A regular quadrilateral pyramid has a slant height of $$25$$ cm, and its base is a square $$ABCD$$ with a side length of $$30$$ cm. Choose the correct statements.

A regular quadrilateral pyramid has a slant height of $$17$$ cm, and its base is a square $$ABCD$$ with a side length of $$16$$ cm. Choose the correct statements.

Find $$x$$ , knowing that $$x^2 - 4x = 0$$ . Select all values of $$x$$ that satisfy.

Mark true or false for the statement: x = 4 is not a solution of the equation.

Mark true or false for the statement: The set of solutions of the equation is S = $$\{0\}$$ .

Mark true or false for the statement: The set of solutions of the equation is S = $$\{0;\,4\}$$ .

Determine the truth value of the following statements with the production cost given by $$C(x)=\dfrac{2x+5}{x-1}$$ (million VND), where $$x>1$$ is the number of units produced: C(2) = 9.

Consider the truth value of the following statements with the production cost given by $$C(x)=\dfrac{2x+5}{x-1}$$ (million VND), where $$x>1$$ : If $$x=3$$ then the cost is 5.5 million VND.

Determine the truth value of the following statements regarding the production cost given by $$C(x)=\dfrac{2x+5}{x-1}$$ : The fraction $$C(x)$$ is undefined at $$x=1$$ .

Consider the truth value of the following statements with the production cost given by $$C(x)=\dfrac{2x+5}{x-1}$$ : When the number of products $$x$$ increases, the production cost $$C(x)$$ decreases and is always more than 4 million VND.

A vehicle travels a distance of $$s$$ (km) in a time of $$t$$ (hours), with an average speed of $$\dfrac{s}{t}$$ (km/h). Consider the truth value of the following statements: The fraction is undefined at $$t=0$$ .

A vehicle travels a distance of $$s$$ (km) in a time of $$t$$ (hours), with an average speed of $$\dfrac{s}{t}$$ (km/h). Consider the truth value of the following statements: If $$s=100$$ , $$t=2$$ then the average speed is 50 km/h.

A vehicle travels a distance of $$s$$ (km) in a time of $$t$$ (hours), with an average speed of $$\dfrac{s}{t}$$ (km/h). Consider the truth value of the following statements: The travel time is $$t$$ (hours).

A car travels a distance of $$s$$ (km) in a time of $$t$$ (hours), with an average speed of $$\dfrac{s}{t}$$ (km/h). Consider the truth value of the following statements: If the car travels 30 km each hour and after 3 hours the distance traveled is $$30t$$ (km).

Consider the expression $$(2a+3b)^2$$ . Evaluate the truth of the following statements: The expansion of the expression yields $$4a^2+12ab+9b^2$$ .

Consider the expression $$(2a+3b)^2$$ . Evaluate the truth of the following statements: With $$a=1$$ and $$b=-2$$ , the value of the expression is 16.

Consider the expression $$(2a+3b)^2$$ . Evaluate the truth of the following statements: For the value of the expression to be 0, then $$a=1$$ , $$b=-1$$ .

Given the expression $$B = \left(\frac{1}{x} + \frac{3}{x+2}\right) - \left(\frac{1}{x} - \frac{1}{x+1} + \frac{3}{x+2}\right)$$ . Determine the truth value of the statement: The conditions for the expression B are that x is not equal to 0 and x is not equal to -1.

Consider the expression $$B = \left(\frac{1}{x} + \frac{3}{x+2}\right) - \left(\frac{1}{x} - \frac{1}{x+1} + \frac{3}{x+2}\right)$$ . Determine the truth value of the statement: The simplified result of the expression B is $$\frac{1}{x+1}$$ .

Consider the expression $$B = \left(\frac{1}{x} + \frac{3}{x+2}\right) - \left(\frac{1}{x} - \frac{1}{x+1} + \frac{3}{x+2}\right)$$ . Determine the truth value of the statement: When x = 0, the value of the expression B equals 1.

Given the expression $$B = \left(\frac{1}{x} + \frac{3}{x+2}\right) - \left(\frac{1}{x} - \frac{1}{x+1} + \frac{3}{x+2}\right)$$ . Determine the truth value of the statement: The expression B takes an integer value when x = −2.

