Given:
Four equations in the options.
To find:
The equation which represents a proportional relationship.
Solution:
If y is proportional to x, then
where, k is the constant of proportionality.
In this case if x=0, then y=0. It means the graph of a proportional relationship passes through the origin.
From the given options, only option B, i.e., 
, is of the , where, 
.
So, the equation represents a proportional relationship.
Therefore, the correct option is B.
Answer: Yes
Step-by-step explanation:
When using the distributive property, 6(2x + 4) becomes 12x + 24
6 * 2x = 12x and 6 * 4 = 24
12x + 24 = 12x + 24
Therefore, the expressions are equivalent.
It would be 2/4. 2/4 simplifies to 1/2.
Answer:
1,687,500,000,000
Step-by-step explanation:
1) 270,000,000 x 6250
Answer:
Step-by-step explanation:
Let's identify what we are looking for in terms of variables. Sandwiches are s and coffee is c. Casey buys 3 sandwiches, which is represented then by 3s, and 5 cups of coffee, which is represented by 5c. Those all put together on one bill comes to 26. So Casey's equation for his purchases is 3s + 5c = 26. Eric buys 4 sandwiches, 4s, and 2 cups of coffee, 2c, and his total purchase was 23. Eric's equation for his purchases then is 4s + 2c = 23. In order to solve for c, the cost of a cup of coffee, we need to multiply both of those bolded equations by some factor to eliminate the s's. The coefficients on the s terms are 4 and 3. 4 and 3 both go into 12 evenly, so we will multiply the first bolded equation by 4 and the second one by -3 so the s terms cancel out. 4[3s + 5c = 26] means that 12s + 20c = 104. Multiplying the second bolded equation by -3: -3[4s + 2c = 23] means that -12s - 6c = -69. The s terms cancel because 12s - 12s = 0s. We are left with a system of equations that just contain one unknown now, which is c, what we are looking to solve for. 20c = 104 and -6c = -69. Adding those together by the method of elimination (which is what we've been doing all this time), 14c = 35. That means that c = 2.5 and a cup of coffee is $2.50. There you go!
