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What is the volume of the triangular prism? A triangular prism. The base of the triangular face is 5.4 centimeters and the heigh

IceJOKER [234]

Answer:

The volume of the triangular prism is 51.84 cm^3.

Step-by-step explanation:

The formula of the volume of a prism is:

V = Ah

where:

V = Volume of prism

A = Area of uniform cross-section or base of prism

h = Height of prism = 6 cm

We can substitute the information given in the problem into this formula.

To find A, we need to find the area of the triangular base.

A = bh / 2

where:

b = Base of triangle = 5.4 cm

h = Perpendicular height of triangle = 3.2 cm

We can substitute the information given in the problem into this formula.

A = ( 5.4 × 3.2 ) / 2

A = 17.28 / 2

A = 8.64 cm^2

Substitute the value of A into the original volume of a prism formula with the other information given in the problem.

V = Ah

V = ( 8.64 ) ( 6 )

V = 51.84 cm^3

7 0

4 years ago

Which of the following is not a way to represent the solution of the inequality 2(x − 1) greater than or equal to −12?

maxonik [38]

First you need to simplify the left side of the equation to get $2x-2 \geq -12$
Then you add by two on both sides to get $2x \geq -10$
Finally you divide by 2 on both sides to get $x \geq -5$

6 0

3 years ago

A Pyramid is placed inside a prism as shown in the pyramid has the same base area B as a prison but half the height H of the pri

guajiro [1.7K]

Answer:

D) V= 1/6 bh

Step-by-step explanation:

The expression that provides the volume of the pyramid is as follows;

As mentioned in the question

It is given that the pyramid put inside a prism

Also the pyramid contains the similar base area but the height is half of the prism

so the base area of the pyramid is b

And, the Height of the pyramid = h ÷ 2

Now as we know that

The volume of the pyramid is

V = 1 ÷3 × base ares × height

= 1 ÷ 3 × b × h ÷ 2

V = 1 ÷ 6 bh

So, the volume is 1 ÷6 bh cube unit.

8 0

3 years ago

Read 2 more answers

Which operation results in an expression equivalent to ? 23y^4 - 6y^3 + 35y^2 - 20y

Tom [10]

Answer:

D. P + Q

Explanation:

Given:

P = 8y⁴ + 6y³ + 8y

Q = (5y² - 4y)(3y² + 7)

Required:

Determine which operation will give an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.

SOLUTION:

Perform each operation given to see which of them gives an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.

Q - P:

P = 8y⁴ + 6y³ + 8y

Q = (5y² - 4y)(3y² + 7)

Q - P = (5y² - 4y)(3y² + 7) - (8y⁴ + 6y³ + 8y)

(5y²(3y² + 7) -4y(3y² + 7)) - (8y⁴ + 6y³ + 8y)

(15y⁴ + 35y² - 12y³ - 28y) - (8y⁴ + 6y³ + 8y)

Open parentheses

15y⁴ + 35y² - 12y³ - 28y - 8y⁴ - 6y³ - 8y

Collect like terms

15y⁴ - 8y⁴ - 12y³ - 6y³ + 35y² - 28y - 8y

7y⁴ - 18y³ + 35y² - 36y

Therefore, P - Q does not give us an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.

PQ:

P = 8y⁴ + 6y³ + 8y

Q = (5y² - 4y)(3y² + 7) = (15y⁴ + 35y² - 12y³ - 28y)

PQ = (8y⁴ + 6y³ + 8y)(15y⁴ + 35y² - 12y³ - 28y)

=(8y⁴(15y⁴ + 35y² - 12y³ - 28y) +6y³(8y⁴ + 6y³ + 8y)(15y⁴ + 35y² - 12y³ - 28y) +8y(8y⁴ + 6y³ + 8y)(15y⁴ + 35y² - 12y³ - 28y))

= 120y⁸ . . . . .

Note: You don't need to perform this operation further anymore. It would definitely not give us the equivalent expression we are looking for. The degree of the leading term (120y⁸) is way too greater than the degree of the leading term (23y⁴) of the equivalent expression we are looking for.

Thus, PQ cannot give us an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.

P - Q:

P = 8y⁴ + 6y³ + 8y

Q = (5y² - 4y)(3y² + 7) = (15y⁴ + 35y² - 12y³ - 28y)

P - Q = (8y⁴ + 6y³ + 8y) - (15y⁴ + 35y² - 12y³ - 28y)

Open parentheses

8y⁴ + 6y³ + 8y - 15y⁴ - 35y² + 12y³ + 28y

Collect like terms

8y⁴ - 15y⁴ + 6y³ + 12y³ - 35y² + 8y + 28y

-7y⁴ + 18y³ - 35y² + 36y

Therefore, P - Q cannot give us an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.

P + Q:

P = 8y⁴ + 6y³ + 8y

Q = (5y² - 4y)(3y² + 7) = (15y⁴ + 35y² - 12y³ - 28y)

P + Q = (8y⁴ + 6y³ + 8y) + (15y⁴ + 35y² - 12y³ - 28y)

Open parentheses

8y⁴ + 6y³ + 8y + 15y⁴ + 35y² - 12y³ - 28y

Collect like terms

8y⁴ + 15y⁴ + 6y³ - 12y³ + 35y² + 8y - 28y

23y³ - 6y³ + 35y² - 20y

Therefore, P + Q will result in an expression equivalent to 23y⁴ - 6y³ + 35y² - 20y.

The answer is D.

7 0

3 years ago

Karen is riding her bike at 4 miles per hour she wants to show this on a graph what should she draw

Radda [10]

4 mph is a rate, and is represented by a straight line thru the origin with slope 4/1.

Draw a set of coordinate axes and label them t (for time) and d(for distance).
Start with your pencil point at the origin. Arbitrarily move this point 3 spaces to the right, and from there move it 4 spaces up. You'll be at (3,4).

Draw a straight line from the origin (0,0) to the point (3,4).

8 0

3 years ago