Given the expression $$M = \frac{x^2 + 3}{x - 2} - \frac{3x}{x - 2} + \frac{x - 1}{2 - x}$$ . Determine the truth value of the statement: The condition for the expression M to be defined is that x is not equal to 2.

Consider the expression $$M = \frac{x^2 + 3}{x - 2} - \frac{3x}{x - 2} + \frac{x - 1}{2 - x}$$ . Determine the truth value of the statement: The simplified result of the expression M is $$2 - x$$ .

Given the expression $$M = \frac{x^2 + 3}{x - 2} - \frac{3x}{x - 2} + \frac{x - 1}{2 - x}$$ . Determine the truth value of the statement: The value of M at x = 2025 is 2023.

Given the expression $$M = \frac{x^2 + 3}{x - 2} - \frac{3x}{x - 2} + \frac{x - 1}{2 - x}$$ . Determine the truth value of the statement: If M = 4, then x = −6.

Assertion: $$x^2 - 6x + 9 - y^2 = (x^2 - 6x + 9) - y^2$$ . Choose true or false.

Statement: Next, using the identity method, we get $$x^2 - 6x + 9 - y^2 = (x + 3)^2 - y^2$$ . Choose true or false.

Statement: Analyzing the polynomial above, we get the result as $$(x - y - 3)(x + y - 3)$$ . Choose true or false.

Statement: The value of the polynomial at $$x = 3$$ , $$y = 3$$ is $$9$$ . Choose true or false.

A regular triangular pyramid has a base edge of $$10\text{ cm}$$ and a height of $$12\text{ cm}$$ . The statement: The height of the base is $$4{,}33\text{ cm}$$ . Choose true or false.

A regular triangular pyramid has a base edge of $$10\text{ cm}$$ and a height of $$12\text{ cm}$$ . The statement: The area of the base of the pyramid is $$43{,}3\text{ cm}^2$$ . Choose true or false.

A regular triangular pyramid has a base edge of $$10\text{ cm}$$ and a height of $$12\text{ cm}$$ . The statement: The total surface area of the pyramid is $$219{,}01\text{ cm}^2$$ . Choose true or false.

A regular triangular pyramid has a base edge of $$10\text{ cm}$$ and a height of $$12\text{ cm}$$ . The statement: The volume of the pyramid is $$173{,}21\text{ cm}^3$$ . Choose true or false.

For the polynomial $$B = x^2 - y^2 - 2x - 2y$$ . The statement: The value of $$B$$ at $$x = 2$$ , $$y = -2$$ is $$0$$ . Choose true or false.

For the polynomial $$B = x^2 - y^2 - 2x - 2y$$ . The statement: Factoring $$B$$ results in $$(x - y)(x + y - 2)$$ . Choose true or false.

For the polynomial $$B = x^2 - y^2 - 2x - 2y$$ . Statement: The minimum value of $$B + 2y^2 + 5$$ is $$-3$$ . Choose true or false.

For the polynomial $$B = x^2 - y^2 - 2x - 2y$$ . The statement: At $$x = y = -1$$ then $$B + 2y^2 + 5$$ reaches its minimum value. Choose true or false.

Please determine whether the statement is true or false: The area of the small square with stripes is $$x^2$$ ; The area of the large square with stripes is $$y^2$$ .

Determine whether the statement is true or false: The area of each rectangle is $$xy$$ .

Determine whether the statement is true or false: The total area of squares and rectangles is $$x^2 + 2xy + y^2$$ .

Determine whether the statement is true or false: With $$x = 2$$ ; $$y = 3$$ , the total area of the original square is 13.

Let the polynomial $$A = n^3 - 5n^2 + 4n$$ . Determine whether the statement is true or false: $$A$$ is divisible by 3.

For the polynomial $$A = n^3 - 5n^2 + 4n$$ . Determine whether the following statement is true or false: $$A$$ is not divisible by 5.

For the polynomial $$A = n^3 - 5n^2 + 4n$$ . Determine whether the statement is true or false: $$A$$ is not divisible by 6.

Let the polynomial $$A = n^3 - 5n^2 + 4n$$ . Determine whether the following statement is true or false: $$A$$ is divisible by 120.

Given the expression $$B = \dfrac{2}{x^2 - 5x - 6} + \dfrac{x - 1}{x + 1}$$ . Determine whether the following statement is true or false: The conditions for definition are $$x \ne \pm 1$$ and $$x \ne 6$$ .

Given the expression $$B = \dfrac{2}{x^2 - 5x - 6} + \dfrac{x - 1}{x + 1}$$ . Determine whether the following statement is true or false: It can be simplified to $$B = \dfrac{2}{x - 6}$$ .

Given the expression $$B = \dfrac{2}{x^2 - 5x - 6} + \dfrac{x - 1}{x + 1}$$ . Determine whether the following statement is true or false: When $$x = 4$$ , then $$B = -\dfrac{1}{3}$$ .

Given the expression $$B = \dfrac{2}{x^2 - 5x - 6} + \dfrac{x - 1}{x + 1}$$ . Determine whether the following statement is true or false: For $$B = \dfrac{1}{3}$$ , $$x = 0$$ or $$x = 7$$ .

Select the correct statements related to the area of the garden, with the following statements.

A team of vehicles plans to use a number of the same type of vehicles to transport 120 tons of goods from location A to location B. Just before departure, the team adds 5 more vehicles of the same type. Knowing that the amount of goods each vehicle carries is the same. Let $$x$$ be the number of vehicles originally planned to be used ( $$x \in \mathbb{N}^*$$ ). Choose the correct statements.

Evaluate the truth of the following statements. Choose the correct statements.

Consider the expression $$(x + 2y)^2 - (x - 2y)^2$$ . Choose the correct statements.

True or false: A monomial that does not contain a variable is a constant.

True or false: 0 is a monomial.

True or false: A monomial with a coefficient of 0 has a degree of 0.

True or false: $$0x^2y^3$$ is a monomial and has a degree of 3.

Consider the regular triangular pyramid I.ABC as shown in the figure; the base is triangle ABC, O is the center of the base, and side AC is labeled 15cm. Evaluate the truth of the statement: Face ABC is a lateral face of the pyramid.

Consider the regular triangular pyramid I.ABC as shown in the figure; O is the center of the base. Evaluate the truth of the statement: The line IO is the height of the pyramid.

Consider the regular triangular pyramid I.ABC as shown in the figure; the edge AC is marked 15cm. Evaluate the truthfulness: The length of the base edge is 15cm.

Consider the regular triangular pyramid I.ABC. Evaluate the truth of the statement: Triangle ABC is right-angled at B.

Consider the fraction $$\dfrac{x}{x+1}$$ . Determine the truth value: The fraction is undefined when $$x=-1$$ .

Consider the fraction $$\dfrac{x}{x+1}$$ . Determine the truth value: The fraction has a denominator of $$x+1$$ .

Consider the fraction $$\dfrac{x}{x+1}$$ . Evaluate the truth of the statement: The numerator of the fraction is $$x$$ .

Consider the fraction $$\dfrac{x}{x+1}$$ . Evaluate the truth value: The value of the fraction when $$x=0$$ is equal to $$0$$ .

For the monomial $$E=-5xy^0$$ . Consider the truth value: The variable part is $$xy^0$$ .

For the monomial $$E=-5xy^0$$ . Consider the statement: The degree of $$E$$ is 1.

Consider the monomial $$E=-5xy^0$$ . Determine the truth value: The coefficient of $$E$$ is 5.

Consider the monomial $$E=-5xy^0$$ . Evaluate the truth of the statement: $$E$$ has a variable part equal to 0 and a negative coefficient.

Evaluate the truth of the following statements about the given expression: Expanding the expression yields $$8x^3 + 3x^2 + \frac{1}{2}x + \frac{1}{8}$$ . Is this statement true or false?

For the above expression, with $$x = \frac{1}{2}$$ , the expression takes the value of $$\frac{8}{3}$$ . Is this statement true or false?

For the above expression, in order for the expression to equal $$0$$ , then $$x = -1$$ . Is this statement true or false?

For the above expression, in order for the expression to equal $$27$$ , then $$x = \frac{5}{4}$$ . Is this statement true or false?

