How many square feet of outdoor carpet will need for this hole

Answer:

The correct option is 2.

Step-by-step explanation:

It is given that the volume of cube is 1,000 cubic feet.

The volume of cube is

[tex]V=a^3[/tex]

[tex]1000=a^3[/tex]

[tex]a=10[/tex]

The side length of cube is 10 feet.

It is given that the other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height.

The area of tilted solid is

[tex]V=\text{Area of base}\times \text{height}[/tex]

Since height and base are same, so the area of tilted solid is

[tex]V=(10 \times 10)\times 10=1000[/tex]

The volume of the tilted solid is 1,000 cubic feet. Therefore the correct option is 2.

The laser will cut the archway at height of 3.5 feet and 4 feet (Option C).

A linear equation exists an equation in which the highest power of the variable stands always 1. It exists also known as a one-degree equation. The standard form of a linear equation in one variable exists in the form Ax + B = 0. Here, x is a variable, A exists as a coefficient and B is constant.

A parabola exists as a plane curve that stands mirror-symmetrical and is approximately U-shaped. It fits several superficially various mathematical descriptions, which can all be proved to determine exactly the same curves.

Refer to the following figure:

The blue line represents eqn of archway: y = -0.5x^2 + 3x, and green line represent eqn of laser: -0.5x + 2.42y = 7.65.

Now to find out the points at which laser cuts archway, we need to equate both the eqns.

[tex]-0.5x^{2} +3x=\dfrac{7.65+0.5x}{2.42}[/tex]

[tex]-1.21x^{2} +7.26x=7.65+0.5x[/tex]

[tex]-1.21x^{2} +6.76x-7.65[/tex]=0

On solving the quadratic eqns, we get x =3.5 and 4 (approximate)

Therefore, point A and B are 3.5 and 4 feet respectively.

To know more about parabola refer to:

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we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

In this problem we have

[tex]p=20.8\\q=31.2[/tex]

Find the value of k

[tex]k=q/p[/tex]

Substitute the values

[tex]k=31.2/20.8[/tex]

[tex]k=1.5[/tex]

The linear equation is

[tex]q=1.5p[/tex]

For [tex]q=15.3[/tex]

Find the value of p

Substitute in the linear equation and solve for p

[tex]15.3=1.5p[/tex]

[tex]p=15.3/1.5=10.2[/tex]

therefore

the answer is the option a

[tex]10.2[/tex]

Due to a lack of information provided, the length of segment DH in the triangle ABC, where H is the incenter, cannot be determined as provided options could all be possible or might be something entirely different.

The question doesn't provide enough information to determine the length of segment DH. In a triangle, the incenter is the center of the inscribed circle (incircle). This is the point where all the angle bisectors of the triangle meet. Segment DH would be a line from the incenter to a point on one of the triangle's sides, in other words, a radius of the incircle. However, without more information such as the length of the sides of the triangle or its area, it isn't possible to determine the length of DH. It could be any of the provided options (14, 7, 18, 21) or something else entirely.

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The incenter of a triangle is the point where the angle bisectors of the three angles of the triangle intersect.

The incenter of a triangle is the point where the angle bisectors of the three angles of the triangle intersect. To find the distance DH, we can use the fact that the incenter is equidistant from the three sides of the triangle.

Therefore, DH = x = (AH + BH + CH)/3 = (2x + 2x + 2x)/3 = 6x/3 = 2x.

Since DH = 2x, the distance DH will be twice the distance from the incenter to any side of the triangle. Without knowing the specific values of the sides of triangle ABC, we cannot determine the exact value of DH. Therefore, none of the given options (a, b, c, d) is the correct answer.

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Sales tax is $ 2.75

How to calculate

Tax = $ 25.00 x (11/100)

Tax = $ 25.00 x 0.11

Tax = $ 2.75

Initial purchase of $ 22.25 + 11% Tax ($ 2.75) = $ 25.00

Or other alternatives:

11% tax

n = sales tax value

11% = $ 25.00 / n

n = $ 25.00 x 11%

n = ($ 25.00 x 11) / 100

n = $ 275/100

n = $ 2.75

So, the sales tax is $ 2.75

Sales tax (VAT) is tax before Value Added Tax (VAT) and is charged each time a sales transaction. A VAT is charged at the manufacturer level / not to retailers (end users). A VAT is collected when delivering goods or services.

Definition of Tax Debt

Debt is an engagement as a result of a special agreement called a debt payable, which requires the debtor to pay the amount of money he has borrowed from creditors.

