Deductive Reasoning is when we use all available facts and principles to reach a specific conclusion.

What is the surface area of the right prism given below?

posledela

Answer: Option D.

Step-by-step explanation:

You can calculate the surface area of this right prism by adding the area of its faces.

You can observe that the faces of the right prism are: Three different rectangles and two equal triangles.

The formula for calculate the area of a rectangle is:

$A=lw$

Where "l" is the lenght and "w" is the width.

The formula for calculate the area of a triangle is:

$A=\frac{bh}{2}$

Where "b" is the base and "h" is the height.

You can observe that the hypotenuse of the each triangle is the width of one of the larger rectangle, then , you can find its value with the Pythagorean Theorem:

$a=\sqrt{b^2+c^2}$

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

Then, this is:

$a=\sqrt{(8units)^2+(15units)^2}=17units$

Therefore, you can add the areas of the faces to find the surface area of the right prism (Since the triangles are equal, you can multiply the area of one of them by 2). This is:

$SA=(10units)(8units)+(15units)(10units)+(17units)(10units)+2(\frac{(15units)(8units)}{2})\\\\SA=520units^2$

5 0

3 years ago

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76.8 of what is 40.32

bearhunter [10]

Hey there

Lets solve this question together,

Convert 76.8% to a decimal.

0.768 * x=40.32

Multiply 0.768 by x to get 0.768x.

0.768x=40.32

Multiply each term by 1 / 0.768 and simplify.

Cancel the common factor of 0.768.

x=40.32 / 0.768

Divide 40.32 by 0.768 to get 52.5

x=52.5

6 0

2 years ago

A box with an open top will be constructed from a rectangular piece of cardboard. The piece of cardboard is 10 inches wide and 1

kupik [55]

Answer:

Domain of the function is { x : x∈R, x>0 } or (0,∞).

Step-by-step explanation:

It is given that the dimensions of a rectangular piece of cardboard are

Length = 14 inch

Width = 10 inch

The box will be constructed by cutting out equal squares of side x at each corner and then folding up the sides. So the dimensions of the box are

Length = 14-2x inch

Breadth = 10- 2x inch

Height = x inch

The volume of cuboid box is

$V=length\times breadth \times height$

The volume function of the box is

$V=(14-2x)\times (10-2x)\times x$

$V=(14-2x)(10-2x)x$

The volume function is V=(14-2x)(10-2x)x.

It is a polynomial function and domain of a polynomial function is all real numbers.

Here, x represents the height of the box. So, value of x must be a positive real number.

Domain of the function is

Domain = { x : x∈R, x>0 }

It can be written as (0,∞).

Therefore, domain of the function is { x : x∈R, x>0 } or (0,∞).

5 0

3 years ago

A window is being replaced with tinted glass. The plan at the right shows the design of the window. Each unit length represents

PolarNik [594]

The answer is $911.68.

After a little research on the internet, I found the design of the window.
First, you need to find the area of the window which is a composite figure made up of a rectangle and a circle. So, the total area (A) is the sum of the area of the rectangle (A1) and the area of the circle (A2).

Area of the rectangle with length l and width w is:
A = l * w
According to the image, l = 5 ft and w = 4 ft.
A1 = 5 * 4 = 20 ft²

Area of the circle with radius r is:
A = r²π
According to the image, r = 2 ft.
A2 = 2² * 3.14 = 12.56 ft²

The area of the window is:
A = A1 + A = 20 ft² + 12.56 ft² = 32.56 ft²

<span>The glass costs $28 per square foot, so to replace the glass will cost:
</span>32.56 ft² * $28/ft² = $911.68

7 0

3 years ago

If there were 36 candies and only 12 children, how many candies would each child get?

8090 [49]

Answer:

3 each

Step-by-step explanation:

36 / 12 = 3

.................................................

7 0

3 years ago

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