Consider the expression $$M = \dfrac{x}{2-x} + \dfrac{-2}{x+2} - \dfrac{x^3}{4-x^2}$$ . Evaluate the truth of the following statements: The condition for the expression $$M$$ is $$x \ne \pm 2$$ . Is this statement true or false?

Consider the expression $$M = \dfrac{x}{2-x} + \dfrac{-2}{x+2} - \dfrac{x^3}{4-x^2}$$ . Evaluate the truth of the following statements: The simplified result of the expression $$M$$ is $$x + 1$$ . Is this statement true or false?

Consider the expression $$M = \dfrac{x}{2-x} + \dfrac{-2}{x+2} - \dfrac{x^3}{4-x^2}$$ . Evaluate the truth of the following statements: The value of the expression $$M$$ equals $$2024$$ when $$x = 2025$$ . Is this statement true or false?

Consider the expression $$M = \dfrac{x}{2-x} + \dfrac{-2}{x+2} - \dfrac{x^3}{4-x^2}$$ . Evaluate the truth of the following statements: The value of $$x = 2$$ when $$M = 3$$ . Is this statement true or false?

Evaluate the truth of the following statements: An integer is also a monomial. Is this statement true or false?

Determine the truth value of the following statement: $$-7$$ is a monomial of degree $$0$$ . Is this statement true or false?

Determine the truth value of the following statements: The sum of two monomials is a monomial. Is this statement true or false?

Evaluate the truth of the following statements: The degree of the monomial $$4x^2y^3$$ is $$5$$ . Is this statement true or false?

A cube-shaped wooden block has a side length of $$x$$ (cm). A part of the cube with a side length of $$12$$ (cm) is cut off. Determine the truth value of the following statement: The volume of the original cube-shaped wooden block is $$x^3$$ (cm $$^3$$ ).

A cube-shaped block of wood has a side length of $$x$$ (cm). A part of the cube-shaped block of wood with a side length of $$12$$ (cm) is cut off. Please determine the truth value of the following statement: The volume of the cut-off cube-shaped block of wood is $$1728$$ (cm $$^3$$ ).

Statement: The volume of the remaining wood is $$V = x^3 - 1728\,(\text{cm}^3)$$ . Please choose True or False.

Statement: With $$x = 26\,(\text{cm})$$ , the volume of the remaining wood is $$15848\,(\text{cm}^3)$$ . Please choose True or False.

Evaluate the truth value of the statement: $$2x^2 + 3x^2 = 5x^2$$ .

Determine the truth value of the statement: $$4x + x^2$$ can be simplified to $$5x^2$$ .

Evaluate the truth of the statement: Simplifying $$3x^2 - 2x + 5 - x^2 + 4x - 2$$ results in $$6x^2 - x$$ .

Evaluate the truth value of the statement: $$2x^2 + 3x^2 - x + x^2$$ simplifies to $$6x^2 - x$$ .

Consider the fraction $$\dfrac{x^2 - 9}{x + 3}$$ . The statement: The fraction is undefined at $$x = -3$$ . Please choose True or False.

Consider the fraction $$\dfrac{x^2 - 9}{x + 3}$$ . The statement: The simplified fraction is $$x - 3$$ . Please choose True or False.

Consider the fraction $$\dfrac{x^2 - 9}{x + 3}$$ . The statement: The solution of the expression is $$x = -3$$ . Please choose True or False.

For the fraction $$\dfrac{x^2 - 9}{x + 3}$$ . The statement: The value of the fraction is $$5$$ when $$x = -2$$ . Please choose True or False.

A rectangular cardboard has a length of $$x + 43\,(\text{cm})$$ and a width of $$x + 30\,(\text{cm})$$ . Squares with a side length of $$y^2 + 1\,(\text{cm})$$ are cut from each corner of the cardboard, and the remaining part is folded to form an open-top box. The statement: The length of the rectangular box is $$x - 2y^2 + 41\,(\text{cm})$$ . Please choose True or False.

A rectangular cardboard has a length of $$x + 43\,(\text{cm})$$ and a width of $$x + 30\,(\text{cm})$$ . Squares with a side length of $$y^2 + 1\,(\text{cm})$$ are cut from each corner of the cardboard, and the remaining part is folded to form an open-top box. The statement: The width of the rectangular box is $$x - 2y^2 + 28\,(\text{cm})$$ . Please choose True or False.

