The length of a rectangle of fixed area varies inversely as the width. If the
length of the rectangle is 6 feet when the width is 12 feet, find the length of the
rectangle when the width is 4 feet

The volume of the liquid in the conical flask is 980 π cm³

What is a Cone?

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.

The volume of a cone is given by the equation

Volume of Cone = ( 1/3 ) πr²h

where r is the radius of the cone

h is the height of the cone

Given data ,

Let the two cones be A and B

Now , the smaller cone be A

The larger cone be B

The radius of the smaller cone is r = 8 cm

The height of the smaller cone is h = 20 cm

Now , the volume of the smaller cone V = ( 1/3 ) πr²h

Substituting the values in the equation , we get

Volume of cone A = ( 1/3 ) πr²h

Volume of cone A = ( 1/3 ) π x 8 x 8 x 20

Volume of cone A = 426.67 π cm³

Now ,

The larger flask is filled with height H = 20 cm

The radius of the larger cone is R = 14 cm

The height of the larger cone is H = 15 cm

Now , the volume of the smaller cone V = ( 1/3 ) πR²H

Substituting the values in the equation , we get

Volume of cone B = ( 1/3 ) πR²H

Volume of cone B = ( 1/3 ) π x 14 x 14 x 15

Volume of cone B = 980 π cm³

Therefore , the volume of the larger cone B is 980 π cm³

Hence , The volume of the liquid in the conical flask is 980 π cm³

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Perpendicular lines have slopes that are opposite signs and reciprocals.

Since the line y = -1/4x + 10 has a slope of -1/4, the slope of the perpendicular line will be + 4/1 or 4.  So any line with a slope of 4 will be perpendicular to  y = -1/4x + 10.

This means A and D will be your answers.

Answer:

I use desmos!

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

How many 1/4 cups fit in a 1/2 cup?

This is a division problem.

We need to divide 1/2 by 1/4.

1/2 ÷ 1/4 =

= 1/2 × 4/1

= 4/2

= 2

Answer: 2

Answer: y=7x-23

Step-by-step explanation:

y-y1=m(x-x1)

Plug them in:

-2-12=m(-2-5)

-14=m(-7)

m=7

y=7x+b

Plug in a coordinate:

12=7(5)+b

12=35+b

-23=b

y=7x-23

Answer:

x < 3 or x ≥ 11

Step-by-step explanation:

(-∞, 3) or [11, ∞)

Step-by-step explanation:

subtract 4 from each side

2x < 6 .     or .         3x  ≥ 33

x < 3 or x ≥ 11

make sure you have an OPEN DOT at 3 pointing to negative infinity and a CLOSED DOT at 11 pointing to positive infinity.  

Answer:

517 birds

Step-by-step explanation:

Subtract 234 from 751, to find how many birds landed on the lake overnight.

The Range of the length of a rectangle having fixed width and area increasing linearly is  = {y ∈ R : c ≠ 0 or y ≠ 0}, and Domain = All real numbers,

An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.

Given:

The width of the rectangle is fixed, and the length is changing.

The line is formed when connected through the graph.

The area of the rectangle = [tex]length\times width[/tex]

So when the width is fixed, the area would increase linearly and directly proportional to length.

Calculate the range of function y = cx,

y = area as shown in the graph, x is the length, and width is constant c.

Range = {y ∈ R : c ≠ 0 or y ≠ 0}

Calculate the domain,

It can be any real number, as the area can't be negative.

Domain = All real numbers.

Therefore, Range = {y ∈ R : c ≠ 0 or y ≠ 0}, and Domain = All real numbers.

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Answer:

do you need help with anything if not hello

Step-by-step explanation:

Answer:

9 - 24x

Step-by-step explanation:

When using the distributive property, the number outside the parentheses (12) is "distributed" to each of the values inside the parentheses. In other words, 12 will be multiplied by 3/4 and 2x:

12(3/4 - 2x)

12(3/4) - 12(2x) <----- so now we successfully got rid of the parenthesis. Next, simplify

12(3/4) = 9

12(2x) = 24x

9 - 24x <----this is the final answer since it can't be simplified further

Step-by-step explanation:

as you wrote correctly, proportional relationships are in the form

y = mx

that means the line has to go through the origin (0, 0). otherwise it is in the form

y = mx + b

which is still linear but not proportional.

