What is the volume of a rectangular prism with a length of 2.5 cm, a width of 3.1 cm and a height of 1.2 cm?



A. 7.75 cm³
B. 8.1 cm³
C. 8.3 cm³
D. 9.3 cm³

x^2 + y^2 - 10y + (-85) is equation of the circle with center (0, -5) containing the point (-√109,-6).

To find the equation of a circle with a given center and containing a given point, we can use the distance formula. The distance formula is given by:

d = √((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) is the center of the circle and (x2, y2) is the point on the circle. In this case, the center of the circle is (0, -5) and the point on the circle is (-√109, -6). Plugging these values into the distance formula, we get:

d = √((-√109 - 0)^2 + (-6 - (-5))^2)

d = √((-√109)^2 + (-1)^2)

d = √(109 + 1)

d = √110

Since the point (-√109, -6) is on the circle, the distance from the center of the circle to this point is the radius of the circle. Therefore, the radius of the circle is √110.

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (0, -5) and the radius is √110, so the equation of the circle is:

(x - 0)^2 + (y - (-5))^2 = (√110)^2

x^2 + y^2 - 10y + 25 = 110

x^2 + y^2 - 10y + (-85) = 0

This is the equation of the circle with center (0, -5) and containing the point (-√109, -6).

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So the angle of the resultant vector is approximately 53.13 degrees.

To find the angle of the resultant vector, you can use trigonometry to break the two vectors into their x and y components and then use the arctangent function to find the angle.

First, let's find the x and y components of the first vector (the one that travels 45 meters at an angle of 25 degrees south of east). To do this, we can use the trigonometric functions sine and cosine. The x component is equal to the distance traveled (45 meters) times the cosine of the angle (25 degrees), and the y component is equal to the distance traveled times the sine of the angle.

In this case, the x component of the first vector is 45 meters * cos(25 degrees) = 39.74 meters. The y component of the first vector is 45 meters * sin(25 degrees) = 22.36 meters.

Now let's find the x and y components of the second vector (the one that travels 30 meters north). The x component of this vector is 0 meters (since it doesn't move in the east-west direction), and the y component is 30 meters (since it travels 30 meters in the north direction).

To find the resultant vector, we can add the x components and y components of the two vectors. The x component of the resultant vector is 39.74 meters + 0 meters = 39.74 meters, and the y component of the resultant vector is 22.36 meters + 30 meters = 52.36 meters.

To find the angle of the resultant vector, we can use the arctangent function (also known as the inverse tangent function). The angle is equal to the arctangent of the y component divided by the x component.

In this case, the angle is equal to arctan(52.36 meters / 39.74 meters) = arctan(1.318) = 53.13 degrees.

So the angle of the resultant vector is approximately 53.13 degrees.

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Find the x and y components of the initial vector first (the one that travels 45 meters at an angle of 25 degrees south of east). The trigonometric functions sine and cosine can be used to do this. The y component is equal to the distance traveled times the sine of the angle, and the x component is equal to the distance traveled times the cosine of the angle, or 45 meters times the cosine of the angle, or 25 degrees.

In this case, the x component of the first vector is 45 meters * cos(25 degrees) = 39.74 meters. The y component of the first vector is 45 meters * sin(25 degrees) = 22.36 meters.

The two vectors' x and y components can be added to determine the resultant vector. The resultant vector has two components: an x component of 39.74 meters plus 0 meters equals 39.74 meters, and a y component of 22.36 meters plus 30 meters equals 52.36 meters.

The arctangent function can be used to determine the angle of the resulting vector (also known as the inverse tangent function). The angle is determined by dividing the y component's arctangent by its x component.

In this case, the angle is equal to arctan(52.36 meters / 39.74 meters) = arctan(1.318) = 53.13 degrees.

So the angle of the resultant vector is approximately 53.13 degrees.

Five different ways to prove the given triangles are similar is given by :

SAS, SSS, ASA, AA, and RHS.

Five different ways to prove triangles are similar is given by:

1. SAS (Side-Angle-Side) : If the corresponding sides of one triangle are in proportion to the other triangle and included angle is of equal measure.

2. SSS(Side-Side-Side): If the corresponding sides of one triangle are in proportion to the other triangle

3. ASA(Angle - Side- Angle) : If the two angles of one triangle are equal to the angles of other triangle and included side is in proportion.