A regular quadrilateral pyramid has a height of 14 cm, and its base is a square ABCD with a side length of 15 cm. The following statement is true or false: The lateral edge of the pyramid is 17.56 cm.

A regular quadrilateral pyramid has a height of 14 cm, and its base is a square ABCD with a side length of 15 cm. The following statement is true or false: The area of the base of the pyramid is 250 cm².

A regular quadrilateral pyramid has a height of 14 cm, and its base is a square ABCD with a side length of 15 cm. The following statement is true or false: The lateral surface area of the pyramid is 476.4 cm².

A regular quadrilateral pyramid has a height of 14 cm, and its base is a square ABCD with a side length of 15 cm. The following statement is true or false: The volume of the pyramid is 1,000 cm³.

Mr. Chau borrows 1.6 billion VND from the bank to buy a house in the form of installment payments; the monthly payment includes the principal divided equally over the number of months of the loan y (months) and the monthly interest calculated based on the monthly interest rate. Let x be the monthly payment (million VND) and r be the annual interest rate. The following statement is true or false: The monthly interest rate is $$r/12$$ .

Mr. Chau borrows 1.6 billion VND from the bank to buy a house in the form of installment payments; the monthly payment includes the principal divided equally over the number of months borrowed y (months) and the monthly interest calculated based on the annual interest rate. Let x be the monthly payment (million VND) and r be the annual interest rate. The following statement is true or false: $$x = 1600/y + 1600\cdot r/12$$ (million VND).

Uncle Chau borrows 1.6 billion VND from the bank to buy a house in the form of installment payments; the monthly payment includes the principal divided equally by the number of months borrowed y (months) and the monthly interest calculated based on the annual interest rate. Let x be the monthly payment (million VND) and r be the annual interest rate. The following statement is true or false: The formula for calculating $$r$$ in terms of $$x$$ and $$y$$ is $$r = \dfrac{3(xy - 1600)}{400y}$$ .

Bác Châu borrowed 1.6 billion VND from the bank to buy a house in the form of installment payments; the monthly payment includes the principal divided equally over the number of months borrowed y (months) and the monthly interest calculated at the monthly interest rate. The following statement is true or false: If Bác Châu pays 20 million VND each month for 10 years, then the annual interest rate (in %) is 4.5%.

The image of a trapezoidal wall with a larger base $$8x$$ , a smaller base $$4x$$ , and a height $$h$$ . There is a rectangular window with dimensions $$2x$$ and $$2h$$ placed in the middle of the wall. Determine the truth value of the statement: The area of the trapezoidal wall (not subtracting the window) is $$12xh$$ (m²).

The image of a trapezoidal wall with a larger base $$8x$$ , a smaller base $$4x$$ , and a height $$h$$ . There is a rectangular window with dimensions $$2x$$ and $$2h$$ placed in the middle of the wall. Determine the truth value of the statement: The ratio of the area of the window to the total area of the wall (not subtracting the window) is $$\dfrac{x}{3h}$$ .

The image of a trapezoidal wall with a larger base $$8x$$ , a smaller base $$4x$$ , and a height $$h$$ . There is a rectangular window with dimensions $$2x$$ and $$2h$$ placed in the middle of the wall. Determine the truth value of the statement: If $$h=2x$$ , then the area of the window is equal to $$\dfrac{1}{3}$$ of the total area of the wall.

The image of a trapezoidal wall with a larger base $$8x$$ , a smaller base $$4x$$ , and a height $$h$$ . There is a rectangular window with dimensions $$2x$$ and $$2h$$ placed in the middle of the wall. Determine the truth value of the statement: If $$x=3$$ (m) and $$h=5$$ (m), then the actual area of the wall (excluding the window) is $$78$$ (m²).

Let $$M=\dfrac{x+3}{x-2}+\dfrac{x-3}{x+2}-\dfrac{2x^2+3x+6}{x^2-4}$$ . Consider the truth value of the statement: The domain of the expression $$M$$ is $$x\ne \pm 2$$ .

Let $$M=\dfrac{x+3}{x-2}+\dfrac{x-3}{x+2}-\dfrac{2x^2+3x+6}{x^2-4}$$ . Consider the truth value of the statement: The simplified result of the expression $$M$$ is $$\dfrac{3}{x+2}$$ .