1a.

the rate of change is between 2 points A and B

(Yb - Ya)/(b - a)

in our case e.g. (4, 5.52) and (8, 11.04)

(11.04 - 5.52)/(8 - 4) = 5.52 / 4 = 1.38

when we use other points we get the same result. we see e.g. that when we double x (pounds), then also y (cost) is doubled.

the rate of change is 1.38.

this is also called the slope of the line.

b.

as mentioned in a., when we multiply x by a factor, then y is multiplied by the same factor. it also means that the function contains (0, 0) : for 0 pounds we pay $0.

c.

y = 1.38x

2a.

the slope is (as it is the same as the rate of change) the ratio of (y coordinate change / x coordinate change) when going from one point on the line to another.

we try to find points with integer coordinates to do that.

I see e.g. (3, 4) and (6, 8).

x changes by +3 (from 3 to 6).

y changes by +4 (from 4 to 8).

so, the slope is +4/+3 = 4/3.

b.

the simplest indicator is that the line goes through the origin (0, 0), which it does.

c.

y = (4/3)x

Answer: -6x

Step-by-step explanation:

Just subtract the coefficients:

The coefficient of 10x is 10

The coefficient of 16x is 16

now do ten minus 16 (TIP: if you don't really like negative numbers, then an easy way of subtracting 10-16 is 16-10=6, then add the negative sign to 6; -6)

10 - 16 = -6

Now put the x back: -6 = -6x

The correct answer is -6x

Answer: (6,-6),(0,1) plot these 2 points

Step-by-step explanation:

Answer: 0.4

Step-by-step explanation:

The question is asking for the probability to own a dog.

40% own a dog.

If you add all of the percentages you get 100%

40/100

=0.4

The probability is 0.4 times to randomly select a resident that only owns a dog.

The equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are 2.3p – 10.1 = 6.49p – 4 and 230p – 1010 = 650p – 400 – p

The equation is given as

2.3p – 10.1 = 6.5p – 4 – 0.01p

Evaluate the like terms on the right-hand side

So, we have the following representation

2.3p – 10.1 = 6.49p – 4

The above equation is an equivalent equation of the given equation

Multiply through the equation by 100

So, we have:

100(2.3p – 10.1 = 6.5p – 4 – 0.01p)

Evaluate

230p – 1010 = 650p – 400 – p

The above equation is also an equivalent equation of the given equation

Hence, the equations with the same solution are represented above

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The triangle's conclusion is that the two triangles are equal because they are congruent.

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We know that Julian has $8.75 using mathematical operations.

A mathematical "operation" is the process of calculating a value utilizing operands and a math operator.

The supplied operands or integers must adhere to a set of predefined rules that are connected to the symbol of the math operator.

The five basic operations in mathematics are addition, subtraction, multiplication, division, and modular forms.

So, we know that:

Juan has $3.50.

Julian has 2½ times Juan.

So, the money Julian has is:

First, calculate 2½:

2½

4+1/2

5/2

2.5 times

The money Julian has is:

3.50 * 2.5

$8.75

Therefore, we know that Julian has $8.75 using mathematical operations.

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The coordinates of P and Q are

PQ have equal slope with BC so they are parallel

The coordinates of P and Q is found using the midpoint formula

The formula is of the form

X= (x₂ + x₁)/2

Y = (y₂ + y₁)/2

solving for P (X, Y) Using points A(2, -1), B(-3, 4)

(X, Y) = ((2 + -3)/2, (-1 + 4)/2)

= (-1/2, 3/2)

solving for Q (X, Y) points A(2, -1), C(-5,-7)

(X, Y) = ((2 + -5)/2, (-1 + -7)/2)

= (-3/2, -4)

Parallel lines have equal slopes

Using BC = (4 - -7) / (-3 - -5) = 11/2

Using PQ = (-4 - 3/2) / (-3/2 - -1/2) = (-11/2) / (-1) = 11/2

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The width of area model is 2x units

Area is the entire amount of space occupied by the shape of an object or a flat (2-D) surface.

According to the given information :

The given expression is [tex]6x^{2}+106x[/tex]

We need to find the width of area model , so The above expression represents the area of rectangle A

By making the factors of the above expression

A = [tex]6x^{2}+106x[/tex]

  = [tex]2x( 3x + 53 )[/tex]

Area of rectangle is defined as

A = l × b

where l is length and b is width

In the above expression

b = 2x

l = 3x + 53

So , The width of area model is 2x units

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89.086 milliliters of juice will be in a glass with 7 ice cubes.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Equation of line: y = -29 202x + 293.5.

