It'd be easier to do #18 if y ou were to break it up:
14* (first term + 14th term)
Sum from n=1 to 14 of n = S = ---------------------------------
14 2
14(1+14)
= ---------------- = 7(15) = 105
2
The sum of twice that is 210. The sum of "1 from n=1 to n=14" is just 14.
The final sum is 210 + 14 = 224 (answer)
Answer:
AB ≈ 14.3
Step-by-step explanation:
We're given <em>two sides </em>(BC and CA) and an <em>angle </em>(C)<em> between them</em>; the <em>law of cosines </em>is a good tool for calculating the third side of the triangle here. To remind you, the law of cosines tells us the relationship between the sides of a triangle with side lengths a, b, and c:

Where C is the angle between sides a and b. c is typically the side we're trying to find, so on our triangle, we have

Substituting these values into the law of cosines:

Answer:
The correct answer is: Option D) 5
Step-by-step explanation:
Given equation is:

In order to find that which values of x makes the equation true, we have to put each value of x in the equation. When both sides of equations will be equal, that value of x will be true for the equation.
Putting x = 2

Putting x = 3

Putting x=4

Putting x = 5

The equation is true for x = 5
Hence,
The correct answer is: Option D) 5
Answer:
8 dolls
Step-by-step explanation:
METHOD 1:
Step 1: Convert 25% into decimal (0.25)
Step 2: Multiply by 32 (32 × 0.25 = 8)
METHOD 2:
25% of a number will be one-fourth of that number. Divide 32 by 4 to get 8 (or multiply 32 by 1/4).
Answer:
The area of the path would be 231.25 squared meters.
Step-by-step explanation:
Consider the path as 45m (the field's area), then add 2.5m to all of the sides. You'll get 47.5m on all sides. Then you do 47.5² to get 2256.25 squared meters. After that, you'll remove the area of the squared field. To do this, do 45m². By doing this, you'll get 2025 squared meters. Lastly, to finish up the question, do 2256.25 - 2025. This would get you 31.25 squared meters, the answer.