Let $$M=\dfrac{x+3}{x-2}+\dfrac{x-3}{x+2}-\dfrac{2x^2+3x+6}{x^2-4}$$ . Consider the truth value of the statement: The value of the expression $$M$$ is equal to $$\dfrac{3}{5}$$ when $$x=3$$ .

Let $$M=\dfrac{x+3}{x-2}+\dfrac{x-3}{x+2}-\dfrac{2x^2+3x+6}{x^2-4}$$ . Consider the truth value of the statement: For all integer values $$x\in\{-1;1;-3;-5\}$$ , $$M$$ takes integer values.

A square has a side length of $$x+5$$ (cm). Inside the square, a smaller square is drawn with a side length of $$x-2$$ (cm). Consider the truth of the statement: The area of the larger square and the area of the smaller square are respectively $$(x+5)^2$$ (cm²) and $$(x-2)^2$$ (cm²).

A square has a side length of $$x+5$$ (cm). Inside the square, a smaller square is drawn with a side length of $$x-2$$ (cm). Consider the truth value of the statement: The area of the remaining part of the square is $$(x+5)^2-(x-2)^2$$ (cm²).

A square has a side length of $$x+5$$ (cm). Inside the square, a smaller square is drawn with a side length of $$x-2$$ (cm). Consider the truth value of the statement: The area of the remaining part of the square when simplified is $$7(2x+3)$$ (cm²).

Let the fraction A = $$\dfrac{x^2 + 4x + 4}{x - 2}$$ and B = $$\dfrac{x + 2}{3}$$ . Consider the truth value of the statement: The condition for the value of fraction A is defined as $$x \ne 4$$ .

Let the fraction A = $$\dfrac{x^2 + 4x + 4}{x - 2}$$ and B = $$\dfrac{x + 2}{3}$$ . Consider the truth value of the statement: Calculate $$C = A : B = \dfrac{x + 2}{3(x - 2)}$$ .

Let the fraction A = $$\dfrac{x^2 + 4x + 4}{x - 2}$$ . Consider the truth value of the statement: When $$x = 4$$ , the fraction A has a value of $$16$$ .

Evaluate the truth of the statement: To make the fraction $$C = \dfrac{x + 2}{3(x - 2)}$$ equal to $$1$$ , then $$x = 4$$ .

A morning store sold $$8x^3y + 5x^6y^5 - 3x^5y^4$$ ; in the afternoon, it sold $$x^6y^5 - x^5y^4$$ (bags of rice). Determine the truth value of the statement: The expression representing the total number of bags of rice sold in one day is $$6x^6y^5 - 4x^5y^4 + 8x^3y$$ .

A morning store sold $$8x^3y + 5x^6y^5 - 3x^5y^4$$ ; in the afternoon it sold $$x^6y^5 - x^5y^4$$ . Determine the truth of the statement: With $$x = 1$$ , $$y = 2$$ the total number of bags of rice sold in a day is $$144$$ bags.

A morning store sold $$8x^3y + 5x^6y^5 - 3x^5y^4$$ ; in the afternoon, it sold $$x^6y^5 - x^5y^4$$ . Determine the truth of the statement: With $$x = 1$$ , $$y = 2$$ , the total number of bags of rice sold in the afternoon is $$32$$ bags.

A morning store sold $$8x^3y + 5x^6y^5 - 3x^5y^4$$ ; in the afternoon it sold $$x^6y^5 - x^5y^4$$ . Determine the truth of the statement: With $$x = 1$$ , $$y = 2$$ , the number of bags of rice sold in the morning accounts for $$\dfrac{3}{4}$$ of the total number of bags.

To commemorate the 30th anniversary of a secondary school, the school's youth union plans to plant 100 green trees in the schoolyard. Let $$x$$ be the initial number of union members of the youth union, and suppose the number of trees each member plants is the same. Consider the truth value of the statement: The number of trees each member is expected to plant is $$\dfrac{100}{x}$$ (trees).

The number of trees each member plants according to reality is $$\dfrac{100}{x+2}$$ (trees).

The number of trees each member plans to plant is more than the number of trees each member actually plants by $$\dfrac{100}{x(x+2)}$$ (trees).

