Answer:
double, real root x = -4
Step-by-step explanation:
Please use " ^ " to indicate exponentation: 2х^2 + 8х = х^2 - 16.
Combine like terms:
х^2 + 8х = - 16.
Re-write in the standard form for a quadratic:
х^2 + 8х + 16 = 0
Recognize that this is the square of the binomial x + 4:
х^2 + 8х + 16 = 0 => (x + 4)^2 = 0
Solving this last result for x yields the double, real root x = -4.
The original recipe is for 36 muffins, they want to make 12:
Find the ratio:
12/36 = 1/3
They would need 1/3 of the recipe, so you would divide all the ingredients by 3.
Flour: 5 1/4 cups = 21/4 cups
21/4 / 3 = 21/12 = 1 3/4 cups.
Oil: 1 cup / 3 = 1/3 cup
Baking powder: 4 1/2 = 9/2
9/2 / 3 = 9/6 = 1 1/2 teaspoons
salt: 1 1/2 = 3/2
3/2 / 3 = 3/6 = 1/2 teaspoons
eggs 3 / 1 = 1 egg
Nutmeg: 1 1/2 = 3/2
3/2 / 3 = 1/2 teaspoons
cinnamon: 3/4 / 3 = 1/4 teaspoon
The amount of sugar and milk aren't listed but just divide those by 3 to find the amount needed.
Answer:
Step-by-step explanation:
If arccos (√3 / 2) = β, then cos β = adjacent side / hypotenuse = √3 / 2. This tells us immediately that the adjacent side length is √3 and the hypotenuse is 2. Via the Pythagorean Theorem, we know that the third side is 1.
This information rules out the 1st and 3rd answer choices.
Because cos 30° = adj / hyp = √3 / 2, we can conclude that the correct answer is the 4th one: 30°, 60°, 90°
It is hard to show work for this problem because it very similar to a basic addition or subtraction problem.
Just so you have the answer and how to solve. -27 is the answer. Think about it like 41-14 then add the negative back. But I would strongly suggest not writing that as work because you teacher might get confused about what you are doing
