Find the volume of each sphere to the nearest hundredth?
1 answer:
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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:
<u><em>Solving equation A: y = x </em></u>
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.
<em>y x</em>
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<em> figure a.</em>
<u><em>Solving equation A: y = x +2</em></u>
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.
<em>y x + 2</em>
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<em> figure a.</em>
<em>Keywords: equation, graph</em>
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Like terms must have the same variables and those variables must have the same powers.
and
are like terms, because they both have
and they both have
.
and
are NOT like terms, because the powers no longer match.
In your example, do you have the same variables and do the variables have the same powers in both expressions?