So, for 7 ice cubes i.e., x= 7

The amount of juice is

y= -29.202 (7)+ 293.5

y= -204.414+ 293.5

y= 89.086

Hence, the juice is 89.086 milliliters

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a) The Volume of space that is not occupied is; 13.80 in³

b) The length, are and volume have distinct final units.

c) The Volume of the composite shape is the sum of the Volume of Cone, Volume of Cylinder and  Volume of Hemisphere

a) Tennis ball is usually considered to be a sphere. The formula for volume of sphere is;

V = ⁴/₃πr³

where r is radius.

Since diameter = 2.6 inches, then radius; r = 2.6/2 = 1.3 inches

Thus;

Volume of each tennis ball;

V = ⁴/₃π(1.3)³

For the three tennis balls;

V₃ = 3(⁴/₃π(1.3)³)

V₃ = 8.788π

Volume of the cylindrical container = πr²h

h is height = 3(2.6) = 7.8 inches

V_cyl = π(1.3² * 7.8)

V_cyl = 13.182π

Volume of space not occupied = 13.182π - 8.788π

Volume of space not occupied = 13.80 in³

b) For length, the unit will be singular

For Area, the unit will be squared

For Volume, the unit will be cubed

c) There are three objects that make up the composite object namely; Cone, Cylinder, hemisphere. Thus;

Volume of composite shape = Volume of Cone + Volume of Cylinder + Volume of Hemisphere

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Answer:

Below

Step-by-step explanation:

e^(-kt) = 1/2     when t = 11.43

so  k = .060642797

e^ (- .060642797 * 1) = .9411  <====   is left after one year

             which means the decay in one year is

                  1 - .9411 = .05884 = 5.88% per year

Answer:

Below

Step-by-step explanation:

The slope of the given line , m = 4/5

  perpendicular slope is  - 1/m = - 5/4

The probability that in tonight's game he misses for the first time on his 6th attempt = 0.2244

What is Probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The Probability that the basketball player made a foul shot = 0.66 or 60%

Then the probability of good shot is = 1-0.66

= 0.34

probability that in tonight's game he misses for the first time on his 6th attempt = (1-p) 5(p)

= ( 1- 0.34)⁵ (0.34)

= 0.2244

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Answer:

-1

Step-by-step explanation:

This line is already in slope, intercept form of   y = mx + b   <===='b' is the y-axis intercept   =  -1

The required area of the polygons is given as 100 ft², 9 ft², 16 ft², and 64 ft².

Given that,
The dimensions of this polygon are shown in feet (ft). 10ft/3ft/4 ft/8 ft. The area, in square feet, of the polygon is to be determined.

A polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,

Examples of polygons, equilateral triangles, squares, pentagons etc

Here,
Assumed that all the polygons are square,
The area of the square is given as (side)².
1,
Side = 10 ft
Area of the square = [10 ft]² = 100 ft²

Similarly,
For side 3 areas is 9 ft²,

For side 4 areas is 16 ft²,

For side 8 areas is 64 ft²,

Thus, the required area of the polygons is given as 100 ft², 9 ft², 16 ft², and 64 ft².

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Answer:

A = 12cm^2 B = 18cm^2 C = 54cm^2

Step-by-step explanation:

area = side 1 x side 2

Answer:

5 y (2 y^4 + 6 y^2 - 3)

Step-by-step explanation:

The given input is 10y^5+30y^3-15y

10y^5+30y^3-15y has factors i.e 5 y (2 y^4 + 6 y^2 - 3)

By verifying each polynomial factor we get the GCF i.e common factor of the polynomial is 5 y (2 y^4 + 6 y^2 - 3) and simplified as 10 y^5 + 30 y^3 - 15 y

The population after 5 years if the starting population is 3000 is 75,000.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The population after 5 years.

= n x 25

Where n is the starting population in thousands.

The expression can be considered as.

= nx²

Where x is the number of years.

Now,

n = 3000

The population after 5 years.

= 3000 x 25

= 75,000

Thus,

The population is 75,000.

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The length of line segment LB is equal by definition of bisector to 6 feet.

In this question we find a geometric system with two right triangles generated by bisector AL, that is, a side that divides line segment CL into two segments of equal length. Then, the length of line segment LB is equal to:

CL = LB

Where CL and LB are measured in feet.

If we know that CL = 6 ft, then the length of line segment LB is 6 feet.

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