Wes is 4 years older than his sister. Let x be his sister's age. Write an expression that tells how old Wes is.

The rectangular prism has a length of 9 units, a width of 10 units (since width = 90 / length), and a height of 5 units (since height = (5/9) length).

What is the area of a rectangle?

A rectangle is a quadrilateral with four right angles (90-degree angles) and opposite sides that are parallel and congruent (equal in length). The area of a rectangle is defined as the amount of space that is enclosed by its two-dimensional shape, and it can be calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is:

Based on the given information, we can determine the dimensions of the rectangular prism as follows:

Cross section A has an area of 90 square units, which is equal to the area of the base of the prism. Since the base of the prism is a rectangle, we can use the formula for the area of a rectangle to find its dimensions:

90 = length x width

Cross section B has an area of 50 square units, which is equal to the area of one of the sides of the prism. Since the sides of the prism are also rectangles, we can use the formula for the area of a rectangle to find its dimensions:

50 = height x width

Cross section C has an area of 45 square units, which is equal to the area of the front of the prism. Since the front of the prism is also a rectangle, we can use the formula for the area of a rectangle to find its dimensions:

45 = length x height

We now have three equations with three unknowns, which we can solve for to find the dimensions of the prism:

90 = length x width

50 = height x width

45 = length x height

Solving for width in the first equation gives us:

width = 90 / length

Substituting this into the second equation gives us:

50 = height x (90 / length)

Solving for height gives us:

height = 50 x (length / 90) = (5/9) length

Substituting this into the third equation gives us:

45 = length x (5/9) length = (5/9) length²

Solving for length gives us:

length² = (9/5) x 45 = 81

length = √(81) = 9

Therefore, the rectangular prism has a length of 9 units, a width of 10 units (since width = 90 / length), and a height of 5 units (since height = (5/9) length).

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Answer:

x = 10, y = 20

Step-by-step explanation:

Because this is a geometric sequence, we'll call the rate of change z. Because 40 is 3 terms away from 5, we can write 5 * z * z * z = 5z³ = 40.

z³ = 8 → z = 2

Now, we simply multiply 5 by 2 to get x, which is 10, and then we multiply x by 2 to get 10 * 2 = 20 for y. Hope this helps!

Final answer:

To find the values of x and y in the given geometric progression, we use the concept of a common ratio. By setting up equations based on the definition of a geometric progression, we can solve for x and y. In this case, x is 10 and y is 20.

Explanation:

To find the values of x and y in the given geometric progression, we need to identify the common ratio between the terms. In a geometric progression, each term is obtained by multiplying the previous term by the common ratio. Therefore, we have:

1. 
   
2.  
3. 5 * r = x
4. 
   
5.  
6. x * r = y
7. 
   
8.  
9. y * r = 40

From the first equation, we can substitute x as 5 * r in the second equation:

5 * r * r = y

Then, we substitute y as 5 * r * r in the third equation:

5 * r * r * r = 40

Simplifying the equation, we get:

r^3 = 40/5 = 8

Taking the cube root of both sides:

r = 2

Substituting this value of r back into the equations, we find that x = 10 and y = 20.

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Answer:

D

Step-by-step explanation: