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!
Answer:
-1/4
Step-by-step explanation:
First we already know it's a negative because it is declining
fall/run
-1/4 is your answer
Enjoy vro!
It's seven becuase 7*7 equals 49.
Answer:
x = 13, y = 26
The length of the sides of Δ QRS are QR = 104, <u>QS = 468</u>, RS = 76
Step-by-step explanation:
In ΔRQS
∵ M is the mid-point of side RQ
→ That means M divide RQ into 2 equal parts RM and MQ
∴ RM = MQ
∵ RM = 4x
∵ MQ = 52
→ Equate them
∴ 4x = 52
→ Divide both sides by 4 to get x
∴ x = 13
∵ P is the mid-point of side QS
→ That means P divide QS into 2 equal parts QP and PS
∴ QP = PS
∵ QP = 9y
∵ PS = 234
→ Equate them
∴ 9y = 234
→ Divide both sides by 9 to get y
∴ y = 26
→ Find the length of each side
∵ RQ = 52 + 52
∴ RQ = 104
∵ QS = 234 + 234
∴ QS = 468
∵ RS = 38 + 38
∴ RS = 76
∴ The length of the sides of Δ QRS are QR = 104, QS = 468, RS = 76
Note: PS = 234 is wrong because it made the length of the sides QS = 468, which could not be because the sum of any 2 sides of a triangle must be greater than the 3rd side. So check it.
