Find the Volume of the following cone.


A. 150.72 in3


B. 16.75 in3


C. 8.37 in3


D. 75.36 in3

Option A : The circle represented in the third quadrant has the centre lying at (-3, -1)

The location of a circle in the Cartesian plane is represented by a circle equation. We can construct the equation for a circle if we know the location of the circle's center and how long its radius is. All of the points on the circle's circumference are represented by the circle equation.

The group of points whose separation from a given point has a constant value are represented by a circle. The radius of the circle, abbreviated r, is a constant that describes this fixed point, which is known as the circle's center. The equation (x- x₁)²+(y-y₁)²=r²describes a circle with a center at (x₁,y₁) and a radius of r.

There are different forms to represent the equation of a circle :

The equation of the circle is

(x + 3)² + (y + 1)² = 9

The centre of the circle will be at (-3, -1) from the equation .

Option A :The circle represented in the third quadrant has the centre lying at (-3, -1)

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The difference between the area of Figure A and the area of Figure B is 2ft, So correct option is A.

A square grid is a two-dimensional pattern formed by a series of equally spaced horizontal and vertical lines that intersect at right angles, creating a regular array of squares. It can be thought of as a flat, two-dimensional lattice with a consistent spacing between the lines. A square grid can be used to represent many things, such as a map, a game board, a city plan, or a spreadsheet. In mathematics and geometry, a square grid is often used to represent coordinate systems, where each intersection of horizontal and vertical lines corresponds to a specific point with a unique set of coordinates. Square grids are also used in graphic design and art as a foundation for creating patterns, textures, and compositions.

The area of A= 3×4= 12 ft

The area of B= 4×3×1/2×4×2×1/2= 10 ft

12ft - 10 ft= 2ft

Cut down the triangle on the right of figure A, move it to left to form a rectangle, and then calculate the area of A.

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The complete question is:

The operation you would use is multiplication; there is about 0.95 liter in 1 quart. Multiply when converting larger units to smaller units. (option C).

Multiplication is the operation that is used to determine the product of two or more numbers. The sign that is used to denote multiplication is ×. Multiplication is one of the operations in maths. Other operations in mathematics ae addition, division and subtraction.

1 quart = 0.95 liters

In order to convert 100 quart to liters, multiply 100 by 0.95

0.95 x 100 = 95 liters

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Answer: The constant of proportionality and the unit rate represent the same value. A constant of proportionality can be any value, including fractions and decimals. The main difference between the constant of proportionality and a unit rate is how they are written.

The graph of the system of equations can be seen on the last image, there we can see that the solution is (-4, -3).

To do so, we just need to graph both equations no the same coordinate axis, and then find the point where the graphs intercept (if they do).

That point will be the solution of the system of equations.

Here the system is:

y = 2x + 5

y = (1/2)*x - 1

And the graph of the equations can be seen below. There we can see that the lines intercept at (-4, -3), so that is the solution.

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The value of variable m is 4.

Two or more expressions with an Equal sign is called as Equation.

We have to find value of m

As Y is between X and Z it is taken as the midpoint.

The values of XY, YZ and XZ are given as below.

XY=9m−3 , YZ=6m+1 , and XZ=13m+6 .

We need to find the value of the variable m.

If we add xy and yx we get xz.

So by the equation xy+yz=xz we get the value m.

9m-3+6m+1=13m+6

Add the like terms

15m-2=13m+6

15m-13m=2+6

2m=8

Divide both sides by 2

m=4

Hence, the value of variable m is 4.

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Answer:

(7x+3)

Step-by-step explanation:

Answer:

[tex]3 {x}^{4} - 6 {x}^{3} - 21 {x}^{2} - 2x + 8[/tex]

Step-by-step explanation:

One root being i, an imaginary number is throwing me off.. but I can give it a shot if youd like.

So a coefficient is the number Infront of the X. so for 6X^2, the coefficient is 6.

It says the Leading Coefficient is 3. The one option for that is 3x^4, so that will be the in the first blank.

The exponents now (the little numbers) start with 4 and go down 1 after each block. Which means the last two blocks will have no little numbers since it would be 1 and 0. Those don't need exponents.

For the block after the 21x^2, we have two choices. Either 6x or 2x

For the last block we have two choices also.

8 or 24

To find if it's 6x or 2x...

Its showing roots of -2, i, and 4 with multiplicity of 1, which means

x^2-4x+2x+8

x^2-2x+8

We have 2x and 8

Those must be the other two blocks

The subject pronoun requested would be they and in Spanish would be "ellas".

