Because they both have ratio consecutive terms constant
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!
Simplifying
6k + -9 = -15
Reorder the terms:
-9 + 6k = -15
Solving
-9 + 6k = -15
Solving for variable 'k'.
Move all terms containing k to the left, all other terms to the right.
Add '9' to each side of the equation.
-9 + 9 + 6k = -15 + 9
Combine like terms: -9 + 9 = 0
0 + 6k = -15 + 9
6k = -15 + 9
Combine like terms: -15 + 9 = -6
6k = -6
Divide each side by '6'.
k = -1
Answer:
x ≈ 4.2 (nearest tenth)
Step-by-step explanation:
The chord of length 4 is the base of an isosceles triangle with height of 3.7 and sides equal to the radius (x).
An isosceles triangle comprises two right triangles, each with:
- base = 2 units
- height = 3.7 units
- hypotenuse = x units
Therefore, to find x use Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ a² + b² = c²
⇒ 2² + 3.7² = x²
⇒ x² = 17.69
⇒ x = √(17.69)
⇒ x = 4.2 (nearest tenth)
Answer:
$8.50
Step-by-step explanation:
multiply 0.50 by 11 to get 5.5 and then add the 3 dollars from the ice cream to get 8.5 - make sure to change 8.5 to $8.50
