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3 years ago

What is the volume of the pyramid?

Mathematics

1 answer:

geniusboy [140]3 years ago

7 0

Answer: 16 cm^2.

Step-by-step explanation: The volume of a pyramid is equal to one-third the product of the area of the base and the height:

$V=\frac{1}{3}A*h$

In this case, the base is a square, so its area is:

A=L^2 where "L" is the lenght of the base edge

So the volume would be:

$V=\frac{1}{3}L^{2} *h$

$V=\frac{1}{3}4^{2} *3$

V=16*3/3

$V=16cm^{2}$

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Hector is rewriting the expression 7 Superscript 11 in expanded form. How many terms will be multiplied in his rewritten express

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Determine whether each equation below does or does not represent a proportional relationship. support your answer using either a

Triss [41]

Answer:

As the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship.
As the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship.

Step-by-step explanation:

Solving equation A: y = x 

Let us consider the given equation A:

y = x

Putting x = 1 in y = x

y = x

y = 1 ∵ x = 1

Hence, (1, 1) is the ordered pair of y = x

Putting x = 2 in y = x

y = x

y = 2 ∵ x = 2

Hence, (2, 2) is the ordered pair of y = x

Putting x = 3 in y = x

y = x

y = 3 ∵ x = 3

Hence, (3, 3) is the ordered pair of y = x

Putting x = 4 in y = x

y = x

y = 4 ∵ x = 4

Hence, (4, 4) is the ordered pair of y = x

Putting x = 5 in y = x

y = x

y = 5 ∵ x = 5

Hence, (5, 5) is the ordered pair of y = x

Lets us consider all the ordered pairs i.e. (1, 1), (2, 2), (3, 3), (4, 4) and (5, 5) to make a table for y = x.

y x

1 1

2 2

3 3

4 4

5 5

As from the table, lets take the ratio of every point i.e. y/x

For (1, 1), the ratio will be y/x ⇒ 1/1 = 1
For (2, 2), the ratio will be y/x ⇒ 2/2 = 1
For (3, 3), the ratio will be y/x ⇒ 3/3 = 1
For (4, 4), the ratio will be y/x ⇒ 4/4 = 1
For (5, 5), the ratio will be y/x ⇒ 5/5 = 1

Hence, the ratio for all the points on the equation y = x is same. Hence, the equation y = x REPRESENTS a proportional relationship. Please also check the graph in attached figure a.

Solving equation A: y = x +2

Let us consider the given equation A:

y = x + 2

Putting x = 1 in y = x + 2

y = x + 2

y = 1 + 2 ⇒ 3 ∵ x = 1

Hence, (1, 3) is the ordered pair of y = x + 2

Putting x = 2 in y = x + 2

y = x + 2

y = 2 +2 ⇒ 4 ∵ x = 2

Hence, (2, 4) is the ordered pair of y = x + 2

Putting x = 3 in y = x + 2

y = x + 2

y = 3 + 2 ⇒ 5 ∵ x = 3

Hence, (3, 5) is the ordered pair of y = x + 2

Putting x = 4 in y = x + 2

y = x + 2

y = 4 + 2 ⇒ 6 ∵ x = 4

Hence, (4, 6) is the ordered pair of y = x + 2

Putting x = 5 in y = x + 2

y = x + 2

y = 5 +2 ⇒ 7 ∵ x = 5

Hence, (5, 7) is the ordered pair of y = x + 2

Lets us consider all the ordered pairs i.e. (1, 3), (2, 4), (3, 5), (4, 6) and (5, 7) to make a table for y = x + 2.

y x + 2

1 3

2 4

3 5

4 6

5 7

As from the table, lets take the ratio of every point i.e. y/x

For (1, 3), the ratio will be y/x ⇒ 3/1 = 3
For (2, 4), the ratio will be y/x ⇒ 4/2 = 2
For (3, 5), the ratio will be y/x ⇒ 5/3 = 5/3
For (4, 6), the ratio will be y/x ⇒ 6/4 = 3/2
For (5, 7), the ratio will be y/x ⇒ 7/5 = 7/5

Hence, the ratio for all the points on the equation y = x+2 is not same. Hence, the equation y = x + 2 DOES NOT REPRESENT a proportional relationship. Please also check the graph in attached figure a.

Keywords: equation, graph

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