Answer:
f(x)=g(x) is the only answer
Step-by-step explanation:
The answer to your question is 30
Answer:
21
Step-by-step explanation:
There are two parallel lines given.
Two transversals cut them.
Here m and n are parallel.
Two transversals cut them so that a triangle is formed.
Let us use the property that sum of angles of a triangle = 180
Bottom angle of triangle = 39 (vertically opposite angles)
Top left angle = 4x+3 (vertically opposite angles)
Top right angle = 180-6x (linear pair property)
Now add these 3 and equate to 180
39+4x+3+180-6x = 180
2x = 42
Or x = 21
Since both α and β are in the first quadrant, we know each of cos(α), sin(α), cos(β), and sin(β) are positive. So when we invoke the Pythagorean identity,
sin²(x) + cos²(x) = 1
we always take the positive square root when solving for either sin(x) or cos(x).
Given that cos(α) = √11/7 and sin(β) = √11/4, we find
sin(α) = √(1 - cos²(α)) = √38/7
cos(β) = √(1 - sin²(β)) = √5/4
Now, recall the sum identity for cosine,
cos(x + y) = cos(x) cos(y) - sin(x) sin(y)
It follows that
cos(α + β) = √11/7 × √5/4 - √38/7 × √11/4 = (√55 - √418)/28
Answer:
Samuel uses 1 11/12 cups of flour.
Step-by-step explanation:
Okay, this is assuming he uses the rest of the flour she didn't use.
The first step would be to find the Greatest Common Factor(GCF) of the fractions
2 1/4 and 1/3 have different denominators, but they both can divide into 12.
1/4 * 3/3 = 3/12
1/3 * 4/4 = 4/12
Now we can also convert 2 3/12 into an improper fraction to make it easier
2* 12/12 = 24/12
24/12+ 3/12 = 27/12
Here's the part were we subtract the two numbers.
27/12- 4/12 = 23/12
The last step is to simplify the fraction
23/12 = 1 11/12 cups