4. AA( Angle-Angle) : If two adjacent angle of one triangle is equal to the measure of other triangle.

5.  RHS(Right angle- Hypotenuse - side). If the hypotenuse and one of one right triangle are in proportion to another.

Therefore, five different ways to prove the given triangles are similar is given by : SAS, SSS, ASA, AA, and RHS.

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Graphing, substitution, and elimination are the three techniques used to solve systems of equations.

There is only one way to know the unknown variable X. As a result, d has a value of 1. To find an equation, we must know the variable(s) that are missing as well as any associated known variable(s).

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

The first-degree equations are linear equations. This is the formula for a straight line. Ax+by+c = 0, where a and b are both zeros, is the conventional form of a linear equation.Anything connected to a line is said to be linear.

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Answer:

9 :)))))))))))

Step-by-step explanation:

directly proportional means

y = kx

to find k we use the first given pair (8, 6) :

6 = k×8

k = 6/8 = 3/4

so, for x = 10

y = 3/4 × 10 = 30/4 = 7.5

To find the inverse of a function you just have to switch the x and the y and then solve for y.

Inverse Function

An inverse function or an anti function is defined as a function, which can reverse into another function. In simple words, if any function “f” takes x to y then, the inverse of “f” will take y to x. If the function is denoted by 'f' or 'F', then the inverse function is denoted by f^-1 or F^-1.

The inverse function returns the original value for which a function gave the output.

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Answer: slope= change in y-intercept and x-intercept

Step-by-step explanation:

1-9=-8

-8- -9=1

-8/1=-8

When two parallel lines are cut by a transversal, eight angles are formed. Interior angles are supplementary to corresponding exterior angles and the sum of an interior and its corresponding exterior angle is 180 degrees.

Two parallel lines are cut by a transversal, eight angles are formed. Four of these angles are interior angles, which are the angles formed between the two lines and the transversal that lie within the region bounded by the parallel lines. The other four angles are exterior angles, which are the angles formed between the two lines and the transversal that lie outside the region bounded by the parallel lines. Interior angles are equal in measure and are supplementary to the corresponding exterior angles. In other words, the sum of an interior angle and its corresponding exterior angle is equal to 180 degrees. Understanding the properties of interior and exterior angles is important in geometry, as they can be used to prove the parallelism of lines.

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D.

The line never increases, so we can cancel out A and C.

The line starts off straight, so it's not B.

So, the answer is D. since it starts off constant and then decreases sharply.

Answer: 8*8=64

               6*6*=216

64-216+21=0

Step-by-step explanation:

Answer:

  C.) x = -3, cross; x = 0, touch; x = 1, cross; x = 3, cross

Step-by-step explanation:

You want the zeros and their multiplicity of f(x) = x^5 -x^4 -9x^3 +9x^2, along with a description of whether the graph crosses or touches the x-axis at each zero.

The equation can be factored as ...

  f(x) = x^2(x^3 -x^2 -9x +9)

The cubic can be factored as ...

  x^3 -x^2 -9x +9 = x^2(x -1) -9(x -1) = (x^2 -9)(x -1)

and the quadratic factor can be factored as the difference of square. The complete factorization is then ...

  f(x) = x^2(x -1)(x -3)(x +3)

The zeros are the values of x that make the factors zero:

When the multiplicity of a zero is even, the graph touches the x-axis. Here, that means the graph will touch at x=0, where the multiplicity of the zero is 2.

When multiplicity is odd, the graph will cross the x-axis. The graph crosses at the zeros -3, -1, +3.

__

Additional comment

As soon as you recognize that the x^2 factor means the multiplicity of x=0 is even, you can identify the correct answer choice: the only one that says "touch" for x=0.

The weekly average proportion of opposed feeling is 0.0375. (Option D)

A sample proportion is the proportion of individuals in a sample who have a particular characteristic of interest. It refers to the number of successes (success means that an individual possesses the characteristic of interest) of the sample divided by the sample size. According to the provided data, the number of successes in the sample size is 30 and the sample size is 100. Hence, the sample proportion is:

Sample proportion = 30/100 = 0.3

As the survey is conducted weekly for eight weeks, the average proportion of the samples is determined by sample proportion divided by number of weeks. Hence,

Average proportion = 0.3/8 = 0.0375

Note: The question is incomplete. The complete question probably is: A Glassboro township is concerned about adverse public reaction to a trash recycling project that is currently in progress. Because of this, the commissioner of public works has authorized a weekly survey to be constructed of township residents. Each week, a sample of 100 residents are questioned on their feeling toward the project. The results to date are shown below. What is the weekly average proportion of opposed feeling? (3 pts.) a. 0.0250 b. 0.1250 c. 0.3000 d. 0.0375 e. None

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The required coordinates of point B are (2, 3) which is the correct answer would be option (C).

