Recall the sum identity for cosine:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
so that
cos(a + b) = 12/13 cos(a) - 8/17 sin(b)
Since both a and b terminate in the first quadrant, we know that both cos(a) and sin(b) are positive. Then using the Pythagorean identity,
cos²(a) + sin²(a) = 1 ⇒ cos(a) = √(1 - sin²(a)) = 15/17
cos²(b) + sin²(b) = 1 ⇒ sin(b) = √(1 - cos²(b)) = 5/13
Then
cos(a + b) = 12/13 • 15/17 - 8/17 • 5/13 = 140/221
C. Is try correct answer
See example in the attached picture
Hi again! ;)
If we want to find the surface area of a cube, we need to find the area of one surface first, and then multiply that by 9, since there are 9 sides/surfaces on a cube.
Since each side of a square is the same, we first find the area of one surface:
9 × 9 = 81
Then, to find the surface area, we multiply 81 by 6:
81 × 6 = 486
The surface area is
Answer:
Half of a number is 15
Step-by-step explanation:
First of all, add commas between each option so it's easier to read I had a hard time figuring out what the options were because of this.
An equation is a statement that the values of two mathematical expressions are equal. An expression is a collection of symbols that jointly express a quantity. This means there has to be an equal sign when the phrases are put into numerical form.
Twice as much as a number: 2X
12 less than a number: X - 12
Half of a number is 15: X/2 = 15
The difference of 20 and a number: 20 - X
As you can see, only one of these phrases is an equation by definition, and that is X/2 = 15, or half of a number is 15. That's because it's the only one that values two expressions as equal.
Answer:
Step-by-step explanation:
According to the diagram MK is the angle bisector of ∠LMJ in the triangle LMJ.
Use angle bisector theorem, which states:
- <em>an angle bisector of an angle of a triangle divides the opposite side into two parts that are proportional to the other two sides of the triangle.</em>
<em />
Applied to the given triangle, the ratios are:
Use segment addition postulate and substitute known values to get:
- (LJ - JK)/JK = LM/JM
- (14 - JK)/JK = 50/48
- 50JK = 48(14 - JK)
- 50JK = 672 - 48JK
- 50JK + 48JK = 672
- 98JK = 672
- JK = 672/98
- JK = 6.86 (rounded)
