)(B + 5)" represents the area of a triangle, where B is the base of the triangle and (B + 5) is the height. This formula is used by the carpenter to calculate the area of a triangle with a given base and height.

Step-by-step explanation:

The value of (f - g)(-1) is 5.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = -5x³ - 8x² - 4x + 3

g(x) = 3x³ - 2x² - 8x - 4

Now,

(f - g)(x)

= f(x) - g(x)

= -5x³ - 8x² - 4x + 3 - (3x³ - 2x² - 8x - 4)

= -5x³ - 8x² - 4x + 3 - 3x³ + 2x² + 8x + 4

= -8x³ - 6x² + 4x + 7

Now,

(f - g) (-1)

Substitute x = -1.

= -8(-1)³ - 6(-1)² + 4(-1) + 7

= -8 x -1 - 6 - 4 + 7

= 8 - 6 - 4 + 7

= 8 - 10 + 7

= 15 - 10

= 5

Thus,

(f - g)(-1) = 5

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The dimensions are 5 units each

The area of the rectangle is 25 units

It is important to note that algebraic expressions are defined as expressions that are composed of variables, terms, cofficients, constants and factors.

They are also described as expressions with mathematical operations.

From the information given, we have that;

x² - 5x + 3x - 15

To solve the quadratic equation, let us use the factorization method

Group the values in pairs

(x² - 5x) + (3x - 15)

factor the terms

x(x -5) +3(x - 5)

Then, x + 3 = 0

x = -3

And x - 5 = 0

x =5

But area of a rectangle is;

= Length× width

= 5 × 5

= 25 square units

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Rounding off the 1004.8 into 3 significant figures will give 1000.

Since significant figures are established as digits, they are also known as significant digits. By counting all of the values beginning with the first non-zero digit on the left, it is possible to determine the number of significant digits.  

For example, the number of significant figures in 567 is 3.
The number of significant figures in 2.671 is 4.  

Here we have a number    

1004.8 need to be rounded off for 3 significant figures  

Since 4 is less than 5 then the resultant number = 1000  

[ 4 and 8 neglected since 4 < 5]

Therefore,

Rounding off the 1004.8 into 3 significant figures will give 1000.

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Answer:

Let's call the total area of the common space "A". Since the quiet area takes up one-third of the space, its area is A/3.

The scale of the plan is 1 ft.: 4 cm, which means that one foot on the plan represents 4 cm in real life. So, the area of the social area on the plan is 4 times smaller than the actual area of the social space.

Therefore, the actual area of the social space is (A - A/3) = 2A/3. And the area of the social area on the plan is (2A/3) / 4.

Area of the social area on the plan is (2A/3) / 4.

Here,

Let the total area of the common space "A".

Since the quiet area takes up one-third of the space, its area is A/3.

The scale of the plan is 1 ft.: 4 cm

So,

One foot on the plan represents 4 cm in real life.

So, the area of the social area on the plan is 4 times smaller than the actual area of the social space.

Therefore, the actual area of the social space is (A - A/3) = 2A/3.

Thus the area of the social area on the plan is (2A/3) / 4.

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The values and graph of the equation 3x - 2y = 6 is attached below while the slope is 3/2

The equation of a straight line can be represented in various forms. One of the most commonly used forms is the point-slope form, which is represented as:

y - y1 = m (x - x1)

where (x1, y1) is a point on the line, and m is the slope of the line, which is the rate of change of y with respect to x.

Another common form of the equation of a line is the slope-intercept form, which is represented as:

y = mx + b

where m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.

In this problem, we need to write the table of values and the find the slope of the line.

3x - 2y = 6

rewriting this equation;

2y = 3x - 6

y = 3x/2 - 3

when y = 0

0 = 3x/2 - 3

3x/2 = 3

3x = 2 * 3

3x = 6

x = 2

when x = 0

y = 3(0)/2 - 3

y = 0 - 3

y = -3

The slope of the line can be calculated using the two points from above.

slope (m) = y₂ - y₁ / x₂ - x₁

m = -3 - 0 / 0 - 2

m = 3/2

The slope is 3/2

The graph of the equation is attached below

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To mode of given data set of number of days worked in october for 10 programmers of a software company is 7 and 14.

The mode of a data set is the value that appears most frequently. In this case, we can see that both 7 and 14 appear twice, while all other values appear only once. Therefore, there are two modes in this data set: 7 and 14.

To solve mathematically, we can use the mode formula:

mode = value with the highest frequency

In this case, we have two values with the highest frequency, which are 7 and 14. Therefore, the mode of given data set is 7 and 14.

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The percentage increase of the gas would be 2.5%.

We can calculate the value of the percentage increase by the following formula,

percentage increase = (final value - initial value) / initial value × 100%

As per the given question, we have

initial value = $2.81 , and final value = $2.88

Substitute the values in the above formula, and we get

percentage increase= (2.88 - 2.81 ) / 2.81 × 100%

percentage increase = (0.07) / 2.81× 100%

percentage increase = 0.0249 × 100%

Apply the multiplication operation, and we get

percentage increase = 2.49%

Thus, the percentage increase of an item would be 2.5%.

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First, use the equation for a hemisphere. Since a sphere's equation is [tex]\frac{4}{3}\pi r^{3}[/tex], and a hemisphere is half a sphere, we can use the equation [tex]\frac{2}{3}\pi r^{3}[/tex]. We know the radius is 6 inches, and we can approximate pi as 3.14, so now let's plug in our values:

[tex]\frac{2}{3}\ (3.14) 6^{3}=\frac{2}{3} \ (3.14)(216)= \frac{2}{3}(678.16)= 452.16[/tex]

The volume of the hemisphere is about [tex]452.16 in^{3}[/tex].

The formula for the volume of a cone is [tex]\pi r^{2}\frac{h}{3}[/tex]. Again, let's plug in our values:

[tex](3.14)(36)\frac{6}{3} =(3.14)(36)(2)=(3.14)(72)=226.08[/tex]

The volume of the cone is about [tex]226.08 in^{3}[/tex].

Subtract 226.08 from 452.16 and you get 226.08.

The volume of the remaining solid will be [tex]226.08 in^{3}[/tex].

Answer: A. Passenger train: 52 mph B. Freight train: 24 mph

Step-by-step explanation: