Layla had 37 feet of tape to share with 5 friends and himself. How much tape does each person get
2 answers:
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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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No, it will not be able to make a right triangle.
<em><u>Solution:</u></em>
Given that,
Joel wants to fence off a triangular portion of his yard for his chickens.
The length of three peices of fencing are 8 feet , 15 feet and 20 feet
For making it a right triangle it must satisfy the "Pythagorus theorem"
Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.
For a right angled triangle with sides a, b, c
Given sides are:
a = 8 feet
b = 15 feet
c = 20 feet
Substituting the values in above formula
Since the pythogoras formula is not satisfied, the given sides cannot form a right angled triangle
Thus , No, it will not be able to make a right triangle.
Answer:
5) y=5
6)x=7
7)a=18
Step-by-step explanation:
5) y= any number will work. don't add a variable like x
6)x= any number will work. don't add a variable
My work for 7 is in the picture. If you'd like me to explain more for 7 lmk :)
