A rectangular pool has a length of 24 feet, a width of 12 feet, and a depth of 8 feet. What is the volume of the pool?

The four ways are 1) Factoring 2) Completing the Square 3) Quadratic Formula  and 4) Graphing

1. Factoring: Factoring is the process of breaking down an expression into its simplest components. To solve a quadratic equation using factoring, you must start by writing the equation in standard form (ax² + bx + c = 0). Then, you must factor the equation into two binomials (x + a)(x + b) = 0. Once this is done, you can solve for x by setting each factor equal to zero and solving for x.

2. Completing the Square: Completing the square is another method of solving a quadratic equation by rewriting it in the form of (x + a)² = b. To do this, you first start by writing the equation in standard form (ax² + bx + c = 0). Then, you must rearrange it so that all the terms are on one side of the equation and the constant is on the other side. Next, divide the coefficient of x² by two and then square this number. Finally, add this number to both sides of the equation, which will then allow you to solve for x.

3. Quadratic Formula: The quadratic formula is a useful tool for solving quadratic equations.

4. Graphing : is another method useful for solving quadratic equation.

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The area of the heptagon is  24. 2 square units

To determine the area of the shape which is a heptagon, we have that;

A = 1/2)nsr.

Such that the parameters of the formula are written as;

From the information given, we have that;

n = 7

s = 2. 77

r = 2. 5

Substitute the values, we have that;

Area = 1/2 × 2. 5 × 2. 77 × 7

Multiply the values, we get;

Area = 1/2 × 48.475

Divide the values

Area = 24. 2 square units

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Answer:

d

Step-by-step explanation:

Answer:

[tex]x=\sqrt{153}[/tex]

Step-by-step explanation:

[tex](\overline{BC})^2 = (\overline{AB})^2 + (\overline{AC})^2\\\\(13)^2=(x)^2+(4)^2\\\\169 = x^2+16\\\\169-16=x^2\\\\153=x^2\\\\\sqrt{x^2} = \sqrt{153}\\\\x=\sqrt{153}[/tex]

Therefore ,As a result, the answer to the provided equation is that a burrito costs $2.50 and a soft taco costs $1.50.

A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation. Word illustration The product of 8 and 3 is 11.

Here,

Let the price of a soft taco be set at s.

Let b be the price for one burrito.

Therefore, we have this system.

3s + 3b = 11.25

4s + 2b = 10.00 (1) (1)

By multiplying the first equation by 3, we get that.

If s + b = 3.75, take b off of both sides.

s = 3.75 - b (2) (2)

Subtract (2) from (1) and you get

Simplify 4 (3.75 - b) + 2 b = 10.00.

15 - 4b + 2b = 10.00

Subtract 15 from both sides (-2b + 15 = 10) to get the total.

Divide both sides by -2 to get -2b = - 5.00.

b = 2.50

as well as (2)

s = 3.75 - 2.50 = 1.50

As a result, the answer to the provided equation is that a burrito costs $2.50 and a soft taco costs $1.50.

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The graph of a line with a slope of 3/5 has an equation of y = 3/5x + 1 and the graph is attached

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

Graph of a line with a slope of 3/5

This means that

Slope = 3/5

And it also means that the equation is a linear equation

A linear equation is represented as

y = mx + c

Where

m = slope

i.e. m = 3/5

So, we have

y = 3/5x + c

Assume that c = 1

So, we have

y = 3/5x + 1

Hence, the equation is y = 3/5x + 1

See attachment for graph

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Answer:

$18.48

Step-by-step explanation:

Find perimiter of room

4+4+7+7 =22

22•0.84 = 18.48

$18.48

Relief refers to the highest and lowest point elevation in an area.

Relief

Relief is the term used for the differences in height from place to place on the land’s surface and it is greatly affected by the underlying geology. Relief relies on the hardness, permeability and structure of a rock.

elevation

The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface.

geology

Geology describes the structure of the Earth on and beneath its surface, and the processes that have shaped that structure. It also provides tools to determine the relative and absolute ages of rocks found in a given location, and also to describe the histories of those rocks.

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Answer: Relief

Step-by-step explanation:

Relief refers to the highest and lowest point elevation in an area.

Slope is the measure of steepness

Topography refers to the arrangement of the land in an area

Elevation on the other hand is the distance above sea level

The function obtained after transformation is given as -x³ + 9x²- 27x + 21.

The graph of a function can be transformed by either shifting it in the right, left, up or down.

When the transformation is rightwards, the function becomes as f(x - a).

For left shifting it is f(x + a).

The function is given as f(x) = x³- 6.

The translation of 3 units towards left can be written as,

f(x + 3) = (x + 3)³ - 6

⇒ x³ + 9x² + 27x + 21

For reflection across y axis replace -x with x as below,

⇒ (-x)³ + 9(-x)² + 27 × -x + 21

⇒ -x³ + 9x²- 27x + 21

Hence, the required form of the transformed function is -x³ + 9x²- 27x + 21.

