1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tanzania [10]
3 years ago
15

Which equation represents a proportional relationship? A. y = x + 1 3 y=x+13 B. y = 1 − 1 3 x y=1-13x C. y = 3 x + 1 3 y=3x+13 D

. y = 1 3 x
Mathematics
1 answer:
34kurt3 years ago
3 0

Answer:

Option D. y=\frac{1}{3}x

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form y/x=k or y=kx

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

<u><em>Verify each case</em></u>

case A) we have

y=x+\frac{1}{3}

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=0+\frac{1}{3}=\frac{1}{3}

so

The line not passes through the origin

therefore

The equation A not represent a proportional relationship

case B) we have

y=1-\frac{1}{3}x

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=1-\frac{1}{3}(0)=1

so

The line not passes through the origin

therefore

The equation B not represent a proportional relationship

case C) we have

y=3x+\frac{1}{3}

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=3(0)+\frac{1}{3}=\frac{1}{3}

so

The line not passes through the origin

therefore

The equation C not represent a proportional relationship

case D) we have

y=\frac{1}{3}x

Remember that

the line must pass through the origin

so

For x=0, y=0

In this case

For x=0

y=\frac{1}{3}(0)=0

so

The line passes through the origin

therefore

The equation D represent a proportional relationship

You might be interested in
The area of a square with side a is S. What is the formula for dependence of S on a?
lawyer [7]

Answer:

S=a^2

Step-by-step explanation:

Note all sides of a square are equal, and the formula for finding the area is length x width of which the length=a and the with =a. So S=a^2.

4 0
3 years ago
Henry incorrectly said the rate 1/5/2/15 can be written as the unit rate 1/75 gallon per minute. What is correct unit rate? What
Gwar [14]

Answer:d

Step-by-step explanation:

8 0
3 years ago
A certain number of sixes and nines is added to give a sum of 126; if the number of sixes and nines is interchanged, the new sum
galina1969 [7]

Answer:

Original number of sixes = 6

Original number of nines = 10

Step-by-step explanation:

We are told in the question that:

A certain number of sixes and nines is added to give a sum of 126

Let us represent originally

the number of sixes = a

the number of nines = b

Hence:

6 × a + 9 × b = 126

6a + 9b = 126.....Equation 1

If the number of sixes and nines is interchanged, the new sum is 114.

For this second part, because it is interchanged,

Let us represent

the number of sixes = b

the number of nines = a

6 × b + 9 × a = 114

6b + 9a = 114.......Equation 2

9a + 6b = 114 .......Equation 2

6a + 9b = 126.....Equation 1

9a + 6b = 114 .......Equation 2

We solve using Elimination method

Multiply Equation 1 by the coefficient of a in Equation 2

Multiply Equation 2 by the coefficient of a in Equation 1

6a + 9b = 126.....Equation 1 × 9

9a + 6b = 114 .......Equation 2 × 6

54a + 81b = 1134 ........ Equation 3

54a + 36b = 684.........Equation 4

Subtract Equation 4 from Equation 3

= 45b = 450

divide both sides by b

45b/45 = 450/45

b = 10

Therefore, since the original the number of nines = b,

Original number of nines = 10

Also, to find the original number of sixes = a

We substitute 10 for b in Equation 1

6a + 9b = 126.....Equation 1

6a + 9 × 10 = 126

6a + 90 = 126

6a = 126 - 90

6a = 36

a = 36/6

a = 6

Therefore, the original number of sixes is 6

7 0
3 years ago
-(-6x - 5) = 4(5x + 3)
Lina20 [59]

Answer:

\large\boxed{B)\ -\dfrac{1}{2}}

Step-by-step explanation:

-(-6x-5)=4(5x+3)\qquad\text{use the distributive property}\\\\-(-6x)-(-5)=(4)(5x)+(4)(3)\\\\6x+5=20x+12\qquad\text{subtrac 5 from both sides}\\\\6x=20x+7\qquad\text{subtract 20x from both sides}\\\\-14x=7\qquad\text{divide both sides by (-14)}\\\\x=-\dfrac{7}{14}\\\\x=-\dfrac{1}{2}

8 0
3 years ago
Simplify the following rational expression and state for what values they are undefined.
QveST [7]

Answer:

d-2  and d cannot = 8

Step-by-step explanation:

d^2 -10d+16

-----------------------

d-8

Factor the numerator

( d-8)(d-2)

-------------------

d-8

The undefined values occur when the denominator is equal to zero

d-8 = 0  

  d= 8

This means d cannot equal 8

Now cancel like terms in the equation ( d-8)

This yields d-2

3 0
3 years ago
Read 2 more answers
Other questions:
  • How do you simplify number fractions
    6·2 answers
  • How would you solve 3x+6x+20=92
    9·1 answer
  • Felicia put $8500 into a CD that pays 2.8% interest compounded semiannual. According to the rule of 72, approximately how long w
    14·1 answer
  • Explain how the number of pieces in a whole relates to the size of each piece
    15·2 answers
  • Pleasaaaaseee answer the all for BRAINLEST answer and thanks
    6·2 answers
  • Express 3/8 in 30 seconds
    12·1 answer
  • An opera house has a seating capacity of 872 people with each ticket costing 50 Rupees .If the opera house is running for 15 day
    7·1 answer
  • Tenzin wants to know how much money he can make by mowing lawns. Which of the following is a statistical question?
    5·1 answer
  • The answer to<br> 6+2(17-13)²
    10·2 answers
  • PLEASE HELP WILL MARK BRAINLIEST!
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!