In the Spanish language, there are two feminine pronouns that are often used as subjects in sentences, these pronouns are:

Ella - This is a singular pronoun equivalent to she

Ellas - This is a plural pronoun equivalent to "they", but again it is exclusively used for feminine nouns such as a group of women.

Based on this, the pronoun you are looking for is the pronoun "ellas", here is an example of how to use it: Ellas son amables.

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The new average of the students is 25.368.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

Given that, in a group of 24 students attending a party, the average age is 25.3 years.

A 27-year-old student joins the party.

So, the new average is (24×25.3+27)/25

= 634.2/25

= 25.368

Therefore, the new average of the students is 25.368.

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The value of a for the given expression will be -3.31.

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.

Given that the expression is 3.6= − a/0.8 − 1.6 − 0.8 a ​ −1.6. The value of a will be calculated as below,

3.6 = − a/0.8 − 1.6 − 0.8 a ​ −1.6

3.6 + 1.6 + 1.6 = -a / 0.8  - 0.8a

6.8 = ( -a - 0.64a ) / 0.8

5.44 = -1.64a

a = -3.31

Therefore, the value of a will be -3.31.

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Answer: Given the function f(x) = -3x^3 +3x^2+ 3x + 3, the following is true:

-It is not necessarily positive or negative as the value of f(x) depends on the value of x.

-It is a cubic function as it contains an x^3 term.

-The domain is all real numbers as there are no restrictions on the input x.

-It has at most 3 solutions as it is a cubic function and cubic functions can have at most 3 real roots.

-It is a polynomial function as it is a finite sum of terms involving non-negative integer powers of x.

Step-by-step explanation:

The polynomial x² + 6x + 9 can be factored as (x + 3)(x + 3).

What is polynomial?

The term "polynomial" in mathematics refers to a mathematical expression that consists of two or more algebraic terms that are added, subtracted, or multiplied (no division!). Constants and positive exponents are frequently used, along with at least one variable, in polynomial expressions. Polynomial definition: x2 = 4x + 7

A polynomial is an equation made up of indeterminates and coefficients that only uses addition, subtraction, multiplication, and positive-integer powers of variables.

The polynomial x² + 6x + 9 can be factored as (x + 3)(x + 3).

Therefore, the correct match is:

x² + 6x + 9 ------> (x + 3)(x + 3)

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Answer:902

Step-by-step explanation:

41×22=902

A line running through the points (2, 0) and (0, 4) has a slope of -2.

The slope of a line is defined as the change in y-axis of the line to the x-axis. Mathematically, it is expressed as:

Slope = Δy/Δx

Using the coordinate points (2, 0) and (0, 4) to determine the required slope:

Slope = 4-0/0-2
Slope= 4/-2
Slope = -2

Hence the slope of the line passing through the point (2, 0) and (0, 4) is -2

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If from the top of a 72 m high vertical cliff, a boat has an angle of depression of 32° then  the distance of boat from the base of the cliff is, 115 m.

An angle is a mathematical term, which we can define, when two straight lines or rays meet at a common endpoint. The common point is called the vertex of an angle. The word angle comes from a Latin word named ‘angulus,’.

Interior angles:- The inner angle made by the intersection of two polygonal sides.

Exterior angles:- The outer angle made by the intersection of two polygonal sides.

We can use trigonometry to solve for the distance of the boat from the base of the cliff.

Let's call the distance from the base of the cliff to the boat "d".

Then we have:

tan(32°) = 72 / d

Solving for d, we get:

d = 72 / tan(32°)

d = 115.22

Rounding to the nearest whole number, d = 115.

So the boat is 115 meters away from the base of the cliff.

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Answer: 23

Step-by-step explanation:

first we put the values a=3,b=4 and d=-5. in a/b-d=2c/b equation which is given in the question. so,it gives us 3/4+5=2c/4,3+20=2c/4×4,3+20=c.so,the value of c is 23

Answer:

[tex]\huge\boxed{\sf c = -17/2}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{a}{b} - d=\frac{2c}{b}[/tex]

Where, a = 3, b = 4, d = 5

[tex]\displaystyle \frac{3}{4} - 5 =\frac{2c}{4} \\\\Take \ LCM\\\\\frac{3-(5 \times 4)}{4} = \frac{c}{2} \\\\\frac{3-20}{4} = \frac{c}{2} \\\\\frac{-17}{4} = \frac{c}{2} \\\\Cross \ Multiply\\\\-17 \times 2 = 4 \times c\\\\-34 = 4c\\\\Divide \ both \ sides\ by \ 4\\\\-34/4 = c\\\\c = -17/2\\\\\rule[225]{225}{2}[/tex]

Answer:

The equation to represent Frederick's account balance after t years is:

A = 1050 * (1 + (0.051/365))^(365t)

Where A is the account balance and t is the number of years.