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Answer:

See below

Step-by-step explanation:

[tex] m\angle ABC = 2\times m\angle AEC = \boxed {60} \degree [/tex]

(By inscribed angle theorem)

[tex] m\widehat{AC} = m\angle ABC = 60\degree [/tex]

(Central angle and its corresponding arc theorem)

[tex] m\widehat {DC} = 180\degree - (60\degree + 80\degree) [/tex]

[tex] m\widehat {DC} = 40\degree [/tex]

[tex] m\angle DBC = m\widehat {DC} = \boxed {40} \degree [/tex]

(Central angle and its corresponding arc theorem)

[tex] m\angle ACE = \boxed {90} \degree [/tex]

(Angle inscribed in a semicircle)

[tex] m\angle DAE = \frac{1}{2}\times 80\degree = \boxed {40}\degree [/tex]

(By inscribed angle theorem)

[tex] m\angle ADE = \boxed {90}\degree [/tex]

(Angle inscribed in a semicircle)

[tex] m\angle FCB = \boxed {90}\degree [/tex]

(By tangent radius theorem)

[tex] m\angle CED = \frac{1}{2}\times 40\degree = \boxed {20} \degree [/tex]

(By inscribed angle theorem)

The length of tile A is 2.36068 inches.

The quantity of square units required to completely fill a square is known as the area of a square.

The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area.

The measurement is made using square units, with square meters serving as the standard unit (m^2).

The square unit serves as the unit of area.

Let us recall that the area of a square is given by;

A = side^2

This is because, all the sides of a square are equal hence

When A = 5 square inches

5 = side^2

side = √5

side = 2.36068 inches

Therefore, The length of tile A is 2.36068 inches.

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The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The numerical expression is given below.

⇒ 12 × [6.3 + 3 × (1.9)]

Simplify the numerical expression, then we have

⇒ 12 × [6.3 + 3 × (1.9)]

⇒ 12 × [6.3 + 5.7]

⇒ 12 × 12

⇒ 144

The value of the numerical expression 12 × [6.3 + 3 × (1.9)] will be 144.

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Answer:

Step-by-step explanation:

fter solving the algebraic equation, Miguel has 4 quarters, 12 dimes and 16 nickels.

What is algebra?

One of the earliest areas of mathematics that deals with number theory, geometry, and analysis is algebra. Algebra is also defined as the study of mathematical rules and symbols through the manipulation of those mathematical symbols.

The number of quarters is taken to be x, then the number of dimes will be 3x, and the number of nickels will be 3x + x = 4x

$3.00 when converted to cents is 300 cents.

The value of nickels is 5 x 4x=20x.

The value of dimes is 10 x 3x=30x.

The value of quarters is 25x.

As the total value of money Miguel has is 300 cents, then the algebraic equation will be -

20x + 30x + 25x = 300

Solve to get the value of x -

75x = 300

x = 4

Therefore, the amount of quarters is x = 4 quarters.

The amount of dimes is x = 3x = 3 x 4 = 12 dimes.

The amount of nickels is 4x = 4 x 4 = 16 nickels.

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Answer: Jesus will have 36 dollars after 8 days

Step-by-step explanation: 8 x 8= 64

100-64=36

No, 1, 2, and 3 are not valid side lengths for a triangle. So 1, 2 and 3 cannot make a triangle.                                                                      

In order for a shape to be a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.                                                              

3 + 2 = 5 > 1

3 + 1 = 4 > 2

1 + 2 = 3 not greater than 3

So as 1 + 2 not greater than 3, these set of side lengths does not follow the theorem. Thus a triangle cannot be formed with sides of length 1, 2, and 3.

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

" Can 1, 2 and 3 make the sides of a triangle?"

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Answer:

u would go 3 to the right three and down three from the origin

Step-by-step explanation:

Answer:

D. an = 4n

Step-by-step explanation:

The formula for finding a term of an arithmetic sequence is:

an = a1 + (n-1)d

where an is the nth term, a1 is the first term and d is the common difference between the terms.

To find d we can take any two adjacent terms and subtract one from the other. e.g. 8 - 4 = 4, 16-12 = 4 etc.

The common difference here is 4, and we can see that the first term of the sequence is also 4, therefore our formula now looks like this:

an = 4 + (n-1)4

Now we can just expand out the brackets to find the final answer:

an = 4 + 4n - 4

an = 4n

Hope this helped!

Answer:

30 + 32 + 34 + 36 = 132

Hope this helps!!

An equivalent  is the amount of a substance that reacts with  an arbitrary amount of another substance in a given chemical reaction.

Arbitrary

It is a relative unit of measurement to show the ratio of amount of substance, intensity, or other quantities, to a predetermined reference measurement.

chemical reaction

chemical reaction is a process in which one or more substances, the reactants, are converted to one or more different substances, the products. Substances are either chemical elements or compounds.

