The interior angles of a triangle add up to 180 degrees
a = 1st angle, b = 2nd angle, c = 3rd angle
c = 6a
b = a + 60
a + b + c = 180
a + (a + 60) + (6a) = 180
8a + 60 = 180
8a = 180 - 60
8a = 120
a = 120/8
a = 15 <=== here is one angle
b = a + 60
b = 15 + 60
b = 75 <=== and another one
c = 6a
c = 6(15)
c = 90 <=== and the last angle
X= 22.5 get the x by itself by dividing by 2
Add all of the interior angles to 1260. Then you simplify for x. After that you plug in what you found for X in the E expression.
Answer:
k = -9
Step-by-step explanation:
subtract 2k from both sides
_5k+8= -37
subtract 8
_5k = -45
divide by 5
_k = -9
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!
