Two rectangles are similar. One has a length of 12 cm and a width of 9 cm, and the other has a width of 8 cm. Find the length of the second rectangle. Round to the nearest tenth if necessary.

If two cuboids are similar, it means they have the same shape but can be different in size. The ratio of the corresponding sides of similar objects is the same.

Let's denote the dimensions of cuboid A as follows:

Length of A: L_A

Width of A: W_A

Height of A: H_A

Let's denote the dimensions of cuboid B as follows:

Length of B: L_B

Width of B: W_B

Height of B: H_B

We know that the volume of a cuboid is given by:

Volume = Length × Width × Height

For cuboid A, we have:

Volume of A = L_A × W_A × H_A = 500 cm³

We're also given that the surface area of A is 15 cm². The formula for the surface area of a cuboid is:

Surface Area = 2(L × W + W × H + H × L)

So, for cuboid A:

2(L_A × W_A + W_A × H_A + H_A × L_A) = 15 cm²

Now, let's consider cuboid B. Since the cuboids are similar, their corresponding sides are proportional. Therefore, we can write:

(L_B / L_A) = (W_B / W_A) = (H_B / H_A)

Now, let's consider the surface area of cuboid B:

2(L_B × W_B + W_B × H_B + H_B × L_B) = 27 cm²

We have a system of equations to solve:

L_A × W_A × H_A = 500

2(L_A × W_A + W_A × H_A + H_A × L_A) = 15

2(L_B × W_B + W_B × H_B + H_B × L_B) = 27

L_B / L_A = W_B / W_A = H_B / H_A

We need to solve this system of equations to find the volume of cuboid B. Since the equations are somewhat complex, you may want to use a calculator or a symbolic math software to find the values of L_B, W_B, and H_B that satisfy all of these conditions. Once you have those values, you can calculate the volume of cuboid B using the formula for the volume.

Answer:

Option D is correct

Step-by-step explanation:

Given the system of equation:

Equation S: y = x + 9  

Equation T: y = 2x + 1

We have to find the following steps can be used to find the solution to the set of equations.

Equate the given equation S and T to solve for x,  we have;

Therefore, the following steps can be used to find the solution to the set of equations is:

Answer:

C. a rotation 180° clockwise about the origin followed by a reflection across the line y = x

Step-by-step explanation:

Let us assume that the coordinate of A in triangle ABC is A(x, y)

A) If there is a reflection across line y = x, the new coordinate is at A'(y, x).

If a reflection across the line y = -x is then followed, the new coordinate is at A"(-x, -y)

B) If there is a reflection across line x axis, the new coordinate is at A'(x, -y).

If a reflection across the line y axis is then done, the new coordinate is at

A"(-x, -y)

C) If there is a rotation 180° clockwise about the origin, the new coordinate is at A'(-x, -y).

If a reflection across the line y = x is then followed, the new coordinate is at A"(-y, -x)

D) B) If there is a reflection across line y axis, the new coordinate is at A'(-x, y).

If a reflection across the line x axis is then done, the new coordinate is at

A"(-x, -y)

Since only option C has a different result from the remaining options, hence option C would not five triangle A'B'C'

Answer:

C. a rotation 180° clockwise about the origin followed by a reflection across the line y = x

Step-by-step explanation:

Let us assume that the coordinate of A in triangle ABC is A(x, y)

A) If there is a reflection across line y = x, the new coordinate is at A'(y, x).

If a reflection across the line y = -x is then followed, the new coordinate is at A"(-x, -y)

B) If there is a reflection across line x axis, the new coordinate is at A'(x, -y).

If a reflection across the line y axis is then done, the new coordinate is at

A"(-x, -y)

C) If there is a rotation 180° clockwise about the origin, the new coordinate is at A'(-x, -y).

If a reflection across the line y = x is then followed, the new coordinate is at A"(-y, -x)

D) B) If there is a reflection across line y axis, the new coordinate is at A'(-x, y).

If a reflection across the line x axis is then done, the new coordinate is at

A"(-x, -y)

Since only option C has a different result from the remaining options, hence option C would not five triangle A'B'C'

Answer:

The required expression is

Step-by-step explanation:

The difference of squares formula is given by

We have been given that one factor is 2x+5. Hence, a = 2x, b = 5

It means that other factor must be (a-b) = (2x-5)

Hence, in order to find the expression, we can multiply the factors.

Using the difference of squares formula

Therefore, the required expression is