To find the coordinates of point B, we can use the midpoint formula.

The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) are given by the formula (x₁ + x₂)/2, (y₁ + y₂)/2.

As per the question, we are given the coordinates of points A and O, which are (4, 5) and (3, 4), respectively.

We can use these coordinates to find the coordinates of point B, which is the midpoint of line segment AO.

Let the coordinates of B would be (x, y)

Substituting the coordinates of points A and O into the midpoint formula gives us :

3 = (x+4)/2 ; 4 = (y+5)/2

6 = x +4; 8 = y + 5

x = 2; y = 3

Therefore, the required coordinates of point B are (2, 3).

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The eccentricity of the conic section below is: A. closer to 0 than 1.

In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.

In Mathematics, there are four (4) types of conic section and these include the following with their eccentricity:

In this context, we can reasonably infer and logically deduce that the eccentricity of the conic section is closer to zero (0) than one (1) because it represents a circle.

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An asymptote is a line that a curve approaches but never touches, so it is not part of the curve itself. As a result, an asymptote is not a function. However, the curve that approaches an asymptote may or may not be a continuous function.

A function is continuous if it is defined for all values in its domain and there are no breaks or jumps in the graph of the function.

For example, consider the function f(x) = 1/x. This function has a horizontal asymptote at y = 0, but it is not continuous at x = 0 because the value of the function is undefined at this point (division by zero is not allowed).

On the other hand, consider the function f(x) = ². This function has no asymptotes and is continuous for all values of x.

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Answer:

width is 3.56

Step-by-step explanation:

Area is = width x length

so Area/length

so 56.96/16=3.56

The width of the rectangle is 3.56 m and the perimeter is 39.12 m.

To find the width of the rectangle,

We need to use the formula for the area of a rectangle, which is:

Area = Length x Width

We know that the area of the rectangle is 56.96 m², and the length is 16 m. So,

We can substitute these values into the formula and solve for the width:

56.96 m² = 16 m x Width

Width = 56.96 m² / 16 m

Width = 3.56 m

Therefore, the width of the rectangle is 3.56 m.

To find the perimeter of the rectangle,

We need to use the formula:

Perimeter = 2 x Length + 2 x Width

We know that the length is 16 m and the width is 3.56 m,

So we can substitute these values into the formula and solve for the perimeter:

Perimeter = 2 x 16 m + 2 x 3.56 m

Perimeter = 32 m + 7.12 m

Perimeter = 39.12 m

Therefore, the perimeter of the rectangle is 39.12 m.

In conclusion, the width of the rectangle is 3.56 m and the perimeter is 39.12 m when the area is 56.96 m² and the length is 16 m.

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Therefore  the probability that the chip belongs to bowl c is 1/3.

Probabilities can be expressed as proportions with a 0–1 range or as percentages with a 0%–100% range. If an event has a probability of 1, it is very certain to occur; if it has a probability of 0, it has no chance of occurring. There are 45 chances out of 100 that an event will occur when its probability is 0.45 (45%).

Here,

A : 2 Red chips

B : 2 White chips

C: One Red and one White chip

P(selecting any bowl) = 1/3

1) We have to find P(W).

The selected chip can be white if it is either selected from Bowl B or Bowl C.

Symbolically this can be written as

P(W) = P(Bowl B and White chips) + P(Bowl A and White chips)

P(W) = [(1/3) × 1/1)] + [(1/3) × (1/2)]

P(W) = (1/3) + (1/6)

P(W) = 1/2

P(W) = 0.5

2) There is only one bowl with both of white and red chips and that bowl is bowl C. So it is possible the other chips in the bowl to red only if it has been selected from Bowl C.

So ,We need to find P(Bowl C | W).

P(Bowl C | W) = P(Bowl C and W)/P(W)

P(Bowl C | W) = (1/3) × (1/2)/(1/2)

P(Bowl C | W) = 1/3

Hence, the required probability is 1/3.

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The mode for a particular set of observations is 2,3,4,5,6 since it occurs the majority of the time.

The mode formula is described in statistics as the formula for calculating the mode of a given collection of data. The value that occurs most frequently in a particular set is referred to as the mode, and the mode differs across grouped and ungrouped data sets. The mode may be calculated quite easily. Put all of the numbers in a given set in order, either lowest to highest or highest to lowest, and then count how many times each number appears in the set. The mode is the one that appears the most.