If the number of trees each member plans to plant is 25 trees more than the number of trees each member actually plants, then the number of members who participated in planting trees is 5 members.

Consider the expression $$A = \dfrac{6}{x^2+6x} + \dfrac{1}{x+6} + \dfrac{5}{x}$$ . Evaluate the truth of the following statements: The conditions for the expression A are $$x \ne 0$$ and $$x \ne 6$$ .

Consider the expression $$A = \dfrac{6}{x^2+6x} + \dfrac{1}{x+6} + \dfrac{5}{x}$$ . Evaluate the truth of the following statements: The simplified result of the expression $$A$$ is $$\dfrac{5}{x}$$ .

Consider the expression $$A = \dfrac{6}{x^2+6x} + \dfrac{1}{x+6} + \dfrac{5}{x}$$ . Evaluate the truth of the following statements: The value of the expression $$A$$ at $$x = 2$$ is $$3$$ .

Consider the expression $$A = \dfrac{6}{x^2+6x} + \dfrac{1}{x+6} + \dfrac{5}{x}$$ . Evaluate the truth of the following statements: With $$x = -3$$ , the expression $$A$$ takes a negative value.

Determine the truth value of the following statements: $$3x^2y^3$$ is a monomial.

Determine the truth value of the following statements: $$\dfrac{5}{7}a^2b$$ is a monomial.

Determine the truth value of the following statements: A variable in a monomial is a letter present in the expression.

Determine the truth value of the following statements: $$3x^2y + 5$$ is a monomial.

Consider the regular triangular pyramid S.ABC, with AC = 6cm, SH = 9cm. Evaluate the truth of the following statements: ABC is the base of the pyramid.

Consider the regular triangular pyramid S.ABC, with AC = 6cm, SH = 9cm. Evaluate the truth of the following statements: Edge BC = 6cm.

Consider the regular triangular pyramid S.ABC, with AC = 6cm, SH = 9cm. Evaluate the truth of the following statements: SH is the height of the pyramid.

Consider the regular triangular pyramid S.ABC, with AC = 6cm, SH = 9cm. Evaluate the truth of the following statements: SA = SB = SC = 9cm.

A tank contains $$x$$ liters of water, a tap with water flowing out at a rate of $$x/t$$ liters/hour. Consider the truth value of the statement: The expression $$x/t$$ is an algebraic fraction if $$t \ne 0$$ .

A tank contains $$x$$ liters of water, a tap with water flowing out at a rate of $$x/t$$ liters/hour. Consider the truth value of the statement: If $$x=120$$ , $$t=4$$ then the flow rate of the tap is $$30$$ liters/hour.

A tank contains $$x$$ liters of water, a tap with water flowing out at a rate of $$x/t$$ liters/hour. Consider the truth value of the statement: The fraction is undefined at $$t=0$$ .

A tank contains $$x$$ liters of water, a tap with water flowing out at a rate of $$x/t$$ liters/hour. Consider the truth of the statement: If the tap can flow $$40$$ liters/hour and after $$4$$ hours the water in the tank runs out, then the initial amount of water in the tank is $$100$$ liters.

Given the expression: $$P=5x^3+2x^2-5x^3+x^2+3$$ . Consider the truth value of the statement: After simplification, $$P$$ is a constant.

Consider the expression: $$P=5x^3+2x^2-5x^3+x^2+3$$ . Evaluate the truth of the statement: $$P$$ has a degree of $$3$$ because it contains $$x^3$$ .

Consider the expression: $$P=5x^3+2x^2-5x^3+x^2+3$$ . Evaluate the truth of the statement: $$P(x)=3$$ for all $$x$$ .

Consider the expression: $$P=5x^3+2x^2-5x^3+x^2+3$$ . Evaluate the truth of the statement: $$P$$ is a polynomial of degree $$3$$ with $$1$$ term.

Consider the regular pyramid below. Evaluate the truth of the statement: This is a regular quadrilateral pyramid.

Consider the regular pyramid shown below. Evaluate the truth of the statement: $$SH$$ is the height of the pyramid.

Consider the following regular pyramid. Evaluate the truth of the statement: $$SA$$ is the height of the pyramid.