The required inequality is 437 + 36x ≥ 500, where x is the number of miles he should walk each day to meet his goal.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

Given,

His trip length was 437 miles, and he had 36 days left.

If x is the number of miles covered each day, then the remaining miles to

Then the remained miles to cover = number of days remained × miles  covered in each day

Thus, his trip length = already completed miles + remaining miles

= 437 + 36x

As per the question,

Total miles ≥ 500 miles

⇒ 437 + 36x ≥ 500

Thus, the required inequality is 437 + 36x ≥ 500.

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The number of digits which one would need to number all 178 buildings on a street is  426 numbers.

This is referred to as a single symbol used alone or in combinations, to represent numbers in a positional numeral system.

1-9 = 1 × 9 = 9

10-99 = 90 × 2 = 180

100-178 = 79 × 3 = 237

The total = 9 + 180 + 237 = 426 numbers.

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The option that shows a proportional relationship is selling 94 cars in 1 year (option D)

Two numbers or elements are said to be proportional if they have the same ratio. In this case, the ratio is 24 cars every 3 months, which can be simplified as 8 cars per month.

Based on this ratio, the option that is proportional is selling 96 cars in a year because this will means 96 cars in 12 months and 96/12= 8, which shows the ratio is the same.

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Using matrix multiplication and addition, the total production cost for the items ordered by a customer is $2,692.

The total production cost consists of the costs of direct materials, direct labor, and overheads.

Overhead costs include indirect costs of materials, labor, and other production costs not traceable to each produced unit.

The total production cost is determined using matrix multiplication where the number of columns of the first matrix equal the number of rows of the second matrix.

                      Desks     Chairs     Tables    Cabinets

Materials         $5            $5           $10           $13

Labor               15              12             10             18

Overhead         5               5              3             20

              Number

Desks         10

Chairs        60

Tables       40

Cabinets     2

Production Costs for the Ordered Items:

                      Desks     Chairs     Tables    Cabinets              Total

Materials       $150         $300       $400      $26 ($13 x 2)     $876

Labor              150            720         400         36 ($18 x 2)     1,306

Overhead        50            300         120          40 (20 x 2)         510

Total costs  $350       $1,320      $920       $102               $2,692

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What is the total production cost of the ordered units?

The area of the rectangle is given by the equation A = ( 9x² - 64 ) yards²

The area of the rectangle is given by the product of the length of the rectangle and the width of the rectangle

Area of Rectangle = Length x Width

Given data ,

Let the area of the rectangle be represented as A

Now , the equation will be

Let the width of the rectangle be W = ( 3x - 8 ) yards

Let the length of the rectangle be L = ( 3x + 8 ) yards

Now , Area of Rectangle = Length x Width

Substituting the values in the equation , we get

Area of Rectangle = ( 3x - 8 ) ( 3x + 8 )

On simplifying the equation , we get

Area of Rectangle = ( 3x )² - ( 8 )²

Area of rectangle A = ( 9x² - 64 ) yards²

Hence , the area of the rectangle is ( 9x² - 64 ) yards²

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Answer:

14/70

Step-by-step explanation:

On solving the provided question, we can say that  Make a table with the x,y coordinates of each vertex.

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

Make a table with the x,y coordinates of each vertex.

Vertical left side of the table  A ,B,C D.. A again (From top to bottom)

Horizontal top of the table : x,y(  From left to right)

Start at any vertex and go around the polygon in either direction.

Add the starting vertex again at the end.

Combine the first two rows by:

Multiplying the first row x by the second row y

Multiplying the first row y by the second row x

Subtract the second product form the first.

Repeat this for rows 2 and 3, then rows 3 and 4 and so on.

Add these results, make it positive if required, and divide by two.

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Answer:

7/2

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

1. 2x + 6 = 8x

2. 8x + 8x = 16x

3. 16x - 11 = 5x

The money that Salma has to pay if she goes on 6 rides is $40 and if she goes on r rides then she has to pay 10+5r

A solution of an equation is any value of the variable that satisfies the equality, that is, it makes the Left Hand Side (LHS) and the Right Hand Side (RHS) of the equation the same value.

Given here: Admission price=$10 and ride fee= $5

Now if Salma goes for 6 rides than we have

Total fee= 10+5×6

               =$40

And if Salma decides to go for r rides than we can express the total cost as some function of the number of rides r

T(r)=10+5r

Hence, The money that Salma has to pay if she goes on 6 rides is $40 and if she goes on r rides then she has to pay 10+5r

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