Here,

given set of observation:

2 2 2 3 3 3 4 4 4 5 5 5 6 6 6

Mode is the number which occurs the highest time.

So here 2,3,4,5,6 occurs the highest times(3 times).

So,2,3,4,5,6 is the mode.

The mode for given set of observation is 2,3,4,5,6 as it occurs most time.

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Katie needs 9.5 quartz of the 12% sugar solution to make the 10% sugar solution.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The volume of the 12% sugar solution required, 'X' for a given volume of the 8% sugar solution, 'Y' is;

X = (2·Y + 15)/2

When the volume of the 8% sugar solution, Y = 2 quartz, the volume of the 12% sugar solution required, X = 9.5 gallons

The data of the sugar solutions are;

The volume of 5% sugar solution Kate has = 3 quarts

The volume of the 12% sugar solution = X

Let 'Y' represent the volume of the 8% sugar solution, we have;

The volume of the resultant solution, Z = X + Y + 3

The concentration of the resultant solution = 10%

0.05 × 3 + 0.08·Y + 0.12·X = 0.1·(X + Y + 3)

Solving gives the relationship between the volume of the 12% sugar solution, 'X', and the 8% sugar solution, 'Y' in quartz, as follows;

X = (2·Y + 15)/2

When the volume of the 8% sugar solution, Y = 2 quartz, we have;

X = (2 × 2 + 15)/2 = 9.5 Quartz

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The solution to the system of equations y = -5x + 3 and y = 1 is x = 0.4 and y = 1.      

Therefore, the answer is (0.4, 1).

To solve the system of equations :

y = -5x + 3                                            (1)

y = 1                                                      (2)

In the given equation, coefficient of y is same in both equations. So subtracting equation (2) from equation (1) we get

y - y = -5x + 3 - 1

0 = -5x + 2

Adding 5x on both sides

0 + 5x = -5x + 2 + 5x

5x = 2

Dividing both sides by 5

x = 2/ 5

x = 0.4  

--The question is incomplete, answering to the question below--

"What is the solution to the system of equations?

y = -5x + 3 and y = 1"

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Answer:

Step-by-step explanation:

To model the relationship between Vreel's rews and corazs, we can set up a system of equations in standard form.

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants and x and y are variables.

We know that Vreel purchased a total of 22 rews and corazs, and that the rews cost $8 each and the corazs cost $3 each. We can use this information to set up the following two equations:

The first equation represents the total cost of the rews: 8x + 0y = 96

The second equation represents the total number of rews and corazs that Vreel purchased: 1x + 1y = 22

Together, these two equations form a system of equations that can be used to model the relationship between Vreel's rews and corazs.

I hope this helps! Let me know if you have any other questions.

Answer:

$48/4 pizzas

Step-by-step explanation:

⭐ A ratio is a fraction that relates one variable to another.

⭐ A proportion is when you make two ratios equal to each other to solve for one of the variables.

We want to find what it costs for Mike to buy 4 pizzas. To achieve this, we must make a proportion.

The given quadratic equation 2x²-4x+3=0 has no real roots.

The roots of the quadratic equation are real and equal if the discriminant equals zero, a, b, and c are real values and a≠0.

The roots of the quadratic equation are real and unequal if the discriminant is greater than zero, a, b, and c are real values, and a≠0.

The quadratic equation's roots are imaginary and unequal if the discriminant is less than zero, a, b, and c are real integers and a≠0.

2x²-4x+3=0

Comparing the equation with ax²+bx+c=0

We know that,

D = b²-4ac

  = (-4)²-4(2)(3)

  = 16- 24

  = -8

Since D < 0

Hence, the given equation 2x²-4x+3=0 has no real roots.

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The radius of the cylinder 37cm.

cylinder's entire surface area is equal to 2r(h+r).

total surface area = 1936 square cm

height=7 cm

radius is

therefore,

2πr(h+r)=1936

2πr(r+7)=1936

44(r+7)=1936

r+7 = 1936/44

r+7=44

r= 44-7 =37

r=37cm.

The radius of the cylinder 37cm.

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Answer:

D. Increase in assets

Step-by-step explanation:

The entry "Cash 750,000" is listed as a debit in the T-account because it is an increase in assets. In double-entry bookkeeping, a debit is used to record an increase in assets and a credit is used to record a decrease in assets. In this case, the business received cash in exchange for the airplane, which represents an increase in the business's assets. So the Cash account is debited and the Airplane account is credited.