Examples of chemical changes include baking soda and vinegar creating carbon dioxide, iron rusting, and wood burning.

There are five types of general chemical reactions: Combination or synthesis, decomposition, single displacement, double displacement, and combustion.

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Answer:

18 + 4√15

Step-by-step explanation:

(3√5+√3)(√5+ √3)

= 3√5 (√5+ √3) + √3 (√5+ √3)

= 3√5 √5 + 3√5 √3 + √3  (√5+ √3)

=  3√5 √5 + 3√5 √3 + √3 √5 + √3 √3

= 18 + 4√15

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The 3 parts of a quadratic equation are standard form, factored form and vertex form.

A quadratic equation is a polynomial equation of degree two in one variable of type f(x) = ax² + bx + c where a, b, c, ∈ R and a ≠ 0.

There are three forms of quadratic equations

Standard form of quadratic equation y = ax² + bx + c

factored form of quadratic equation y = a(x − r₁)(x − r₂​)

Vertex form of quadratic equation y = a(x − h)² + k

Each of the above quadratic forms looks unique, allowing the different problems to be more easily solved in one form than another.

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Answer:

an expression.

Step-by-step explanation:

have a nice day! ʀɪʙʙɪᴛ

~tsu-chan (>_<)

Answer:

value/expression

Step-by-step explanation:

Answer:

hey!

Step-by-step explanation:

i really don't know if you added an image along with it, but if you did i can't necessarily see it?? it's weird ik but even when i refresh nothing shows. It just blurs it and says "Oop!"

The distance of each chord from the centre of the circle are √119  and √128 respectively .

Given,

Radius of a circle = 12 cm

AB = 10 cm

CD = 8 cm

Now, we get

BG = 10/2 = 5 cm

HD = 8/2 = 4 cm

(A perpendicular coming from the centre, which is not a diameter, bisects the chord.)

Now,

BE = ED = EF = 12 cm (All radii of a circle are equal.)

Now, by Pythagoras Theorem, we get

H² = P² + B²

For GE —

(BE)² = (GE)² + (BG)²

or, (12)² = GE² + (5)²

or, 144 = GE² + 25

or, GE² = 144 — 25

or, GE² = 119

or GE = ±√119

or GE = √119 (Since, length cannot be negative.)

For HE —

(DE)² = (HE)² + (HD)²

or, (12)² = HE² + (4)²

or, 144 = HE² + 16

or, HE² = 144 — 16

or, HE² = 128

or, HE = ± √128

or, HE = √128 or 8√2(Since, length cannot be negative.)

Hence , the distance of each chord from the centre of the circle are √119  and √128 respectively .

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Answer: [tex]15000\ lbf.ft[/tex]

Step-by-step explanation:

Given

Force acting is [tex]200\ Pounds[/tex]

The direction of action is from [tex](0,0)\ to\ (-75,0)[/tex]

Work done is given by

[tex]W=F\cdot ds[/tex]

As the displacement occurs in the x-direction

[tex]\therefore W=200\cdot 75\\\Rightarrow W=15000\ lbf-ft[/tex]

Answer:

Answer is X<5

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Step-by-step explanation:

The simplified form of 21b − 32 7b − 20b would be 8b - 32.

Reducing an equation is a technique for rewriting it in a more straightforward format. Although some mathematical equations are not in the form of linear equations, they can be converted into linear equations by applying certain mathematical operations to them. These equations can be easily solved after being reduced to linear form, and the value of the unknown can be determined.

21b – 32 + 7b – 20b

= 21b + 7b – 20b – 32

= 28b – 20b – 32 = 8b – 32

21b - 32 + 7b - 20b

= 21b + 7b - 20b -32

= 8b - 32

=8b - 32.

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Answer:

Here is the graph to the intercepts.

Step-by-step explanation:

Graph of (6, 4), (4, 3), (-2, 0)

Hope it helps :)

To find the MEAN of Natural numbers, such as  1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, a + b + c3 is the sum of the three numbers a, b, and c. Therefore, 5.5 is the MEAN of the first 10 natural numbers.

Firstly The Given set of numbers Represents Natural numbers,

A natural number is an integer greater than 0. Natural numbers begin at 1 and increment to infinity: 1, 2, 3, 4, 5, etc.

Therefore, the first ten natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

And the mean of three numbers a, b, c is a + b + c3

Then the mean of 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 is:-

⇒1+2+3+4+5+6+7+8+9+1010

Adding and dividing we get the value of the above term as,

⇒1+2+3+4+5+6+7+8+9+1010=5510=5.5

Hence, the mean of the first 10 natural numbers is 5.5.

Note: To solve this problem, you must understand that the integers greater than zero are natural numbers and that the mean of the three numbers a, b, and c equals a + b + c3. Knowing how to calculate the average number of elements and being familiar with natural numbers can help you arrive at the correct conclusion.

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