Sales tax / value-added debt or Sales tax payable is the company's debt to the tax office for sales tax collected by the company from customers for the sale of goods/services. Sales tax rates are deposited by the tax office multiplied by sales / net sales (net sales).

Example

$ 12 cash sale including 10% VAT

Tax Amount: 10 / ÷ 100 × 12 = $ 1.2

Sales Amount: 12 - 1.2 = $ 10.8

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Details

Class: High School

Subject: Mathematics

Keywords: VAT, Tax, Sales

Final answer:

To find the volume of a cylindrical can, one must apply the formula for volume of a cylinder, V = πr²h, with the given dimensions. The can's volume is approximately 603.19 cubic centimeters or milliliters, translating to about 0.603 liters.

Explanation:

The student is asking about the volume of a can, which is the measure of how much space it occupies or, in this context, how much liquid it can hold. To find the volume of a cylindrical can, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

Since the can is 12 cm high and 8 cm wide (which is the diameter), the radius would be 4 cm (which is half of the diameter). Substituting these values into the formula gives us V = π(4cm)²(12 cm), which simplifies to V = π × 16 cm² × 12 cm). When calculated, the volume of the can is approximately 603.19 cubic centimeters.

Since the student may also be interested in capacity in terms of common liquid measurements, it is useful to know that 1 cubic centimeter is equivalent to 1 milliliter.

Thus, the can would be able to hold approximately 603.19 milliliters. Given that 1000 milliliters make up 1 liter, the can's capacity would be roughly 0.603 liters, which is a little over half a liter.

A triangle cannot have two right angles because the sum of the interior angles in any triangle is equal to two right angles. Having two right angles would necessitate that the third angle also be a right angle, forming a straight line instead of a triangle.

Proof that a Triangle Cannot Have Two Right Angles

The notion that a triangle cannot have two right angles is fundamentally rooted in the geometry axiom stating that the sum of the interior angles in any triangle is equal to two right angles (or 180 degrees). If a triangle were to have two right angles, the third angle would also have to be a right angle to satisfy the sum of 180 degrees. However, if the third angle is a right angle, this contradicts the definition of a triangle being a three-sided polygon with three angles that add up to 180 degrees; with three right angles, the figure would no longer be a triangle, as the three lines AC, CD, and BD would line up to form a straight line, eliminating the closed polygon structure of a triangle.

If we consider the work of notable mathematicians such as Legendre and Dehn, we find substantial evidence supporting the statement that the sum of the interior angles of a triangle cannot be greater than two right angles. Legendre's attempts to prove this led to understanding the consistency of triangle angle sums across all triangles; that is, if one triangle's angles added up to two right angles, it would be the same for all triangles. Furthermore, Dehn's hypothesis indicated that without parallel lines, the sum of the angles of a triangle is greater than two right angles.

Overall, every triangle must have at least two acute angles, and any attempt to form a triangle with two right angles would result in a shape that does not adhere to the fundamental properties of a triangle.

To find the values of sin, tan, csc, sec, and cot, we use trigonometric identities and given information. Sin x = 3/5, tan x = 3/4, csc x = 5/3, sec x = 5/4, and cot x = 4/3.

To find the values of sin, tan, csc, sec, and cot, we can use the trigonometric identities. From the given information, we know that cos x = 4/5. Using the Pythagorean identity, sin² x = 1 - cos² x, we can find sin x as:

sin x = sqrt(1 - (4/5)²) = sqrt(1 - 16/25) = sqrt(9/25) = 3/5

Now, we can calculate the remaining trigonometric values:

tan x = sin x / cos x = (3/5) / (4/5) = 3/4

csc x = 1 / sin x = 1 / (3/5) = 5/3

sec x = 1 / cos x = 1 / (4/5) = 5/4

cot x = 1 / tan x = 1 / (3/4) = 4/3

Answer:

(a-6)(a-1)(a+6)

Final answer:

The lowest common denominator for the fractions [tex]6/(a^2-7a+6)[/tex] and [tex]3/(a^2-36)[/tex] is (a-6)(a-1)(a+6).

Explanation:

To find the lowest common denominator for the fractions [tex]6/(a^2-7a+6)[/tex] and [tex]3/(a^2-36),[/tex] we need to determine the least common multiple of the denominators.

The denominator of the first fraction can be factored as (a-6)(a-1) and the denominator of the second fraction can be factored as (a-6)(a+6).

The common factors are (a-6) and (a-1)(a+6).

Therefore, the lowest common denominator is (a-6)(a-1)(a+6).